THE UNIVERSITY OF MICHIGAN INDUSTRY PROGRAM OF THE COLLEGE OF ENGINEERING DIGITAL COMPUTER SIMULATION OF OSCILLATORY FLOW IN CARBURETOR FUEL METERING CHANNELS *..:, E. i. Stephen J'...Deezinsk. A dissertation submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy in the University of Michigan Department of Mechanical Engineering 1972 April 1972 P-8h30.

,e- h\

Stephen Joseph Derezinski 1(2 Al.R. I''s I.All Rights Reserved

ACKNOWLEDGMENTS I wish to thank all of the members of the Doctoral Comittee for thir council during this project. I am particularly grateful to Profssor Jay A. Bolt, whose mature guidance was a determining factor in the completion of' this project. Also, I would like to especially thank Professor Victor L. Streeter for aiding me through many of the difficulties of the simulation. The assistance of Doctor David L. Harrington, especially during the early phases of this program, is greatly appreciated. I also wish to thank the other members of the committee, who are Professor Robert B. Keller, Professor Franklin H. Westervelt and Mr. Paul Braun. The financial aid of the United States Public Health Service is gratefully acknowledged. It would not have been practical to conduct this research at the University of Michigan without this support. I am grateful for the assistance of Mr. William Zoller., whose mrany talents greatly simplified the building of workable test equipment and gathering data. The assistance of Miss Ruth Howard in preparing the original manuscript is gratefully acknowledged.

TABLE O1' CONiTENTS page LIST OF TBLES............ i LIST OF ILLUSTRATIONS........................................ vii NOMeENCIATUIRE. xiv I. INTRODUCTION.1.. II. PRESSURE PULSATIONS IN TIE CARBURETOR: ENGINE TESTS.4 2.1 Reasons for Engine Tests....................... 4 2.2 Previous Studies................................ 2.3 Testing Procedure.........9 2.4 Results of Engine Tests........................9 2.5 Manifold Pressure Pulsations....................15 2.6 Venturi Pressure Pulsations..................... 2.7 Main Channel Pressure Pulsations...........17.... 2.8 Waveshape of Pressure Traces....................17 2.9 Comparison of Engine Tests with Flow Stand Tests 19 2.10 Conclusions of Engine Tests.....................22 III. INCOMPRESSIBLE OSCILLATING FLOW THROUGH ORIFICES.....24 3.1 Introduction...................................24 3.2 Previous Work.....o............... 25 3.3 Objectives of Orifice Tests.5o...o........ 1 3.4 Orifice Testing Rig Description.5.......... 2 3.5 Instrumentationi..................... 3 3.6 Fluid. Compres-sion: Blanked. Orif'ice Test.... o. 42 3.7 Test Procedure................... 48 3.8 Ideul Oscillating Pilow Through ani Orifice....... 55 3.9 Ideal Coeffiicient of Discharge............. b 3.10 Results of' Orifice Tests................ o5 3.11 Conclusionis to Orif'ice Tests............. 86 IV. IMUIATIOA O 01' lJL MvITERINU NETWORKS............ 89 4t.1 Reasons for Simula-tion...........89 4.2 The Typical Air-Bleed. Carburetor.90.......... g 4.3 Previous Wor-k.90....o........o.... g 4.4 Objcctives of' Simulation................ 94 4.5 Overall Soolution Plan...o..o...o...o.. 95 4.6 Describingt the F-uel MeteringT Network......... 90 4.7 Basic Assumptions..............il0i4i.8 Steady-State Flow................... 105I

'I'A13L1' O CON'T'fIJ''T, (COI1''D) Page 4.11 Resultsof Steady-State Flow Simulation of a Simple Network.............................11 4.12 Solution of Transient Flow; Linear Density Method. 115 4.1 Checking the Linear Density Solution.......125 4.14 Simulation of a Ford Carburetor............127 V. COMENTS AD RECOMMEIDATIONS..................... APPEIX A - ENGINE-CARBURETOR TEST EQUIPMENIT AND PROCEDURE 147 APPENDIX B - COEFFICIENTS OF DISCHARGE WITH OSCILIATING FLOW... 155 APPENDIX C - LISTING 01' DIGITAL COMPUTER SIMULATION (FORTRAN IV).............................25 BIBLIO.RAPHY................................................... 25

LIST OF TABLES ~~~~Table ~Title Page I Equlipment List for Orifice Testing Rig..... II Orifice Specifications.......................49 III Orifice Test Variables...................... 51 IV Steady-Blow Results for a Simple Network.....114 V Steady-Flow Results for the C8AF-L Carburetor at the Junctions.............................10 VI Steady-Flow Results for the CSAF-L in the Elements...........12 VII Equipment of Engine-Carburetor Tests...152..... VIII Variables of Engine-Carburetor Tests.......... 54 IX F-50 OriIice Data............................22 X Oriflice Data, L/D = 7.23.....................22 xi Orifice Data, L/D = 3.63.....................21 XII Orifice Data., L/D = 0.62......255

LIST OF ILLUSTRATIONS ~~~~Figure ~Title Page 1 Cut-away Drawing of the Test Carburetor..1..0.. 2 Intake Manifold Pressure Pulsation..11........... 3 Main Venturi Pressure Pulsation....................... 2 4 Boost Venturi Pressure Pulsation.......1........ ~5 Main Channel Pressure Pulsation..14.............. 6 Comparison of Laboratory Airbox (Steady Flow) lFuel/Air with Engine Fuel/Air (Pulsating Flow) 20 7 Mean and Alternating Components of Pressure and Flow............26..................... 8 Schematic of Orifice Testing Rig............... 9 Cut-away of Orifice Test Block.4 10 Orifice Testing Equipment and Instrumentation.. 11 Orifice Testing Equipment.5.........7 1-2 Orifice Test Block and. Pressure Transd.ucer... o.0 40 13 Pressure Transd.ucer Calibration Curve.41 14 Drive Mechanism for Stead.y-Flow Piston.45 15 Cam Mechanism for Alternating-Flow Piston.44 16 Schematic for Blanked. Orifice Test.46 17r Results of Blanked. Orifice Test....o..o...o 47 18 Stead.y-State Flow Coef'ficients of Discharge.o 50 19 Test Fluid. Properties.52 20 Control Volume for Orifice Analysis.55 21 Example of Dimensionless Id.eal Head. Function.... 58 22 Compriso_r-.qn of' Id.eal HeTad. and. Actual Head. Furnctions 59

LI'1 Ol' ILLUST'RATIONS (CONIT'D) Figure Title Page 24 Ideal Coefficients of Discharge versus Head Ratio... 64 25 Coefficient of Discharge versus Flow Ratio, F-50 Orifice........................................ 67 26 Coefficient of Discharge versus Head Ratio, F-50 Orifice........................................ 68 27 Coefficient of Discharge versus Flow Ratio, L/D=O.62.............................. 69 28 Coefficient of Discharge versus HIead Ratio, L/D0O.62....................... 7o 29 Coefficient of Discharge versus l'low Ratio, L/D=3.371 L/D=3. G3............................................? 30 Coefficient of Discharge versus Head Ratio, L/D=3.63............................................ 72 31 Coefficient of Discharge versus Flow Ratio, L/D=7.24............................................ 73 32 Coefficient of Discharge versus Head Ratio, L/D=7.24.................................74 33 Percent Change in Fuel/Air and Coefficient of Discharge versus Head Ratio......................... 76 34 Alternating Coe'fficient of Discharge versus Flow Ratio, F-50 Orifice............................ 79 35 Alternating Coelfficient of Discharge versus Head Ratio, 1'-50 Orifice............................ 80 36 Alternating Coelficient of Dischlarge versus Plow Ratio, L/D=0.62................................ 81 37 Alternating Coefficient of Discharge versus Head Ratio, L/D=O.62................................ 82 38 Alternating Coefficient of Discharge versus Flow Ratio, L/D=3.63 and L/D=7.24........... 83 39) Alternating Coefficient of Discharge versus Head Ratio, L/D=3.63 and L/D=7.24................84 viii

LIST OF ILLUSTRATIONS (COXN'D) ~~~~~Figure Title Page 40 Soimplified Version of' a Typical Air-Bleed Carburetor........................................... 41 Schematic of a Simple Network..................... 98 42 Direction Cosines of an Element..................... 01 43 Control Volume for Transient Flow in an Element.. 117 44 Finite Difference Form of the Second Derivative.. 121 45 Comparison of Linear Density Method to Method of Characteristics........................ 126 46 Schematic Network for C8AF-L Carburetor.........128 47 Data for Simulation of CSAF-L Carburetor.........129 48 Simulated Steady-State Results for C8AF-L Carburetor.......................................... 5 4)- Simulated Transient Pressure for C8AF-L Carburetor, 1500 RPM................................ c50 Simulated Transient Pressure for C8AF-L_ Carburetor, 2000 RPMvI..............157 51 Simulated Transient Pressure for C8AF-.L Carburetor, 2500 RPm............... 0 138 52 Simulated Transient Pressure for C8AF-L Carburetor,, 3000 RPM.......0.......... 139 53 Simulated Transient Flow for C8AF-L Carburetor, 150RM141 54. Simulated Tran8sienit Flow for C8AF-L Carburetor,, 3000 RPM................. 142'1 ~Schemat-ic of. En!'Jgine Testinig Rig............ 148 5u Engine-, Testing Ri and Instrumenitationi.14)..... 57 Carbur-etor- on the Engine with Priessure Transducer-s...................... 151

LTS1' O01 ILLUSTRA'TIONS (CONV'D) FP.'~~igure ~Title Pag 5 Mean Coeffic:ient of Discharge versus Flow Ratio for L/D=7.24, RE=2910-3320.1.................a.157 60 Mean Coefficient of Discharge versus Flow Ratio for L/D=7.24, RE=4134-4393.....158.............. 61 Mean Coefficient or Discharge versus Flow Ratio for L/D=7.24, RE=5202-5554..........15........ 62 Mean Coefficient of Discharge versus Filow Ratio for L/D=3.63, RElLO=1104-1218.................. 63 Mean Coefficient of Discharge versus Flow Ratio for L/D=3.63, RE=2349-2638.................16 6-4 Mean Coefficient of Discharge versus Flow Ratio for L/D=3.63, RE=3422-3751................. 62 65 Mean Coefficient of Discharge versus Flow Ratio for L/D=3.63, RE=4521-4751..........1.......6, 66 Mean Coefficient of Discharge versus Flow Ratio for L/D —o0.62, RE=1099-1198.................. 67 Mean Coefficient of Discharge versus Flow Ratio for L/D=o.62, RE-2369-2612.16......... l5 68 Mean Coeifficienit of' Discharge versus Flow Ratio f'or L/D-O.62., RE=3387-3713.160....... (99 Mean Cobe ffi ci enit o fDischarge versus Plow Ratio for L/D=O.62, RE-4470-4721.1...67 70 Mean Coeffiicient of Discharge versus FlowRatio f'or F-50 Orifice., RE=1800-2200......... 168 71 Mean Coef'ficient of' Discharge versus Flow Ratiofor -50 Orifice,, RE=2800-3200....169 72. Meaii Coefficienit of Discharge ver-sus Flow BLtLio f'or 1-50 Orifice., RE=3800-42O00......... 170 73 Mean Coefficient of' Discharge versus Flow Ratio f'or 1'-50 Orif'icel, REJi49oo-5200......... 171

LIST OF ILLUJSTRATIONS (CONT'DI) ~~~~Figure ~Title Page 75 Mean Coeffi(ient of Discharge versus Head Ratio for L/D=7.24, RE=2910-3320................. 76 Mean Coefficient of Discharge versus Head Rtio for L/D=7.24, RE=4134-4393.................175 77 Mean Coefficient of Discharge versus Head Ratio for L/D-7.24, RE=5202-5554.................... 176 78 Mean Coefficient of Discharge versus Head Ratio for L/D-3.63, RE=1104-1218.................177 79 Mean Coefficient of Discharge versus Head Ratio for L/D=3.63, RE=2349-2638................... 78 8 Mean Coefficient of Discharge versus Head Ratio for L/D=3.63, RE=3422-3751................179 81 Mean Coefficient of Discharge versus Head Ratio for L/D=3.63, RE=4521-4751.................18 82 Mean Coefficient of Discharge versus Head Ratio for L/D=O.62, RE=1099-1198.................18 1 83 Mean Coefficient of Discharge versus Head. Ratio f'or L/D=o.62,, REh=2369-2612....182 84 Mean Coefficient of Disc-harge versus Head. Ratio for L/D=0.62, RE=3387-3713.......... 183 85 Mean Coefficient of Discharge versus Head. Ratio for L/D=o.62,, RE=44170-4721.- -.1 0.9 184 86' Mean Coefficient of Discharge versus Head. Ratio for F-50 Orif'ice, RE=18OO0-2200......185 87~ Mean Coefficient of Discharge v-ersus Head. Ratio for F-50 Orif'ice., RE=2800-.3200.186 868 Mean Coef'ficienit of' Discharge versus Head. Ratio for FI-5( Orif'ice, RE=38oo-4200.......187 8) Mean Coeff'icient of' Discharge versus Head. Ratio for- IO50 Orifice,, RE=48oo-5200O.....188

LIST OF ILLUSTRATIONS (CONT' D) ~~~~Figure ~Title Page 91 Alternating Coefficient of Discharge versus F'low Ratio for L/D=7.24, STA=2.68............ 92 Alternating Coefficient of Discharge versus Flow Ratio for L/D=7.24, STA=3.22....192........ 93 Alternating Coefficient of Discharge versus Flow Ratio for L/D=7.24, STA=4.28............ 19 94 Alternating Coefficient of Discharge versus Flow Ratio for L/D=3.63, STA=O.87.....194....... 95 Alternating Coefficient of Discharge versus Flow Ratio for L/D=3.63, STA=l.35............ 195 96 Alternating Coefficient of Discharge versus Flow Ratio for L/D=3.63, STA=l.61.....1.......00 96 97 Alternating Coefficient of Discharge versus Flow Ratio for L/D=3.63, STA=2.15............97 98 Alternating Coefficient of Discharge versus Flow Ratio for L/D=0.62, STA=0.15............ 991 AlternatingE Coef'ficient of' DischargLe versus Flow Ratio f'or L/D=O.6-2, STA=O.23(...........219 100 Alternating~ Coefficient of' Discharge verosusFlow Ratio for L/D=0 O62,e SrTA=O074.200 101 Alternating Coef'ficient of Discharge versus Flow Ratio f'or /D50 Ori2ce STA=1O1.3(...201 102 Alternating Coefficient of Discharge versus Flow, Ratio f'-.or 1P-50 Orif'ice., STMO1.745.202 105 Alternating Coefficient of Discharge versus Flow Ratio for F-50 Orifice, STA=1.96.205

LIST OF ILLUSTRATIONS (coE''D) i:%le -LA.~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 107 Alternating Coefficient of Discharge versus Head Ratio for L/D=7.24, STA=2.68................ 207 108 Alternating Coefficient of Discharge versus Head Ratio for L/D=7.24, STA=3. 21................208 109 Alternating Coefficient of Discharge versus Head Ratio for L/D=7.24, STA=4.29................... 209 110 Alternating Coefficient of Discharge versus Head Ratio for L/D=3.63, STAO. 87................10 111 Alternating Coefficient of Discharge versus Head Ratio for L/D=3.63, STA=l.35................ 211 112 Alternating Coefficient of Discharge versus Head Ratio for L/D=3.63, STA=1.61................212 113 Alternating Coefficient of Discharge versus Head Ratio for L/D=3.63, STA —2.15................ 21 114 Alternating Coefficient of Discharge versus H115 Alternationg Coefficient of Discharge versus15................ Head Ratio for L/D=0.62,~ STA=0.23...o.......215 116 Alternating Coefficient of Discharge versus Head-Ratio for L/D=o.62, STA=0.27.......... 216 117 Alternating Coefficient of Discharge versus Head Ratio for L/D=0.62, STA=0.37...........217 118 Alternating Coefficient of' Discharge versus Head Ratio for F-'50 Orifice, STA=O. 74.........218 11) Alternating Coeff'icient of Disclhargc- versus Hiead Ratio for Y-50 Orifice7S, 51A=112.........21) 120 Alternating Coefficient of' Dischiarge versus Head Ra-tio f'or Y-50 Orifice, STA:=-1*45.220 121 Alternating Coef'ficient of' Discharge versus Head Ratio f'or F-50 Orif'icels, TA==l.q6.........221

CD Coefficient of Discharge CDA Altenating Coefficient of Discharge CDAD Ideal Alternating Coefficient of Discharge CDAID Ideal Alternating Coefficient of Discharge CDMID Ideal Mean Coefficient of Discharge CDP Coefficient of Discharge for Pulsating Pressure CDS Coefficient of Discharge for Steady Pressure CS Direction Cosine CSG Direction Cosine of Gravity D Diameter DPj Pressure Diifference Between Reference Junction and Junction "j" DPZ Pressure Difference Due to Elevation DZ Elevation Difference EL Element F Force, Friction Factor f Frequency FA Friction Factor Due to an Area Change FB Friction Factor Due to a Bend Fl'T Sum of' All F,riction Factors Cl (rCavi tLy Modulas 9 Gravity Modulas H IHead HA Alternating Component of Head t{M Mean Component of Head HIMAX Maximum Value of Head xiv

1OI1\L1CIAITjR ( CON14'D) HMh Minimum Value of Itead ~HR Ratio of Two Heads ~i One End of an Element Jji Junction, End of an Element Jo Origin Junction JT Junction Type LD~ Length ~LT El,,ement T'ype Mass Flow Per Unit Time ~n Normal NELS Total Number of Elements NFLU Fluid Number NL Number of Elements Attached to a Junction or Between Reference Junction and Boundary Junction P Pressure PA ~ Alternating Pre-ssure Amplitude P11 ~Pressur-e of' an Element p- ~Pressure at Point i P.i Pressure at Pointj PM ~ Mean Component of Pressure PR ~Ratio of Two Pressures PT ~ Total Pressure PG Pressure Cr-adeline PZ Prtessure Due Lo Elevation

NOMENCLATURE (CONT'D) Volume Flow Out of a Junction Mean Component of Flow RE Reynolds Number, V*D/v REL Conveyance of Flow of an Element RHO Density RJ Mass Ratio of Air at a Junction ST Strouhal Number, uiL/V STA Alternating Strouhal Number, uL/VA STM Mean Strouhal Number, caL/VM STM Mean Strouhal Number Based on Head, c4,/ 4 2g ZSM ~t Time ~T Temperature V Velocity'V Volume VA Alternating Component of Velocity VM Mean Component of Velocity Vq Quality on a Volume Basis X Square root of Pressure Dif'ference x Integer Array., Distance or Unknown A ~~Used as a Prefix to Denote Finite Difference 0 ~~Angle D ens ity

NOMENCLATURE (CONT'D) PS Rate of Change of Density Along Length of Element LAngular Frequency

CHAPTER I J)..'.EIJAL CO)t4I' [Jt, U SJJION OF' OSCILLATORY L,'W 11J C A'I3UJi<JRJ''OR Fl'UEL MJ7I'f ERING ]LETWORKS It is known that carburetors meter fuel at a different rate when they are tested on an engine than when they are tested on a flow-stand. Since the manifold pressure of an engine is known to pulsate, and the simulated manifold pressure during a flow-stand test is relatively free of pulsation, the difference in flow is thought to be, in part, d.ue to oscillations which are induced into the flow by the pressue pulsations. Therefore, the overall objective of this thesis is to develop a technique utilizing the digital computer to analyse and simulate oscillating flow in carburetor metering channel The modern day, air-bleed type of carburetor can be described as a complicated network of interconnecting tubes and orifices. Liquid fuel flows in some of these elements, air flows in others and a mixture of air and. fuel flows in still others. The liquid. fuel is introd.uced. into the network from a reservoir, which is commonly called. a float bowl., and. ambient air is introd.uced. into the network at various points,P which are called. air bleed.s. The fuel and. bleed. air mix in the network., and. the mixture then flows out of the metering network via several ports. Somie of these ports are located. in the venturi walls of the carburetor, and. the puls'ating pressure force at these ports causes the flow in the metering network to oscillate. In ord.er to analyse transient flow phenomena in such a complicated. d.evice, the computer is ind.ispensable. Recently,, d.igital computer

-2~s~~rrington o20f ) Other investigators, such as Streeter have used the computer extensively to study transient flow in pipelines and piping networks. Therefore, the goal of this thesis is to extend the technology of analyzing carburetor fuel-flow with the computer to include the influence of oscillating flow. Existing techniues of analyzing transient flow with the computer will be used wherever possible, and new methods will be developed when necessary. In order to make an accurate analysis of carburetor flow, precise knowledge of the flow characteristics of the metering orifices is necessary. Orifices are used extensively in the fuel metering network to control both the fuel flow from the float bowl and the flow of bleed air at several points. Since the flow through the orifices oscillates, and since flow oscillation is known to influence the coefficient of discharge., it is necessary to gain quantitative information on this effect. Therefore, another major objective of this thesis is to experimentally determine the coefficient of discharge of small orifices for oscillating flow of an incompressible fluid, and to find the dimensionless parameters which are needed to describe the results. There are many variations of carburetor designs., and., without a comprehensive simulation., it is almost impossible for the carburetor engineer to evaluate the effect that design variations have on carburetor flow characteristics without building and testing a prototype. For this reason., the simulation is to be as general as practical. This will be accomplished by making the f low network of the carburetor a variable in the simulation program. That is., the lengths and diameters o)f' all the+ ~ flow=''MC elmnts,Q as weglI as th patternnn+ - VInr41- which% they are' co-I

-3altering the computer program. This information be designated as input data and must be specified each time it is used. This featue allows the flow-path of the gasoline and air in the carburetor to easily be changed., as well as the lengths and diameters of the eleents which constitute the flow-path. Other parameters, such as the force due to gravity or other accelerations, or the fluid properties of the fuel., will be also specified. as input d.ata. Thus, the influence of many factors on the fuel metering by carburetors will be evaluated. and. the performance of d.ifferent carburetor d.esigns can be stud.ied. without the need. of build.ing and. testing them. It is, therefore., hoped. that the carburetor,engineer will use the method.s d.eveloped. in this thesis to ease his burd.en in d.esigning carburetors which will have d.es-irable performance unader all operating cond.itions.

CHAPTER II PRESSURE PULSATIONS IN THE CARBURETOR: ENGINE TESTING 2. 1Reasns or Engine Test Since carburetors meter fuel differently on an engine than they do on a flow bench with steady air flow, it is beneficial to investigate the amount of this difference for a typical carburetor. At the same time measurement of the pressure pulsations, which exist at several points in the carburetor which is on an engine, would be useful in explaining the difference in fuel flow. Therefore, one of the goals of this test program is to measuxe the fuel-to-air ratios provided by a carburetor which is in operation on an engine, and to compare the results to fuel-to-air ratios for flow-bench operation. Simultaneously, highly responsive pressure-transducers will be used to measure the amplitude and frequency of the pressure pulsations, which will be related to fuel-to-air ratio differences that exist between the engine test and the bench test. Another reason for testing an engine-carburetor combination is to obtain detailed data on the carburetor pressures., as a function of time., with which to compare the computer simulation. The venturi pressures are used as input variables for the simulation. The simulation program then calculates the main-metering channel pressure as a function of ti'me., which should then be the same as the measured main-channel pressure. When agreement is accomplished., it is assumed that the computer simulation is accurately predicting the oscillating flow in the carburetor. A third reason is to provide some quanititative knowledge of the extenit of pressure pulsations in the carburetor venturis for the use of' future investigators. Even though this data is only for one partic

-5-'This is particulaly true of the influence of the throttle plate on the pressure pulsations, since the butterfly design of throttle is most universally used. 2.2 Previous Studies Experimental studies on the effect of pressure pulsations on fuel metering by carburetors have been performed by a few investigators. Prien (28) did an experimental study of the influence of pressure pulsation on the fuel-to-air ratio for a simple carburetor, which lacked air bleeds, on a single-cylinder engine. He tested his carburetor with stead air low, with air flow for the engine motoring, and with air flow for the engine firing. For his simplified carburetor he obtained fuel-to-air ratios for firing and motoring conditions which were as much as three times greater than for stead.y air-flow- cond.itions. Hosho (21) also tested. a simplified. carburetor,, w-hich w-as very similar to that used. in the work of Prien. However., his carburetor had. an air bleed. and. he used. a stroboscopic light and. a high-speed. camera to stud.y the flow- oscillations at the fuel d.ischarge port. He varied. the air bleed. d.iameter and. the venturi suction and. noted. the effect on the amplitud.e of pulsations and. the fuel-to-air ratio. He found. that flow oscillations which occurred. when no bleed. air was introd.uced. were largest for low venturi vacuum. He also found. that the introd.uction of air caused. the flow oscillations to be greatly increased.. The greatest amount of oscillation was found. to be for small venturi vacuum at the minimum mixture ratio, and. that the flow mod.e for the fuel and. bleed. air was slug flow for maximumn oscillations. He also tested. three typi

-6In a later work, Hosho (22) continued his photographic study ol flow oscillation of the fuel as it leaves the main discharge nozzle. He studied a Stromberg type down-draft caxburetor, with a high-speed movie camera, in operation on an engine and on a flow stand. He concluded that, "Pulsations will occur regardless of whether the carburetor is operated in an engine with a pulsating air flow or in a Cox carburetor test stand with constant flow". He found that the pulsations are minimized by the elimination of bleed air. He further states that, "the pulsations during fuel jet of the main fuel system are caused by the air introduced through the air bleed, not by a pulsating air flow". However, his photographic testing technique is qualitative in nature and it will be shown by more accurate testing methods that the pulsating back-pressure at the venturi is the only source of pressure pulsations at low engine speeds and large throttle-openings. Oyama, Tejima and Hosho (27) continued this study of the transient flow phenomena caused by the bleed air by creating a one-dimensional flow model of the two-phase flow in the caxburetor emulsion-tube. For this model they divided the flow elements into small increments along the direction of flow, and assumed an average fluid density which was based on the relative volume of fuel (liquid) and air (gas) to enter each incremental section. They then solved the equations of motion and continuity, for increments in time and space, with the computer, and were able to accurately compute fuel-discharge lag-time for the Stromberg carburetor for sudden acceleration. Their experimental results compared very well with their calculated values, but they did not extend their analysis to the flow oscillations which they found to occur under steady engine-load conditions in the previous work of Hosho.

-7Many investigators have measured and analyzed the pessure pulsations in the manifold of an engine, and much discussion is available on the topic. Taylor, Livengood and Tsai (30) experimented with a single-cylinder engine in order to study the pulsing phenomena with regards to the ram effect" on the intake air and improvement of volumetric efficiency. They measured the inlet port pressure and cylinder pressure as a function of time for different lengths of inlet pipe. Their work contains considerable discussion of the physics of the pulsating pressure in the intake manifold. Later work on the "ram effect" was done by Huber and Brown (23) in which they simulated the engine cycle with the digital computcr in order to study the influence of dimensional changes of valves and manifolds on the induction process and volumetric efficiency. Their work included the effects of heat., finite time of combustion and varia-ble gas-specific heat, but it was done for single-cylinder engine only and does not include the influence of a throttle or other restrictions in the intake and exhaust systems. More recent studies of intake and exhaust systems of singlecylinder engines were performed by Goyal, Scharpf and Borman (19). Their work includes experimental study of the wave damping within the manifold during the time the intake valve is closed. In the same work they perform a digital-computer solution of the Pressure in the intake and exhaust manifolds for which they assume one-dimensional compressiblef'low in a straight pipe of constant area w-ith friction and heat. However, the work does not include the influence of a throttle valve, and it isol oasnl-yine9nie

-8A study of the formation of the combustible mixture in the intake manifold., which includes the influence of flow oscillations, was performed by Brandstetter (17). The study was performed on an idealized intake manifold, which consisted of a straight pipe with each end connected to a plenum chamber. A vacuum was created in one chamber which induced flow through the pipe. The flow was caused to oscillate by a rotay type of sleeve valve, which was located in the pipe, and the influence of liquid and vapor fuel, which was introduced into the flow, was investigated. The transient flow was analyzed with the digital computer by the method of characteristics, and the calculated values of air flow, fuel flow, and air-to-fuel ratio compared well with the experimental results. The same investigator continued his work (18) by modeling single-cylind.er engine flow with intake and. exhaust pipes. In this later effort he includ.ed. the influence of the throttle plate and. intake and. exhaust valves. The work is only theoretical., and. contains no supportive experimental results. It was found. that much stud.y has been performed. on the intake manifold. of a four-stroke engine. However., in all cases-only a singlecylind.er engine was stud.ied., and. the pulsating pressure phenomena in a multi-cylind.er manifold. was not found. to be d.iscussed. in the literature. Theref'ore., the analysis of the transient flow, i-n a multi-cylind.er manif-old. is a. topic which should. be investigated.. It was also found. thl-at fVew investigators have stud.ied. the pressure pulsations which are causedt in the carburetor fuel-metering network by the pulsat-ing back pressure -1 - _. 1 _ 4 at the venturi, and. how- thseplstin can un.e stead.y_ --- 3

-9This is the problem which has been chosen for further study in this thesis. 2.3 Testing Procedure A Ford C8AF-L 2-barrel carburetor was specially modified to accept highly responsive electronic pressure transducers to measure boost venturi pressure, main-venturi pressure above and below the throttle, and in-metering-channel pressure. Tubes of 1/8 inch diamneter were inserted through the carburetor walls to provide pressure taps at the desired points. The transducers were then attached to the ends of the tubes on the outside of the carburetor. The tubing length was made as short as possible to minimize frictional damping of the signal, and the diameter of the tubing was small to minimize capacity for absorbing pressure signal. Figure 1 shows the location of the four pressure taps to which the transducers were connected. Appendix A gives more details on the test equipment and procedure for the enginecarburetor test. 2.4 Results of Engine Tests The results, as shown by Figures 2 through 5,, illustrate that pressure fluctuations do occur throughout the carburetor and in the intake manifold. The pressure pulsations occur at all times in the manifold., as shown by F'igure 2., but they only occur at throttle angles greater than about 30 degrees (90 degrees is. wide open throttle) in the main venturi and boost venturi, as shown in F'igures 3 anid 4. This is expected since the flow at small throttle openings is choked which prevents changes in manifold pressure from being transmitted upstream of the

-10 - MAIN AIR FLOW * AIR BLEED BOOST VENR FULLEVEL MAINORIFICE PRES SURE TRANSDUCERS SLt~~~~~~~~~~O 2 VALVE' IDLE PORT TO INTAKE MAN IFOLD 0o 2 3.APPROXI SCALE, INCHES F'igure 1. Cut-&way Drawing of the Test Carburetor.

-111.4 FORD 308 CU. IN. V-8 1.3 AUTOLITE C8AF-L CAR B URETOR 1.2 V) 1. 0 250~~~~000RPM 1. 1 0. c~0.96 0.85 0.7 ~-0.5 0 0 10 20 3 10 5 0 7 0 9 THROTTLE ANGLE, DEGREES 900 = WIDE OPEN THROTTLE

1. 2 FORD 308 CU. IN. V-8 AUTOLITE C8AF-L CARBURETOR 1.0 V)~~~~~~~~~~3 0L. 0.9 0.8 0.7 ~~~~~~~~3000 RPM o 0.6 7.' V r V c~~~~~~ 0.5~~~~ 0 P i- 0.64 LU z- 0.3 0.2 ALL RPM ______________ 0.1 ~~~~~~~~~1000 R PM 0. 10 20 30 40 50 60 70 80 90 THROTTLE ANGLE DEGREES- 90 WIDE OPEN THROTTLE Figure 3. Main Venturi Pressure Pulsation.

-151. 6 FORD 308 CU. IN. V-8 1. 5 AUTOLITE C8AF-L CARBURETOR 1.4 3000 RP 1.3 2500 RPM 1.2 VI 1.1 1L0 2000 RPM ~0.9 0 0. 8 V) 0. 7 0.6 -0.65 v) 0.54 0.3 0. 2 0. 1

0.6 FORD 308 CU,IN, V-8 AUTOLITE C8AF-L CARBURETOR 0 5 3000 RPM 25 00RPM 0.3 LU <r 0.2 0 10 20 30 40 50 60 70 80 90 THROTTLE ANGLE1 DEGREES 900 WIDE OPEN THROTTLE

-15The frequency of all of the pulsations is equal to twice that of the engine revolutions. For the dual level manifold, each venturi of the carburetor services four cylinders, and each cylinder performs an intake stroke every 720 degrees of crankshaft rotation. Since the four-intake strokes are nearly evenly spaced in time, they occur at 180 degree intervals of crankshaft rotation and create a pressure pulse at the same interval. Therefore, two intake strokes occur for each complete rotation of the crankshaft so that the pressure pulsations have a frequency which is twice the engine speed, or equal to rpm/cps. This frequency corresponds to the number of intake strokes per second for the 8-cylinder engine. 2.5 nifold Pressure Pulsations Figure 2 shows that large pressure pulsations exist in the intake manifold, for all combinations of engine speed and throttle angle. The greatest amplitude of pulsation is seen to occur at the highest engine speed., and the influence of the throttle opening is seen to depend upon engine speed. Larger throttle opening makes the fluctuations smaller at low speed (1000 and 1500 rpm), and larger at high speeds (3000 rpm). At intermediate speeds., the throttle angle has a small influence upon the pressure pulsations in the intake manifold. This phenomena has been well researched for single-cylinder engines., as previously mentioned., but little has been published on analyzing pulsating pressure in multi-cylinder engine intake manifolds. 2.6 Venturi Pressure Pulsations The pressure pulsations., which have been shown to exist in the

-16same position as the ports for the main-system fuel flow as shown in Figure 1, which means that the fuelJmetering network will be exposed to these fluctuations. The figures clearly indicate the lage effect the throttle has on the pressure pulsations, because no pulsations are present at throttle angles less than 30 degrees (90 degrees is wide open throttle). This phenomenon is explained by the fact that the air flow reaches sonic velocity at the throttle for small throttle openingL, and, therefore, no pressure disturbance can be transmitted from the manifold, upstream from this point. At throttle openings between 30 and 50 degrees, the amplitude of the pressure pulses in the carburetor are measurable, but the throttle still substantially restricts the amount of pulsation which is transmitted from the intake manifold. However, at throttle angles greater than 50 degrees, the throttle does little to dampen the pressure amplitude. The pressure amplitudes are substantial in size, and for the boost venturi., are even greater than those in the intake manifold. The analysis of the oscillatory flow which occurs in the manifold and in the venturis., as shown in Figures 2-4., is very complicated and presents a formidable problem. As mentioned earlierl, many investigators have tested and analyzed simplified versions of the air intake system., but none were found who attempted to analyze the oscillatory flow in the multi-cylinder engine intake system. Harrington (21) studied the problem for steady flow., and included the influence of compressibility., fuel droplet size., fuel atomization., and the throttle plate., where sonic flow occurs. The problem is also complicated by the influence of flow-path curvature., two-phase flow with part of the liquid

-17this complicated system, which has oscillatory flow, is a challenging problem for future investigators. 2.7 Main uel Channel Pressure Pulsations Figure 5 shows the amplitude of the pressure in:the main fuel channel which is immediately downstream of the main metering orifice (see Figure 1). The frequency of these pulsations is the same as the frequency of the pressure in the manifold and the venturis (rm/30 cPS), which indicates that the venturi pressure fluctuations are causng the pressure in the main fuel-metering channel to pulsate. Further evidence of this is that the metering-channel pressure-pulsations at these frequencies do not exist at throttle angles less than 30~, because pressure pulsations do not exist in the venturis for the same throttle angles. Thio- indicates that only the main-metering system transmits pressure pulsations to the main fuel channel., and that the idle system has a large damping effect on the pressure pulses which are transmitted to the metering network via the idle port. The pressure pulsations at the idle port are similar to those of the manifold., hence,. they are always present. The damping effect of the idle system was substantiated by testing the engine for two identical points of speed and throttle angle with the idle screw open in one instance and closed for the other. No difference could be noted between the amplitudes of the pressure wave in the main channel of these tw-o cases. 2.8 Waveshape of Pressure Traces Most of the pressure-time traces taken from the carburetor could be approximated very well with a single harmonic of fundamental

-18deviated noticeably from a purely sinusoidal wave shape. However, it appeared to be very close to a sinusoid for all speeds at throttle angles which are equal to or less than 60 degrees. just above the throttle, at the point in the main venturi, the pressure wave shape always contamiied noticeable amounts of higher harmonics, but the mgnitude of the fundamental harmonic was still predominant. Similar results were noted for the pressure wave of the boost venturi, which appeared to contain a substantial second harmonic because the wave was well rounded at high pressure, and pointed during the other half of the cycle at low pressure The fundamental frequency of the pressures in the venturis and the manifold was always equal to twice the engine speed. The pressure pulsations in the main channel also had a frequency of twice the engine speed. However, another pulsation also occurred which had a frequency between 15 and 25 cps., regardless of engine speed. Therefore, the waveshape of the pressure in the main channel was a combination of a 15-25 cps wave and a wave w-ith a frequency equal to twice the engine speed. The 15-25 cps portion of the wave did not exist at or below 1000 rpm., but became evident at 1500 rpm. At speeds greater than 1500 rpm., the amplitude of the 15-25 cps pulsations became proportionally larger., and the amplitude of the pulsations with a frequency of rpm/50 also increased. All of the data for the pressure amplitude in the main channel., which is shown in Figure 5, is for the harmonic of frequency which is equal to twice the engine speed. This means that the pressure amplitude shown in Figure 5 is only caused by the pulsating pressure at the boost venturi. The total pressure amplitude is actually greater, bccaz t inluds a 5-2 rcp comonnt

-19Some phenomena, other than the pulsating back pressure at the boost venturi, must be causing the pressure disturbance of 15-25 eps the main channe. This phenomena has been noted by Hosho (22) who did high-speed photographic studies of carburetor fuel-flow. Unfortunately he drid. not measue the pressures, so that the results of his studies are only qualitative. He was only able to determine the frequency of the flow oscillations, and had no way of measuxing their magnitude. The oscillations had a frequency of 10-20 cps for his carburetor, and these were independent of engine speed. Also, the same phenomenon occurred. when the carburetor was operated on a flow bench with constant venturi pressures. He was able to minimize these oscillations by making the air-bleed flow zero, and he concluded that the flow oscillations in the carburetor are due to the two-phase flow and are not due to fluctuating back pressure in the engine manifold. or carburetor venturis. However,. the d.ata of Figure 5 d.oes show that, for this particular carburetor., pressure fluctuations d.o occur at the main metering orifice which are d.ue to the pulsations of the back pressure in the venturis. At engine speed.s below 1500 rpm., these are the only pulsations which arc present in the main fuel channel., and. the influence of the bleed. on pulsation is negligible. At greater engine rpm, the pressure fluctuations d.ue to the bleed. air are comparable to the fluctuations d.ue to the pulsating back-pressure in the venturis. 2.9 Comparison of Engine Tests with Flow Stand. Tests The venturi pressures and. the manifold. pressure have both been shown to pulsate (Figures 2-4), and. these pulsations are now known to be transmitted- -.-. into _-_.0 1-A -_!_ -i —_ _ — the ainfue metrin-chnne (Fgre 5). Sinc these1 1 --

-20912 ENGINE: FORD 302 IN.3 V8 CARBURETOR: AUTOLITE 2- BARREL *1 I TYPE C8AF- L ENGINE TEST FLOW BENCH TEST.0 oI Pu Isating Flow * Steady Flow -m ~ 29.15 In. HgBr 291 1n. Hg. Bar 29.11 o o 0 ~m 85 F Air Temp. 74 F Temp. -J.0o9 Standard Gasoline Mineral Spirits 1000 RPM NL D~ W.O.T., ENGINE TEST w ~~~~~15OO RPM.:.08.07 E3 ~ FLOW BENCH TEST 0 200 400 600 800 1000 1200 1400 AIR FLOW, LB/HR Figure 6. Comnparison of Laboratory Airbox (Steady Flow) Thel1/Air with Enigine Tuel1/Air (Pu.lsating Flow).,

-21investig-ate the effect they may have on the average fuel-to-air ratio provided by the carburetor. A comparison of engine fuel-to-air ratios with flow-bench fuel-to-air ratios is shown in Figure 6, which is a plot of fuel-to-air ratio versus air flow, and shows many data points for different throttle angles and engine speeds. The data indicate that the carburetor performed on the engine almost exactly as it did on the flow bench at air flows greater than 600 pounds per hour. This is particularly true of the upper curve, or full power line. However at air flow rates less than 600 pounds per hour, the engine fuel-to-air ratios re shown to be greater ( at full power), than the flow-bench fuel-toair ratios. These points coincide with the points of low engine rpm and large throttle opening, which is when nearly all pressure pulsations in the main fuel-metering channel are caused by the fluctuating back pressure in the boost venturi. These fluctuations in the boost venturi only occur when the carburetor is operated with an engine., and are., therefore, thought to be the cause of the difference between the test bench and engine fuel-to-air ratios. The difference between the engine test points and the flowbench test-points is also noted for the lower curve in Figure 6., or the off-idle and cruise ranges of operation. This difference cannot be attributed to boost venturi pressure pulsation,. because it has been shown that small throttle angles (large pressure ratios or choked flow) greatly. dampen the pressure amplitude at the boost venturi. This difference in fuel-to-air ratio between engine operation and flow-bench operation can be attributed to fuel property variations. The flow test was performed with a speci-al testing fluid,r a ndr ~ thepi r eni ne.=Q+ tests ~ were, % aT peformedn wthI-+I

-22property variations can cause substantial differences in fuel metering by carbuetors, and their engine test data, for the same type of carburetor and engine, shows that this is particularly true in the idle, off-idle, and low power ranges of operation. Pressure pulsations are thought to be the cause of the fuel-to-air ratio difference between flow bench tests and engine tests at wide open throttle and low air flow (low engine speed), and it is postulated that it is the influence of these pulsations on the metering characteristics of the min-metering orifice which cause this difference. This leads to an important Lphase of this thesis, which is the influence of pressure pulsations on the time-average flow through small orifices. 2.10 Conclusions from Engine Tests 1. Pressure pulsations were found to exist in the induction and fuel metering system of a Ford V-8 engine with a C8AF-L two-barrel carburetor. The frequency of the pulsations was always rPm/30 cPs, with exception of the metering channel. The waveshape of the pulsations was primarily of one harmonic., but noticeable amounts of second harmonics and some higher harmonics were also apparent. 2. The throttle angle was found to greatly influence the amplitude of the pulsations at the main venturi and boost venturi. The amplitude was maximum at wide open throttle (90 degrees). The throttle angle had a minor influence on the pressure amplitude in the intake manifold. 5. Greater engine speed resulted in increased pressure fluctuation amplitude in the intake manifold., main venturi., and boost venturi. 4. The pressure wave in the main channel was generally com

and one at a frequency dependent upon engine speed or rpm/30. The amplitude of the former did not appear to be related to engine speed or throttle angle, and the amplitude of the latter followed a relationship to engine speed and throttle angle which is very similar to that of the boost venturi pressure fluctuation. The constant-frequency component has been shown by Hosho (22) to be caused by fuel pulsations due to the introduction of bleed air. 5. Different fuel/air ratios between the engine test data and the flow-bench data for the same carburetor was found to exist at low air flows (low engine speed). At wide-open-throttle, this difference at sma11 throttle angles can not be attributed to the same cause. At high air flows and wide-open-throttle, no difference between the fuel/air for bench test and engine test is noted.

CHAPTER III INCOMPRESSIBLE OSCILIATING FLOW THROUGH ORIFICES 3.1 Introduction A carburetor contains many small orifices which serve to control the flow of fuel and bleed air. These orifices are on the order of 0.05 inches in diameter and range in length from 0.05 to 0.2 inches. Most of them are of a "square-edged" design; that is, their geometry ogruent to a drilled hole. However, the main-metering orifice, which controls the main fuel-flow from the float bowl, has unique geoetry It has sections of different areas, camfers, and a screwdiver slot. It is easily removed with a screwdriver since it is threaded into place, whereas the rest of the orifices are permanently pressed into place. The main orifice is made to be removable because it is a major flow-controlling element of the carburetor., and. the metering characteristics of the carburetor can be easily ad.justed. by changing it. The importance of the ma~in metering orifice,, and. the other orifices, makes the knowled.ge of the flow characteristics of these elements vital to Tlhe accur-acy of' any carbure-,.tor analysis. Fluid. -flow through the, o:rziiicesust'be knowni iii terms of' any ind.epend.ent variables w-hich could. change d.uring carburetor operation. The variables w-hich influencei flow- through orifices for stead.y flow have been thoroughly stud.ied. by Harrington (20), and. the results applied. in his d.igital computer simulation of the carburetor. It has previously been shown here that the pressure at the main orifice is pulsating. Therefore, the task is now, to d.etermine how pressure pulsations and. the correspond.ing flow-oscil

-25The study of periodic flow of an incompressible fluid involves several variables which are; the frequency of the pulsation, the amplitude and mean values of the pressure differential, and the amplitude and mean values of flow. Figure 7 illustrates the meaning of the variables for a sinusoidal flow, which is typical of carburetor flow. However waveshape is an important variable, and the results contained here can only be applied to flow which resembles a sinusoidal form. The variables can be combined into three dimensionless groups as follows: - Strouhal number, STM = flow ratio, QR, and = pressure ratio, APR. As the literature indicates., all three of these dimensionless numbers are pertinent to oscillating flow through orifices. 3.2 Previous-Work The influence of flow oscillations on metering by orifices has wide-spread practical application because many fluid systems inherently contain oscillations due to the use of a piston pump or a flow instability. The metering characteristics of any orifice are influenced by the flow oscillations, and their effect must not be overlooked when precise metering is desired. Hence., considerable study has been performed about the influence of flow oscillation on fluid metering by orifices. However,, little analytical study of oscillating flow through

-26Mw: Pres er/od - L Period — M~~~~~~TM A/f F/w Q, J V c/) ~~ ~ ea /o,~ and. Flow. ~~ow i

Een though a complete theoretical analysis of oscillating flow through orifices has not been performed, the solution to the closely related problem of transient flow in an infinite tube has been ~publishyed. Daneshar (5) solved this problem for a pressure gradient which is an arbitrary function of time. However, the results of his studies can only be used in a qualitative way in reference to the orificc problem because entrance and exit effects and flow turbulence, which lare not included in his studies, are most important. Benson and Shafie (4) performed a theoretical and experimental study of the use of sharp-edged orifices to measure instantaneous air flow. They modeled the orifice as if it were composed of two lsections: 1) sudden contraction and 2) sudden expansion. They then solved the one-dimensional, non-steady equations of continuity, energy and. momentum for the two sections., and. equate the solutions at their common plane, which is the exit plane of the orifice. Their experiments show that their analysis is limited. to large orifice-to-pipe arearatios and. small pressure d.ifferences. They conclud.e that their analysis can be used. to d.etermine instantaneous mass flow rates if the aforementioned. limitations are maintained.. The literature primarily contains experimental solutions to the orifiCe problem., and. includ.es stud.ies of both incompressible and. compressible oscillating flow. For this work., incompressible flow is of interest, but the results of previous experiments w-ith compressible fluid. are also useful since many similarities d.o exist. Most of the -previous testing has been d.one with compressible fluid., and., in

-28A very comprehensive study of experimental work on pulsatingflow measurement by Oppenheim and Chilton (11) summarized the techniques of measuring oscillating flow. They presented a discussion of the fundamental aspects which must be considered when measuring oscillating flow, and then discussed the merits of several different methods of measuring it. This work also contains a large bibliography which makes it very useful to any further study of the subject. Earles and Zarek (7) studied the flow of air through orifices of diameters 0.75 to 1.75 inches for oscillations up to 16 cycles/second. They measured a correction factor which is needed to adjust the Steadystate coefi'ficient of discharge to account for the influence of pressure pulsations. They correlated their correction factor with the dimensionless numbers of pressure intensity and Strouhal number, but they did not consider dependence of the correction factor upon Reynolds number, which varied from about 30,000 to 60,000, or upon Mach number, which varied approximately from.03 to.09. They did investigate the dependence of flow upon geometry and found that the position of the orifice along the pipe-length had a small measurable influence in most instances. Since their results are for a compressible fluid, it is not possible to quan-titatively compare them to the results which are presented in this study. However, they do state that pressure intensity and Strouhal number are both important parameters in determining the influence of pressure pulsations on fluid flow. Jeffery (9), under the supervision of Zarek, continued the study of the influence of pulsations on air metering by orifices. He extended the range of frequency to 33 cycles/second, and found that the time-average flow for pulsating pressure is dependent upon frequency,

-29 - presure intensity, orifice-to-pipe area-ratio and mean flow. His data contains information on the influence of waveform of the pulsations upon the time-averaged flow. In a later work, Zarek (14) summarized the efforts on measuring oscillating flow. He applied recent findings to the problem and made recommendations as to how inaccuracies, encountered in flow measurement with orifices, due to flow oscillation can be minimized. His data, plus that of Earles and Jeffery, showed that the true flow ca be greater or less than that predicted by the average square-root of the pressure differential. Sparks (12) measured the instantaneous flows of air through orifices in order to study the influence of pressure pulsations on time-averaged flow. He accomplished this with a hot-wire anemometer and attempted to plot his data as a function of flow ratio,, but his plots show no consistent pattern. He further admits that he needed to con-. sider the additional effects of Reynold.s number, Eulers number, DUch number., pressure ratio and Strouhal number. He did observe the timeaveruged Iflow- to be different for pulsating pressure compared to the steady pressure., and his data show that flow- oscillations can cause time-averaged flow to be greater or less than that for steady flow. He stated that he needed an order of magnitude of additional data in order to fully investigate the influence of all of the dimensionless v-ariables. Moseley(lO)studied the influence of pulsation on water flow. He measured the periodic flow with a ma.gnetic flow-meter up to fre

-30Reolds numbers ranged from 65,000ooo to 400,000. He presented a quasisteady teory for accounting for the pulsations, and shows that the neglected. effect of temporal acceleration is a good approximation for his low-frequency data. He plots his data in the form of an error parameter as a function of flow ratio. The error parameter is defined. by coefficients of discharge for steady and pulsating flow as follows: CDS error = D - 1 CDP His data show that pipe diameter-to-orifice diameter ratio has a small influence on the error parameter, and that the error can be negative at low flow ratio, which means the average flow under pulsating condition can b greater than for steady conditions with the sme average prsure differential. Almost all of the recent literature oi measuring oscillating f'low- mentions the square-root error. This is based. upon the mathematical fact that in general: t t 0 0 or the square root of the integral d.oes not equal the integral of the squar-e root. F'low is known to be approximately proportional to the square root of pressure d.ifferential., but a manometer measures the average pressure-d.ifferential. Hence., the square-root error arises when the average flow is taken as proportional to the square root of the average pressure-differential,, as measured. by the manometer., and. not proportional to the average of the square root of the pressure d.ifferential. To summarize, no theory was found to accurately pred.ict the

no experimenter was found to have taken sufficient data to corr(lat,( the lflow with all o' the necezsary dimensionl1ss niunb(rs. A.1l of,] L,w data f'ound shows scatter of at least +10%, and any correlation of ~'low or coefficient of discharge with any dimensionless variable has been for limited ranges of the other important dimensionless variables. Most important, as to the work performed here, no data was found for the influence of flow oscillations on small orifices. Also, few investigators attempted to measure instantaneous flow, but rather only measured the instantaneous pressure differential, and most data is for relatively low frequency (less than 50 cps). 3.3 Objectives of Orifice Tests The main objective of the orifice test program was to determine the influence of flow oscillation, and, consequently, pressure pulsation of a sinusoidal wave form, on the time-average flow through an orifice. This was to be done for one incompressible fluid (mineral spirits) and several geometrically different, small orifices (about.050 inch in diameter). Instantaneous pressure and flow were to be measured for steady-oscillatory flow conditions at frequencies up to 100 cps. The fluid viscosity and density were to be accurately determined for dse in analyzing the data. The objectives were also to include the correlation of the data in terms of the important independent variables. Several independent dimensionless variables, which have been suggested in the literature, were to be investigated as to their influence on the flow through small orifices. A systematic method of organizaing the data for the small orifices was sought, which would include a simplified analysis to indicate the relative importance of the many independenlt vrariables.

-323. Description of Orifice Testing Rig Figure 8 is a schematic diagram of the testing facility, which is used to determine the influence of flow oscillations. Its most unique feature is the use of pistons to force the fluid through the orifice, and, thereby, provide the desired volume-flow. As shown, two pistons are used: one piston is moved at a steady rate to provid stady flow, and the second piston is moved at an oscillating rate to provide an oscillating component of flow. A strain-gage pressure transducer is used to measure the instantaneous pressure differential. The entire facility can also be pressurized to minimize the possibility of cavitation, which would destroy the coatinuity -elationship needed to calculate the flow from the motion of the pistons. The dtail of the orifice test-block can be more closely examined. in Figure 9, which is a cutaway scale d.ra-wing of it. As the f'igure indicates., all of the seals are of the 0-ring type,, including the Sliding seal f'or the oscillating piston. The f'igure also indicates the l-ocation of' the pressure transducer with respect to the orifice and the alternating piston. The fluid. reservoir and. valve which connect it to the or-ifice block are also shown as well as the fluid-flow-path through the orif ice block. Figure 10 shows the entire orifice testing rig., including the instrumentation., which is sho-wn on the rack at the left. The Visicorder., which is used. to record. the time traces of pjressure and. flow, is on the top shelf of the rack., two Carrier Bridge amplifiers., which power the strain gage circuits and. amplify their signal., are on the

-33AlIR PRESSURE (S'/ceAIR) DIFFERENTIALPRESSURE AIR TRANSDUCER -- -- TEMP ~AC-DC TEMP. MOTOR +CAM VARIAC ~IFICr.~, J — ALT. F LOW DRAIN GEAPFRRTED FLOWV GEAR- ~~~VARIAC hAn~~i gue8rceatco rfceTsigRg

-34_; ~~~~~L t~~~ 1A~~~~~~~_c~ ~ ~ ) [~~~~~~ ~izs l. CH ~~~~II ~~~~~~~~~J~~~~~ LL 00 C) bO tro w~~~~~~~~~'

-35Figure 11 shows an overall view of the testing rig. The large cylinder with the temperature and pressure gages is the fluid reservoir. The orifice block is connected to the fluid reservoir on the right by a valve. The cam and motor drive mechanism for the oscillating piston are sho to the right of the orifice block. The mean-flow cylinder is hidden immediately below the orifice test block, but its gear-motor and screw drive mechanism are visible to the left. Two Variacs are visible in the foreground which are used to control the speed of the motors. The switches in the box at the left are used to turnon the gear-motor and reverse its direction. 3.5 Instrumentation Basically, five quantities must be measured which are: 1) mean pressure differential, 2) alternating pressure differential, 3) mean flow, 4]) alternati-ng flow., and 5) frequency. A standard commercial pressure transducer is used to obtain mean and alternating pressure differentials. Mean flow is obtained from the period of the signal from the ma~gnetic pick-up. Alternating f low is determined from a strain gage displacement transducer mounted to the oscillating piston., and frequency is found with the use of a timing mark provided by the Visicorder. Table I lists the commercial instruments which w-ere used in the testing as well as the other commercially made apparatus. Pressure Transducer The pressure transducer., which is connected to each side of the, orifice block as shown in Figure 12 was initially calibrated with a water mnanometer. A pressure (or vacuum) was applied to one side of thie

>~~~~~~~~~~~~~~~~~~~C ~~~~~~~~-3~"t ~~~C) 4-p 0.4At b.D 4-. X'n U

-37-!i i i i! i!i i i ~;,.......... ~?........*:........i'*...~i 4,r -P..... b..........i i jirl,.,.-,.,,,.,,iiii.,'!1,:....i 3s zt_iiiii.! i!iii!11 i.~. " ".,'~......i.. e idat t W S t1 _~ SrA i'11i;iii;;'!;i!i;~'~''~ ~ ~ ~ - "!H? I!i i,i i! i' ~'

TABLE I EQUIPMENT LIST FOR ORIFICE TESTING RI Model Serial Item Brand Number Number agnetic Electro-Mation 3010-AN pick-up Thermometer Tagliable 0-1000F Pre ssure 30 in Hg. vac gage Marsha,lltown 100 psi. Varia.c SupDerior 116-B 1. 4 kva,. 0-140 volts out Gearmotor Dayton 41(872 0-306 N/L rpm AC -DC 0-100 F/L rpm Motor Dayton 2M139 1/5 IiP at AC-DC 101,000 rpm. Differential Viatran PTB 209 142469 +10 psid. Pres sure Transd.ucer

-39The deflection of the Visicorder trace was recorded for each pressure point. Then a plot was made of inches of water pressure versus inches of recorder deflection. Figure 13 shows the calibration curve for the pressure transducer. The calibration curve also shows values of deflection (in tabular form) for calibration resistors. These are special resistors which are contained in the amplifier and can be switched in parallel with one of the strain gages of the 4-gage bridge circuit of the pressure transducer. When this is done, an electrical unbalance in the transducer bridge circuit is created which simulates the same unbalance created by pressure on the transducer. These calibration resistors can then be used to later set the gain of the amplifiers to different values without the need of recalibration. That is, if the deflection for a given calibration resistor is twice what it is for the calibration curve, then the gain of the amplifier must be double what it was for the calibration curve. Therefore, values of pressure taken from the calibration curve are twice the actual pressure, or the actual pressure is only half the indicated value on the calibration curve. Steady Flow As previously mentioned, the steady flow is measured with a gear and magnetic pick-up arrangement. The gear is connected to the drive screw of the steady-flow cylinder, as shown in Figure 14. The drive screw has a pitch of 0.1 inch and the gear has 54 teeth, so that the period of the signal from the magnetic pick-up corresponds to 1/540 inch of piston travel. The diameter of the piston is one inch; therefore, the period of the signal corresponds to.00144 cu. in. of

-40-" 2/ ~~~~~22~~~~i#~~~~/f /~1? fg,~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~J Al C) 0q

-4160 VIATRAN PRESSURE TRANSDUCER CALIBRATION WITH VISCORDER CARRIER CHANNEL NO. 9 CAL RES. DEF, IN. ~40 +1 2. 063 - 1 2. 159 AI 0 20 (-) 0 LU20 LU L/_ LV) LU -60I -1.0 -0.5 0 0. 5 1. 0 INCHES DEFLECTION ON RECORD Figure 13. Pressure Transduacer Calibration Curve.

piston displacement. Maximum no-load speed of the gear motor is 306 rpm, which gives a maximum flow capacity of 6.25 gph. Alternating Flow Figure 15 shows the transducer used to measure the displacement of the alternating piston. It is constructed of a piece of flat spring steel (.020 x 0.500 inch in cross-section; 2-1/2 in. long) which is firmly attached to the orifice block at one end and to the alternating piston at the other end. Four strain gages are mounted to the flat part of the spring to measure the strain in the spring, hence indicate the motion of the end of the spring which is attached to the piston. The I our strain gages are wired in a Wheatstone bridge circuit and are powered by a Carrier Amplifier, the same as for the pressure transducer. The trace recorded by the Visicorder indicates the displacement of the alternating piston. A dial-gage indicator is used to calibrate this displacement transducer to thousandths of an inch of accuracy. Also, the frequency of the displacement is used to determine the frequency of the flow. 3.6 Fluid Compression: Blank Orifice Test The means of measuring the alternating flow from the motion Ut tl(w oscillating piston requires that the, Iflow be inlcompressible, and the; testing rig be infinitely stiff. This, of course, is not true, and some f'luid compression and testing rig strain will occur when the fluid pressure within the orifice test block is changed. The fluid compression and testing rig strain represent a volume change; hence, part of the alternatiulW-pisLon motJion. This leads to an error in flow measurement if ttle f1 pstough the] oriflice is arssumed equal to the swept volune of the piston. Thlerefore, a blank test ws performed. to measure the amout of

i!ii-~~ ~~~~a.':igure 14. Driere Mechan~~~~~~ismfr;. " ayl -ise.,

.... l'~ b-0 I al~~~~~~a

pi sLoul in(Lic whlich serves to strailn the orifice teotintg-ri and Lo compress the fluid. A blank was installed in place of an orifice, as shown in Figure 16 which made the orifice test block, mean flow cylinder, and pressure transducer into a sealed cavity full of mineral spirits. Any piton motion, therefore, represented fluid compression and system strain. The alternating piston was then oscillated at a very small amplitude and the corresponding increase in pressure measured with the pressure transducer. This was done for several frequencies and the results of pressure amplitude versus frequency are shown in Figure 17. The results show that the pressure amplitude is relatively constant up to a frequency of 80 cps, and the pressure of the system is in phase with the piston motion. in other words, quasi-steady conditions prevail, and any change in volume created by the piston motion is offset by comnpression of' the f'luid and strain of the orifice testing block. On the other baund, at frequencies greater than 100 cps-, the pressure amplitude is much greater than the constanit value at low,er frequencies. A phase shift is also noted between pressure and displacement., which means that the system remained in a state of strain while the piston partially returned to its starting position. In other words, the response of the strain is limited to 100 cps, and considerable error will be encountered'if data for frequencies greater than 100 c-ps are taken. Any air., that is trapped in the system., will also negate the assumption of incompressibility which is needed to calculate the flow

DIAPHRAGM PRESSURE TRANSDUCER 1/4 INCH COPPER TUBE 318 INCH THICK BRASS CAVITY 1 INCH DIAM. 1 INCH LONG BLANKED OR IF ICE CAM ~.0037 INCH 114 INCH INTHICKNESS; -* 0N-6-------' ~~182 x 10' CU. IN. ALTERNAT I NG P I STON D I AMETER = 0. 25 INCH 118 INCH COPPER TUBE TEFLON O-R ING SEAL - MEAN-FLOW CYLINDER AND PISTON, DIAM' 1 INCH HELD STATIONARY FOR THIS TEST Figure. Schetic for BlankedNGH 6 rifice Test. Figure 16. Schematic for'Blanked-> Orific Ts.- -,..

-4750 DI SPLACEMENT -6 3 AMPLITUDE = 182xlO IN. LU \ \ AMPLITUDE LU, -I-~~~~~~~~~~_ -.30 60~ PHASE V < 20 40~ LU Z~~~~~~~~~~~UJ ~10 20~ 0 20 40 60 80 100 120 FREQUENCY, CPS Figure 17. Results of Bla~nked. Orifice Test.

-48partially filled with fluid to form a miniscus, the shut-off valve was opee, and the valve to the reservoir was closed. Pessure was alied (about 1.0 psi) to the open end of the tube, and any motion of the miniscus was noted. When the test cavity was completely full of liquid with no entrapped air, only a slight motion (about.030 ich) of the iniscus was caused by a pressure of 1.0 psi. This represents little compression since the tube is only.125 inch i.d. Any slight bubble of air, which was trapped in the system, caused a large increase in miniscus motion (greater than 0.5 inch). The miniscus motion was so sensitive to entrapped air that the mean flow cylinder had to be completely assembled while immersed in test fluid. This insured that no air was trapped in the tiny cavities between o-rings and o-ring groves, and was the only method found successful in eliminating entrapped air. 3.7 Test Procedure The proced.ure for taking d.ata is started. by setting the speed. of thie alternating piston motor to correspond. to some desired. frequency. The variac for the meani-flow piston motor is then set to a value to give some desired. mean flow-rate. The mean flow is then started. by switching on tlhe gear motor. About 100 cycles is record.ed. on the Visicord.er paper for the data of one setting of flow and. frequency. The setting of the mean flow is then changed. and. the procedure is repeated.. When the frequency of the alternating flow is to be changed., the cam which drives the alternating piston must also be changed. in order~ to maintain the same magnitud.e of alternating flow-rate., because the alternating flow is proportional to the product of the piston

-49TABLE II ORIFICE SPECIFICATIONS Test Orifice Diam., Lengt No. Type inches inches iam. 2470 F-.5O** 0.0497 0.1837 5.70 7770 S E. x- 0.0518 0.0375 7.24 78701 S.E.* 0.0518 o.i88o 36 78702 S.E.* 0.0518 0.0319 0.62 *S. E.: Square Ed.ge Orifice **F-50: Stand.ard. Ford. Main-Metering orifice

- 500 0 oi us 0 o 0 *0~~~~ 0~~ D. C) 0~~~~~~~~~~~~~ 0 < 0 0) ~ ~ ~ ~ ~ ~ ~LJ~~ CM~~~~~~~~~~~~~~~~~~~~~~~~~~~C C8 co U) 0 Q Q 0 0 0 0 0~~~~~~~~~~~~~~~~~z Q J9~~~iVHZ~~~~SIG ziO 1N3DW~~~~~~~~~OZ~~~ JHJ.4

-51TABLE III ORIFICE TEST VARIABLES Test Fluid Max. Max. Flows Max. Pressure Diff. No. Temp Freqa. Mean Alt. Alt Men A OF cps u.ft/x Cu. ft/hr'. Mean psi. Mean 2470 77.8.. 99.7 0.85 0.49 2.54 2.45 2.44 7.80 84.2 7770 88.8- 91.7 o.85 0.52 2.04 2.42 25.90 8.50 89.2 78701 75.1-.88.0 0.80 0.50 1.65 1.95 5.18 3.8o 78.9 78702 75.2- 90.9 0.79 0.51 1.60 5.01 2.58 1.59 75.7

-520. 81 MINERAL SPIRITS 0. 80.. C-D~~~~~ 0. 79 1. 8 LU 0 0.78 1. 6 _ 10~ 1. 20 40 60 80 100 TEMPERATURE- 0F F'igure 19. Test Fluid Properties.

-53 - an allen-head, set screw, which can be seen in Figure 15, and are easily changed.. The test orifices are similar to those found in carburetors (about.050 inches in diameter) and are of different lengths as shown in Table II. The square-edged orifices (S.E.) are made of brass, while the F-50 orifice is of steel. Steady flow data for the orifices is shown in Figure 18, and it was obtained by a means independent of the tests performed here. The data is, however, for the very same orifices, but the method for measuring only the steady-flow performance was much more accurate than the method used here. This is the data used by Harrington (21) in his digital computer simulation of carburetor metering, and his work discusses the details of the steady-state flow measurements. As indicated in the figure., stead.y-state coefficients for the F-.50 orifice were also taken with the oscillating-flow test rig for comparison to the d.ata of Harrington. The amount of scatter ind.icates that the accuracy with which the average flow can be measured. with the oscillating-flow test rig is about +5%. A total of four tests were run, and. the variables of the tests are listed. in Table LIII. About 200 data points were taken for each orifice for various combinations of frequency., average flow., and. alternating flow. The fluid. used. for the tests was mineral spirits, a fluid. similar to gasoline, and. its properties are shown in Figure 19. 3.8 Ideal Oscillatding Flow Through an Orifice In ord.er to gain some insight into the flow of an oscillating fluid. through an orifice, a very simple mod.el of the flow was d.evised..

experiments. More important, however, is that the model also gives an idealized function which relates the dimensionless variables. Therefore, not only are the axes determined on which to plot the data, but also an approximation of the function which the data should follow. Ideal flow through an orifice is described by the equation of motion for the orifice flow. Frictionless flow and a uniform velocity profile are assumed. Also, all of the fluid which oscillates is assumed to be contained within the orifice length. These assumptions make the solution ideal because frictional losses are not considered, nor are the inertial forces which are caused by the oscillation of the luid outside the orifice length. Consider the orifice and control volume shown in Figure 20. The equation of motion for this control volume is written as: A(P -p) A pVd.V (3.1)V 1 2 dt d.t 31 p p pL dV 1- 2 pLdt (3.2) The pressure tap at the upstream point, Fl, w-ill record the total pressure which is given by the Bernoulli equation as: 2 PTl = l p+ 2~- (3.3) whereas the downstream pressure tap will record the static pressure of the jet of the fluid issuing from the orifice. Therefore, the equation of motion can again be written as: PT1 P2 = p~L d.V ~T 2- d.t (3.1la)

-55lip F —-'P__. P L - -i DiaMeter Orifice L englih Figure 20. Control Volume for Orifice Anialysils.

-56where AP is the pressure difference which would be recorded by the meter with taps immediately upstream and downstream of the orifice, as shown in Figure 20. It must be noted, however, that when the flow reverses, the pressure at tap #1 would be static pressure, and at tap #2 would be total pressure. Equation 3.lb then becomes: 22p+~ pL dV 2a+Z p dt (3. lc) or, in general, for both cases of flow direction: -p _ pV. = pL dV3.d The flow through the orifice is oscillatory and has a mean component and a sinusoidally varying alternating component so that it can be expressed mathematically as follows: Q(t) = QM + QA SIN (wt) (3.4) v = Q/A (3.5) v(t) = VM + VA SN (wt) (3.6) d-V w eVA COS (t )(3- 7) By substituting the above relationships, Equation 3.ld becomes: ZP(t) = wVAPL COS(wt) + L (VM + VA SIN(ct))IVM + VA SIN (ct)l (3.le) Since; H(t) = AP(t)/pg (3.8) Eqluation can be finally written as; ~S)VAr 1 11(t) = g.COI(ct(t) + V IN(o) | (3.li') 11(L) =, O(t)+ (VM + VA SIIN(Wt)) IVM + VA SNoLj (.i

-57The above equation gives the instantaneous head differential across the orifice in terms of the mean and alternating components of sinusoidally varying flow or velocity. The equation becomes that for stead.y ideal flow (Bernoulli equation) when the alternating term of the velocity is made zero. The equation is made dimensionless by dividing 2 it by M /2g to form; 2g H(t) 2Thw VA VA VA - COS(Wt) + (1 + vA SI (t) |l + V SIN(Wt) (3 ) Four dimensionless terms are formed which are: 1 2gI(t)/V2M, dimensionless instantaneous head differential 2. VA/VM = VR, velocity ratio 3. VM = STM, mean Strouhal Number 4. wt., angle in rad.ians Therefore, the instantaneous id.eal head. differential is a function of three dimensionless groups; velocity ratio,, mean Strouhal Number,, and. angle., or mathematically; 2gH(t)/2 f (VR, STM, wt) The function is represented. by Equation 35.lg and. contains two terms,, temporal acceleration and. convective acceleration. Figure 21 shows the form of these terms for a Strouhal Number of 1.0 and. a velocity ratio of 1.5. The function is also shown as the total of the two terms anid ind.icates the instantaneous ideal d.imensionless head. differential for an orifice. Of course the actual d.imensionless head. is not the same as the ideal d.imensionless head.. Figure 22 shows the id.eal d. imensio nless~n- head. I inr fu i nction %"-,% "n 1 for a trouha'Number,- — 4 of.213 and a veloc~ - -

-58DIMENSIONLESS IDEAL INSTANTANEOUS ORIFICE HEAD DROP FOR SINUSOIDAL FLOW STM=VM=1. o VR=V/VM-l 5 v( t)/VM=1+VRSIN () e o=~t TOTAL: TEMPORAL+CONVECTIVE 6.0-!~~~ ~~~ r! i -!'~ i! l';;~ f! iICONVECTIVE TERM (l+VRSIN()) 1+VRSIN() 2 \0-1/ l - 2STMVRCOS(@)~1+RSl(Q RLAD IAN S

-591o.501 II I H ~~~~~DATA 1.25 POINT i#4,. FLOW' 0 *00 4-'3 ~~~~~~~CURVE 0.75 DIMENSIONLESS INSTANTANEOUS ORIFICE HEAD DROP TEST 2470 DATA POINT #4 0 00.50 -ORIFICE F- Q Nq DIAM.0497 in. LENGTH.1837 in. lFLUID Mineral Spirits,TEMPERATURE 77.80F SG.7839 0.25 ~VISC 1.280 cp STM.213 SA196 V:108 liBel8 C *869 C 37 0DM 994 CDA.230 MID AID 0.0 0 100 200 300 400 ANGULAR FREQDUENCY X TIME, DEGREES

-60point!/4 of test 2470, which has the same value of Strouhal Number and velocity ratio. It is readily apparent from the fig that the real head. is greater than the ideal head at any instant during the cycle. The greater instantaneous head of the real flow indicates that the ideal analysis has not fully accounted for the forces which exist in the actual flow. Therefore, experimental work is necessary in order to accuately determine the flow through an orifice which has oscillating flow. The ideal flow analysis does provide a useful guide as to what general form the exerimental results should be, and that two important parameters for plotting the results are velocity ratio and Strouhal Number. 3.9 Id'eal Coefficient of Discharge In ord.er to study the influence of flow oscillations on average flow, it is desirable to define the average value of the dimensionless head. function as follows: 2gIHM/V2M 2g(Hlna + Hmin) x.5/V2 M (3.9) Ma~king the average head. as one-half the sum of the maximum and. minimum values instead. of an integrated. average is preferred. because it is much simpler. This is particularly true when the same averaging process is to be d.one on the d.ata for flow and. pressure., for which no mathema~tical function is available. However, both must be nearly sinusoid.al to be applicable to this analysis. The average value of d.imensionless head. is now seen to be a form of a mean id.eal coefficient of d.ischarge: 2gHy/V = 1/CDMID (3.10) The averaging process has eliminated. time., so that the mean id.eal

IDEAL ORIFICE COEFFICIENTS OF DISCHARGE FOR OSCIL~LATORY FLOW D'RMI -D''tM CDAIDVA/~ 2gH()-2L vC0(Wt)=+(v SIN(wt)) VfVSNw) AMA HM HAX+HMIN)xo5, A, AH,'' IN)I S TM= IJ/9VM VR =V/V': " *',I t I- - F t-,/,;/ o + s-~~t~ ST =0 / /2 _ I!/, ti 3... 0... 0 6 z~~~ 3 0. F-I~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~I FX4~~~~~~~~~~~~~~~~~~~~~~~ J lll4'{,Ii lDMID DAID 0 0. 5 1.00 1*5 o 2't5 V VELTOCITYV RArPTrI

-62CDMI = fl(STM, VR). (3.11) The maximum and minimum values of the ideal instantaneous head were found from Equation 3. lg for many combinations of flow ratio and Strouhal Number, and the results were used to calculate the ideal coefficient of discharge from Equation 3.9. Figure 23 shows the resulting ideal coefficients. Another useful number which can be derived from the dimensionless head function is the alternating value of dimensionless head. This is calculated by; 2gHA/V2M - 2g(Hmx - Hmin) x *5/V2M (3.12) This value is also a function of velocity ratio and mean Strouhal Number. Furthermore, it can be divided by the square of the velocity ratio to yield a new value which is still only a function of velocity ratio and mean Strouhal Number. The quotient is given by: (2gHA/V2M)/(vA/vR)2 = 2gHA/V A. (3.13) The alternating form of dimensionless head is now used to define the ideal alternating coefficient of discharge; 2gHA/VA2 l/C2DAID (3.14) The ideal alternating coefficient of discharge, as defined above, is a f'unction of the velocity ratio and the mean Strouhal Number, as given by; CDAID = f2 (STM, VR) (3.15) It is also represented graphically as a function of the two independent variables in Figurxe 23. Both of the independent variables used for determining the ideal mfean and alternating coefficients of dischargre knowledge of tbhe orifice flow versus tine. However, in practice orifice flowr

-63will probably not be knlown, but head difference will be known. l-h;r'w-n fore it i2 desirable to represent the ideal coefficients ol' discharge in terms of independent variables which contain values of head, rather than flow. Some different dimensionless numbers, which do not contain flow, are now defined., and used as independent variables. The first new number, head ratio, is defined as: HR (CDMD/CDAID) x (VR)2 A/iM (3.16) Another useful number is the mean Strouhal Number which is based on mean head and it is defined as; STMH = STM x CDMID = / T2gHM (3.-17) It must be emphasized that nothing new has really been added to the analysis, since the previous dimensionless variables have been combined only to make the functions more convenient to use. Therefore, the ideal values of the coefficients of discharge can be also written as functions of the new variables which are defined above; CDMID =f3(STMH, HR) (3.18) CDAID =f4 ( STMH, HR) (3.19) where the independ.ent variables in f3 and f1 do not contain flow terms. These two functions are shown in Figure 24. Finally, the last number, which proves useful in examining the alternating coefficient data, is the alternating Strouhal Number, as defined by: STA = L w1/VA = STM/VR (3.20) It is particularly useful for studying the data of these tests because it; is constant for each cam used. to oscillate the flow. This is true

IDEAL ORIFICE COEFFICIENTS OF DI SCHAR$E FOR OSCILLATORY FLOW CDMID VM/ V2gAHM CDAID*VA/ 2g 2MA V(t)=V + SIN (t) 2gH( t )-2LaVACO S(St)+(VM+SI t VASIN ((Wt) ) IVMVAIN (t)1'~4 ( AXHMIN )Xi H -(HMAX-HMIN) X HR= AHA/ AHM 1.0 ~'" to o.75 o'5 Figure24.IdealCoefficie i o Discharge vei s Ha Ratio. 0 {ij D'""t)_'_ _! _Di D 0 1.0 2.0 3.0 4, HR. HEAD RATIO Figure 24. Id.eal Coefficients of Discharge versus Head. Ratio.

-65because oscillating flow is a product of cam displacement and frequency, therefore: STA = L w/DISIh = L/DISP (3.21) since CDA = f(STA, VR), and STA = STM/VR, then CDA = f(STA, VR) and for constant "STA",; CDA = f(VR) (3.22) The data for alternating coefficient of each cam then follows one curve when plotted as a function of velocity ratio. Figures 89 through 105 of Appendix B illustrate this point. 3.10 Results of Orifice Tests The ideal orifice equations show that the coefficient of discharge is a function of two variables; Strouhal Number and velocity ratio. However, actual orifice flow also depends on frictional forces, and requires the consideration of fluid viscosity and orifice geometry. Dimensional analysis shows that the Reynolds number can be used to account for viscous effects. Geometry is also an important influence on the flow; hence, it must be considered by including the dimensionless geometrical variables. The number of these variables depends upon the complexity of the geometry, and for the tests performed here only one, L/D, was used. Therefore, the functions, which are used to represent the experimental results are as follows: CDM = fl (VR,STM,Re,L/D) (3.23) CDM = f2 ( HR,STM, Re,L/D ) (3.24)

CDA =f3 (VR,STA) (3.25) CDA = f4 (HR STA) (3.26) Figures 25 through 32 show the mean coefficient of discharge data as represented by the first two functions for four different orifices: the F-50 main orifice, and three square-edged orifices. Figures 25 and 26 show the results of pulsation on the coefficient of discharge for a typical main metering orifice. It is immediately apparent that the influence of the pulsation is to increase the flow if the flow ratio is sa11ll (0-.3). This phenomenon has also been noted by Mosely (10) and Zarek (14), and is illustrated by both figures. However, the ideal flow analysis does not predict this phenomenon. Compared to steady flow, slight pulsations diminish the viscous losses, which are not included for the ideal flow, and cause a slightly larger coefficient of discharge. However, as the flow ratio is increased, the influence of the inertia of the oscillating flow becomes evident, which is predicted by the ideal equation. At flow ratios greater than.3, the curves are similar to the idealized curves for which friction is neglected. It is also interesting to note that the coefficient of discharge is substantially influenced by the Reynolds Number. The Strouhal Number lies within a small range (0-.6) so that its affect is minimal for this data. Figures 27 and 28 show similar data which is plotted for a very short, square-edged orifice. In contrast to the data for the main orifice, the Reynolds Number has little influence on the

MEAN COEFFICIENT OF DISCHARGE VERSU S FLO t RATIO TEST 2470 STROUHAL NUMBERS= 0-0.6 ORIFICE F-50 DIAM.0497 in. LENGTH.1537 in. FLUID Mineral SpiSits TEMP 77.8-84.2 F S3G.7839-.7809 VISC 1.219-1.280 cp 00i I I.9'.I ___ RE= 00: J 00 I'.5 i- _: F-50 Orifice.::> i 2 4 *6 l' FLOW RATIO ALT FO/ENFO F-S0 Orifice.

MEAN COEFFICIENT OF DISCHARGE VERSUS HEAD RATIO TEST 24L70 STROUHAL NUMBERS= 0-0.6 ORIFICE F-50 DIAM 0.0497 in. LENGTH 0.1837 in. FLUID Mineral Spirits TEMP 77.8 -84.2 SG.7839-. 7809 VISC 1.280-1.219 cp 1 09 i:RE=5000 ~ ~ ~ ~ ~ ELQQ 10 i -.-.} Rm=5ooo!~: I RE=3000S t - ~: i i:'e! 1 ~ i' ~T:;f I Ii ~ "RE.m2... -, i I 5 75 1.0 1.25 MEAD RATIO, ALT HEAD/MEAN HEAD l/' ~i L.~Ti-~ I:' i,,..: "'t,,~.m~=4o0.... i~'-.. o)r,3:...... - e~ —-~ —-C — - ligureH26 Coefficient of D v H Ratio, 0 i! i* F 50 Orifice,, i,, I,-4! E~rn~~~~~~~~~~~~'. i1 I:, ~II~ ~ i RE-2000'., n~~~~~~~~~ ~'IC' I i i,i,,I ~~~~~~~~~~~~~~ t o.j~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~..,._._ o.25.'50.7~5 ~,o ~.125 HEAD RATIO, ALT HEAD/MEAN HEAD F'igure 26. Coefficient of Discharge versus Head Ra-tio, F-S0 Orifice.

MEAN/ CO~FF ICii'T-J,T OF DISCOII'R.J" FLO.i LRATIO TEST NUMBER 73702 ORIFICE: SQUARE EDGED DIAMETER: 0. 0518 inch LENGTH: 0. 0319 inch L/D: 0.6158 FLUID: MINERAL SPIRITSo TEMPERATURE: 75.2-75.7 F SPECIFIC GRAVITY:. 7852-. 7850 VISCOSITY: 1.306-1.301 cp I,1i-t' -' H - -- o1 -1l LI EGEND a0 I+-+tt-....tl < tt 1 RE: 1099-1198 -. -< 1i;.~ —2i-t-+ _..,,'ST:.112-.238 0..:9 2 RE: 2369-2612 - G. i-'"~ -- i - 4 ST:.0- *514- 1834::^K t-l W-i F::-i,3 RE: 3387-371 i3 I$,'P 1i t ST: *0337-.1313.~ ~- - t- -i-", — h-tN - --. —..- _...... - -tC.....- -...... -- - e 0,,-li i ittt!;-t- - -- t — -t — 1; 4 RE: 4470-4721 -,< ~ -t- I., 1-:: X l i -- t C t -..- - ST:.0283-_ 1044 -i j 0,7 0 Li o2 4 L Oo 6.~0 o m CI f 0 0.2 0. 6o o5 l FL0,' R{AT-", c Q' ALT. FLO:'/I"AN FL0]'f Figure 27. Coefficient of Discharge versus Flow Ratio, L/D=0. 62.

-70MEAN COEFFICIENT OF DISCHARGE VERSUS HEAD RATIO TEST NUMBER 78702 ORIFICE: SQUARE EDGED DIAMETER: 0.0518 inch LENGTH: 0.0319 inch L/D: 0.6158 FLUID: MINERAL SPIRITS0 TEMPERATURE: 75.2-75.7 F SPECIFIC GRAVITY:.7852-.7850 VISCOSITY: 1.306-1.301 cp:1::-4 -0 4- __ _i tLzJ' t i:4 l -k iL __; -L1 T-08 fot -LftX-0;X t 1 RE: 1099-1198 0.9 1-* —. - ST:.112-.238' — 01-4-9 2 4tll t 4tt - r Il t 2 RE: 2369-2612 ST: 0514-.1834 i ~^ t 3 RE: 3387-3713'~ 0X — 1X t1 —Wi-40t 70t-1 4Xe-'-1 XST:.0337-.1313 0.8l- t-IX I!tt|4 RE: 4470-4721.~ -' W001' ST: *283-.1044~ 0 2?. - 0-8 -40 6 4K-4- - -. H 0.~ O 0o2 0.4 0.6 0.8 1.0 HEAD RATIO, HR, ALT. HEAD/MEAN HEAD It'igure 28. Coef ficient of Discharge versus Head Ratio, L/D=0. 62.

-71~ESN CO,I"'IO T O,? DI S-. -I VESiUS FLO, RATIO TEST NU,._ER 78701 DiAS{iTER' 0. &51i~!ixch L'D GIH:' T EIn ch L/D: 30- -9 -b UR' F bP! FLUID:,.IiN:.:.. z b?-IT6 TEiiPZ'AYUiSR:?.io1-78. POF VISCOSITY: i.307-1.269 cp SPECIFIC GRAVIT.:'.7853-.7834 4- -ftl - 1, ~ t- _- ~- -< 1 tLEGEND I!i~I: i..... 3ST: 0.66-1.57 4<tal i!-i- 1 RE: 1104-121.0 0,9 7 I. j 2 RE: 2L9 638 M:... t3 RE: 3422 -751 -!0.8 t- 4 4 RE: 4521-4751 ~'i..C 0.- 1' 14 - )7, % 7. -t izt 1-. - i$II{i.ij T - - 0.7 if_ i~:~':- -t 1 —- - -j - T,.i, 0 0.2 0.4 o,6 00. i4. - FLOT. RAT'tO QR ALT. FT LOJ/M-AN FLO" Figue 29 Coefficient of Discharge versus Flow Ratio, L/D..6..f

-72MEAN COL' Fi CIENT OF DI SCPLHi3E VERSUS HEAD RATIO TEST NUMBER 78701 GRIFICE: SQUARE EDGED DTI4.ETER' 3 "5 II inrch LEN GTHT:, 0 r c L/D: 3. 293 FLUID: M1I -,::A; SPIRITSO TE.IAERATU: 7 5. 1-783 9 F VISCOSITY: 1.307-.26) cp SPECIFIC GRAVITY:.7853-.7834 o 4,./ /L 7 TLEGEND' ST: 0.66-1.57 i~ 0.9 jj $~1-1 t. 9 W t |. X 4 | | t t 00 g 2 RE: 2349-2638 + Sj -1 +-_ Wt W. ST:.c53 2-0 70 744: 0-. -3 -< L;3 RE: 3422-2751 ST: 0 21-0.51 0,81 4 RE: 4521-4751 K.~ ~~~~~~~~ST: 00037-0.59 H ii ~0 6 0.5 0 0.2 0.4 0.6 0.8 1.0

-73MIvEAN COFFO CIENT OF D C&r.r'E_ VERSUS FLO,' RATIO''ST NU.BE"R 7770 ORIFiCE: SQUARE3 D`ED DIA;,iETER: 0.0321 in. LbiJTH: 0o3750 in. L/D:.7 2394 FLUID: MINERAL SPIRITS TE\,;P..iANGE:, 88,8-89 2~F VISCOSITY RANGE: 1. 179-1.176 cp S'ECIFIC GRAVITY:.7786-.7788 (\t 2 RE; 2910-3320 ST9 0 s49-1.277 - t _RE: 4134-l14393! ST: 0.34-0,90 M- 0 9o __O+\^J RE$ATIO,, ALT M20 FL n/lr 1L, A\ ST: 0.26-1.72 -~~ T-::iL{ 7. -7i FLOW RATIO, Q ALT. FLOW/MEAN FLO;_ Fgr3.CefinoficagvruFoRai

-74MEAN COEFFICIENT OF DISCHARGE VERSUS HEAD RATIO TEr, -iNuI"ER 7770 Or,L i'CE': SQUARE EDEDGED D_I.&iiER: 0.0518 in. -L~[.TH: 0.3750 in. L/ID: 702394L FLUID: MTIh\ERAL SPIRITS TEi. iUN GE: 88o 8-89o 2~F VIS iOSITY AKi\GE: 1. 179-. 176 cp S1ECIFIC GRAVITY:. 7786-. 7738 m~ 1.0 ~~~~~~~X' LEGEND ~0 ~ ~ "~I 1 RE: 1399-1-549 ~i')_ST: 0. 89-2.30 i-2-RE2 2910-3320 ST: 0.49-1.27 HEAD RATO,HR3 ARE: 4134-4393 ST 8: 0.34-0.90 4 RE: 5202-5554 0.8 ST: 0.26-0.72 0.7 E)4 mX 06 C)~4~~~~~ ~4 0.5 0 0.2 0.4'0.6 0.8 1.0 HEAD RATIO, HR, ALT. HEAD/MEAN HEAD l,ux'i u'5.' 3'-Coel'f.i.'i..tnl, of' Discharg;e vr"us tierecd.1l{tlo, L/D="7. 24.

-75coefficient for the very short orifice. This is similar to coefficient data for short orifices under steady flow in that little change in the coefficient is measured for Reynolds numbers greater than 2000. However again, an increase in the coefficient is seen to occur at small velocity ratios. The Strouhal Number for this orifice is also within a small range (0-.238) which minimizes its influence. Figures 29 and 30 show data for a square orifice which has an L/D nearly equal to that of the main metering orifice (data of Figures 25 and 26). The influence of the Reynolds number is not as pronounced as it is for the main orifice, but it is greater than that of the very short orifice (data of Figures 27 and 28). The greatest affect of Reynolds number is seen to occur at a value of about 1000, and Reynolds numbers greater than 2000 show little influence on the coefficient. Again, the Strouhal number is small, which minimizes its affect. Figures 31 and 32 show the data for a long orifice (L/D = 7.24). For the range of independent variables shown, the coefficient of discharge varies very little. The flow oscillation (Figure 31) and the head pulsation (Figure 32) show almost no affect. Also, the data indicates that the influence of the Reynolds number is also almost constant. It is also interesting to note that the Strouhal number range is considerably larger (0-2.3) for this data than for the data of the shorter orifices owing to its dependence upon length. This may partially be the reason for the relative flatness of the curves since the ideal analysis showed that large Strouhal numbers decrease the influence of pulsations on average flow. The increase in coefficient of discharge can now be related to the test data of Chapter II, which shows that the fuel air ratio is

-r60 C8AF-L FORD 2-BARREL CARBURETOR, WIDE OPEN THROTTLE 200-600 LB/HR OF AIR A MAIN ORIFICE COEFFICIENT _ — VC/) LLLO _o Q C, 2 O 0 I I I. 0,1,2,3,4,5 MEASURED HEAD RATIO Figure 33. Percent Change in Fuel/Air and Coefficient of Discharge versus Head Ratio. ui: L u

-77greater when the carburetor is functioning on an engine with pulsations than when it is operated under steady flow conditions. Figure 33 shows the percent increase of fuel/air ratio for the engine test of Chapter II as compared to the steady bench test of the same carburetor. It is plotted as a function of head ratio which was measured across the main metering orifice during the engine tests. Similar data from the orifice tests is also plotted as a percent increase in the coefficient of discharge for oscillating flow over steady flow as determined experimentally. As can be seen, the influence of' the pressure pulsations on the orifice metering characteristics accounts for the difference between fuel/air ratio for the carburetor on an engine and on a test bench. This is due to the increase in the average flow through the main metering orifice which is caused by slight flow oscillations. Experimental results for the alternating coefficient of discharge, as defined by Equation 3.14, are shown in Figures 34 through 39. It must be emphasized that this data is for the same test runs as the time-average flow results in the preceding section. However, now the relationship of oscillating flow to oscillating pressure difference is being investigated rather than the relationship of the average values of flow and pressure. This relationship has been defined as the alternating coefficient of discharge, and is given as: cDA = vA/ 2g4HA The alternating coefficient of discharge is shown as a function of flow ratio and alternating Strouhal number or head ratio and alternating Strouhal number. The curves for the main orifice (Figures 34 and 35) and the curves for the very short square-edged orifice (Figures

-7836 and 37) are unique. That is, they cannot be plotted together as was the data for the medium and long square-edged orifices, as shown by Figures 38 and 39. The alternating Strouhal Number accounted very well for the influence of orifice length on the fluctuating flow for medium and long orifices. However, the data for the main orifice and short square-edged orifice could not be plotted in Figures 38 and 39 and give results consistent with the orifices of medium lengths. The experimental data for the alternating coefficient of discharge shows that it is always less than or equal to the ideal value of alternating coefficient. At low velocity ratios, the ideal alternating coefficient is very nearly equal to the experimental value for all four orifices. At velocity ratios greater than 0.1 the experimental values are less than the ideal values. The amount of this difference is dependent upon the orifice, the velocity ratio, and the Strouhal Number. It must be noted that the variation in Reynolds number was obtained for these tests only by varying the average flow, and that the viscosity of the fluid never appreciably changed. Therefore, the results should only be applied to orifices with fluids of similar viscosity to mineral spirits. Also, the diameters of all four orifices were nearly nearly equal (.050 inch) so that orifices which are much larger, or much much smaller, may not give the same results, even though they may be geometrically similar (same L/D). The waveform of the flow oscillation and the pressure pulsation was always nearly sinusoidal. No attempt was made to investigate the influence of different wave shape on the time-average flow. Study of these limitations is a worthwhile topic for further investigation.

-79o~C I.i t: -IC t1 80t-4 cp- ht H 1 t 1 12 0.0o T -T t 0t!. 2. V- - Flow Ratio, O. i. F' Oice v It~~~~~~~-~ 0.5 E: VEL Ta= 14.96 -~ Flo Rato, -50Orifice. DIAM:. 0497 in. - 0. VI p 18: 1.' p 0.0 0.0 0.5 lo.0o 1.5 2.0 2.5 ALT. VlJmE VEL.

-.800.7 ~0.6 | 0 — STa = 074 ST = 1.12 0-.5,,, 0.4 ALTERNATING COEFFICIENT VERSUS' TEST 2470 F| 00 f i ORIFICE: F-50 DIAM:. 0497 in. LENGTH:.1837 in. 1 | -FLUID: Mineral Spirits TEMP: 77.8-84.20F SG:. 783 9-. 7809 1, tVISC: 1.280-1.219 cp 0.,0 I,- - 77i t. 0 1 2 3 4 5 ALT. HEAD/MEAN HEAD HEAD RATIO 1%'igure 35. Alternating Coefficienrt of Discharg; versus Head.atio, F'-50 Orifice.

0.7 - I-~I iLLLLLLL.LLLi _ JLIJ LLL I I' I I ALTERNATING COEFFICIENT OF DISCHARGE VERSUS X __ -[ FLOW RATIO 0C 6 x -— 0.6 E - — i'-I.i-. _: _. -O.0 1 _)__.STA0._01 ST 0 023 Flow Ratio, L/D=O. 6.0 0 C) o 0.2 TEST NUI4BER 78702 -- ORIFICE: SQUARE EDGED - E-4 A00518 inch 0,O'12" "~-LENGTH: 0.0319 inch 00.204L/D: 0.60158 1 FW T FLUID: MINERAL SPIRIOA O.'; TEMPERATURE: 75~2-757 Fi VISCOSITY: lo 306-1.301 cP _ E-r E0.2 o0.4 0.6 0.8 1.0o Figure 56. Alternating Coefficient of Discharge versus Flow Ratio, L/D~-.62.

-820.7 I I I I I I t' I 1 1 T ALTERNATING COEFFICIENT OF DISCHARGE VERSUS HEAD RATIO ('4 c: t c i; 1. I- -UME 8. ST-. 15 0.,, STA=O 27 m _ iL: _ & —0.,4 STEST 0.M23 -78,a —L/D:O.61 — -i ___ - V I FLUID: MINEAL SPIRITS, 1 1 1 I 1 S I SII CIFICE GRAVITY: *7..?..785O - r 1LL VISCOSITY: 1.306-1.301 ST p0 o 0.4 0.6 0.8,~ -% DIAMETER: 0.18 inch r,'~t+f,I~tTf-~ tFLUID: MINERAL SIT L -~ Z ~PEPTuM: 75. 2-?5.7 0oF__ BE- ECIFICE GRAVITY: 7 2-" f-2. 7`850' 0 0.2 0. 4 o 0.6 0.8 l.0

-830. 7- I r i j t, —,-I I,I,',-. -1,,I., I { i i4 ALTERNATING COEFFICIENT1;.. t.. 1 i f i. -4 OF DI SC IARGE VERB "W'SJS FLOW RATIO ~..............................BTAl0.35 i 0.5 e- ST =le61 _ 0.5;- __S _116 Ltt S S =2,$l5 o4 AFlow Ratio,/T2.6 8 ~TEST% 7770& 1STA0.2 SQUARJE EDGED ORIFICES DIAMETERS: 0.0518 inch LENGTHS: 0.3750 & 0.188 inch. z _: i t. _:i: L/D: 7.2_394 & 3.6293 -1 —. i FLUID: MINERAL SPIRITS;.-:"" - -TPE&.IE'jRATUR: 7:".1-89.20F SPECIFIC GRA'TITY:.7853.77 86 VISCOSITY: 1.307-1.176 cp o0.5.q. 1.5 2.0 2.5 FLOW RATIO 0 l, ALT. FLOW/MEAN FLOW Figure 38. Alternating Coefficient of Discharge versus Flow Ratio, L/D=3.63 and L/D=7.24.

~07 ii 11, fiiiTZz I 1 1/ I>lie., ALTERNATiNG COEFFICIENT tOF DISCHARGE i, ~~VER SUS..i.i. HEAD RATIO l 0.6 -' I 0,5 0.- 4 = 1 ih A 1,) 0.5:tt01 ST = 6ST1 9 = —1 fBT 1 f6:11 A' F-IfiPf;1 - T A0S TESTS 7770 & 78701 r Ha mLENGTHS: 0.3750 & 0.188 inch.,3 FLUID: MINERAL SPIRITS TB2PERATURE: 75.1-89.2?F SQUAR EDGED OSPECIFICE GRAVITY:.7853-.778 H -- VISCOSITY: 1.307-1.176 cp Head Ratio, L/D=7.62 and L/D=7.24.

-85Any further experimental study of orifice flow with oscillations should be done with control over the dimensionless numbers. For the experiments done here, no attempt was made to maintain any independent dimensionless variable at a constant value. That is, in the test procedure, when the mean flow was changed, three dimensionless numbers, Re, ST, and VR, also changed. It would, therefore, be advisable for future tests to be able to vary only one dimensionless number in order to generate the test curves. Much of the scatter in the present data could have been eliminated if this had been done. The data for the mean coefficient and the alternating coefficient provides a method for calculating the instantaneous flow from pressure measurements in the following way. From Equation 3.4 Q(t) = QM + QA SIN (wt) (3.4) From the definition of the mean coefficient; QM = CDM A 4 2g (3.27) and from the definition of the alternating coefficient QA = CDA AT2gAHA (3.2(,) Therefore, the instantaneous flow is given as: Q(t) = A (CDMf2gaH + CDA2f2gaLHA) (3.29) The two coefficients can be found in the experimental data of Figures 25 through 39. Equation 3.29 gives the instantaneous flow from values of mean and alternating head difference, both of which can be easily measured.

-863.11 Conclusions to Orifice Tests 1. The time-average flow of incompressible fluid through a small orifice can be related to the time-average head difference by a mean coefficient of discharge as given by: VM CDM = 2. The coefficient of discharge for time-average flow through a small orifice is a function of three dimensionless variables: 1) Velocity ratio, 2) Strouhal number, and 3) Reynolds number. 5. The influence of the velocity ratio can either cause the coefficient to be greater or less than that for steady-state flow. Small velocity ratios cause a greater coefficient with a maximum occurring at velocity ratios of 0.12 to 0.16. At velocity ratios below this range, the coefficient tends toward the steady-state value. At velocity ratios greater than this range, the coefficient decreases as velocity ratio is increased. 4. The influence of the Strouhal number on the coefficient of discharge depends greatly upon the velocity ratio. At velocity ratios less than 0.5, its influence is negligible but it becomes noticeable at velocity ratios which are greater than 0.5. An increase in the Strouhal number increases the time-average flow. 5. The influence of the Reynolds number on the average flow is very similar to its influence upon steady flow without oscillations. In general, an increase in the Reynolds number increases the mean coefficient of discharge. The Reynolds number has its greatest influence upon the flow of the main metering orifice and the square orifice of

L/D equal to 3.63. The influence of it upon the coefficient of the long and short square edged orifices is negligible. 6. The coefficient of discharge for time-average flow is also a function of head ratio, Strouhal number based upon head, and Reynolds number. The influences of each of these new variables is similar to those of velocity ratio and Strouhal number. The maximum value of coefficient occurs at a head ratio of 0.2 to 0.25. 7. The coefficient of discharge for the long orifice (L/D = 7.24) is not substantially influenced by pressure pulsation and flow oscillation. The greatest influence of flow oscillation on average flow occurs for the short orifice (L/D = 0.6) and for the main metering orifice (L/D = 3.63). 8. The alternating flow of an incompressible fluid through a small orifice can be related to the alternating head difference by an alternating coefficient of discharge as given by: VA 0DA= A2gAHA 9. The coefficient of discharge for the alternating component of flow through a small orifice is a function of two dimensionless numbers: 1. alternating Strouhal number and 2. velocity ratio. 10. An increase in the velocity ratio causes an increase in the alternating coefficient of discharge for alternating Strouhal numbers less than 3.5. Above 3.5, the curve of alternating coefficient versus velocity raotio is maximum at a velocity ratio of about 0.4. 11. An increase in the alternating Strouhal number decreases the alternating coefficient of discharge.

-8812. The alternating coefficient of discharge is also a function of head ratio, and the curves are very similar to those plotted as a function of velocity ratio. However, no maximums occur in the curves of alternating coefficient as a function of head ratio. 13. The alternating Strouhal number accounts for the influence of length and frequency very well for square orifices which have L/D between 3.5 and 7.24. An increase in the alternating Strouhal number, which is caused by an increase in length or an increase in frequency of oscillation, will cause the same change in alternating coefficient. However, this is not true for very short orifices, or orifices of complex shape.

CHAPTER IV SIMULATION OF FUEL METERING NETWORKS 4.1 Reasons for Simulation Carburetors have been in use on automobiles for many years, so a logical question is:'"Why make a detailed study of something that has been working satisfactorily for over half a century?" The answer lies in the fact that today's problems of air pollution and dwindling resources require further understanding of how best to use our resources. Specifically, in the case of carburetion, this means developing better techniques for understanding the metering process so that the internal combustion engine can be made more efficient. Until now, practically all carburetor study has been done by cut-and-try experimentation methods. Now, the digital computer allows a much more detailed theoretical study of the metering process than ever before possible. All that is required is that the proper techniques for using the computer to calculate fuel flow be developed. Even though this study is directed specifically toward carburetors and the fuel metering process, the possibility of so-called "spin-off" benefits also exists. Many fluid flow problems involve flow through networks of pipes. For example, the water distribution system and sewage disposal system of a city is a very complex network of pipes. Also, many chemical processes require the accurate metering and mixing of different fluid components in order to produce a desirable product. Even the human circulatory system can be described as a fluid network with oscillating flow. Therefore, the possibility exists that some of the technology developed herein can have wide spread applications. -89

-9o4.2 The Ty?pical Air-Bleed Carburetor The fuel metering system of a carburetor is a very complex network of interconnecting tubes and orifices. Fuel enters the network at atmospheric pressure from a float bowl, or reservoir as shown in Figure 40o, and floWs towards the venturis where it enters the lowpressure stream of engine intake-air. Each carburetor, depending on manufacturer, has its own flow scheme, which will include several points where the fuel enters the intake air. The typical metering network also includes several points where ambient air can enter the fuel flow, which creates a two-phase mixture of air and fuel. The points at which air enters are called air bleeds, and the amount of air which is in the metering network is called bleed air, which distinguishes it from intakeair. Figure 40 illustrates the flow scheme of fuel and air in the metering network of a simplified version of a carburetor. An actual carburetor contains many more elements (about 50) in its metering scheme than the simple carburetor of Figure 40. Therefore, analysis of the fuel flow in the various elements is nearly an impossible task if it is to be done by hand calculations. This is especially true if the effects of flow oscillations, viscosity, and the mixing of air and fuel are to be considered. Therefore, any detailed analysis of carburetor metering requires the use of a computer. This will require the translation of the metering network into an algorithm which can be manipulated by the computer. The technique of making such a transformation and its results comprises the subject of this chapter. 4.3 Previous Work In the past, the carburetor has been greatly studied. Most of the work on carburetor research has been of a purely experimental nature,

BLEED AIR INTAKE AIR BOOST VENTURI FUEL, MAIN VENTURI IDLE FLOW INTAKE AIR + FUEL + BLEED AIR TO THE ENGINE Figure 40. Simplified Version of a Typical Air-Bleed Carburetor.

-92and any theoretical analysis has contained so many simplifing assumptions as to make the results very questionable. Such simplification was necessary in order to limit the mathematics enough to allow a solution by hand calculations. However, the great speed and large storage capacity of the digital computer now allows the analysis of the carburetor in much greater detail. Recently, Harrington (20) used the computer to do a comprehensive analysis of carburetor operation. His analysis included the interacting influences of the carburetor, engine, and vehicle at a certain steady condition of engine speed and load. In order to accomplish this, he had to simulate the carburetor metering network, the carburetor venturi system and throttle plate, the intake manifold, the engine, and the vehicle. However, for his metering network analysis, he assumed steady flow, and the analysis was restricted to one metering network. Therefore, a logical extension of his effort is to include the effects of flow oscillation as caused by pressure pulsations which exist in the venturis, and to make the simulation general enough to allow analysis of any metering network. This is the task which has been undertaken here. The feasibility of modeling transient flow in carburetors was demonstrated by Oyama, Tejima, and Hosho (27) in their investigation of the influence of bleed air on fuel-discharge lag-time. They showed that the transient flow of a mixture of air and gasoline in the emulsion tube can be accurately approximated by single-phase flow which has the same volume-weighted density. Their flow schematic does not contain the idle system and the air is considered to be incompressible, but the results compare very well with experimental results. However, they do

-93 - not apply their technique to solving steady oscillatory flow, nor is their method general enough to be applicable to any carburetor flownetwork. Although very few have applied computer solution techniques to carburetors, many have studied methods for solving transient flow in pipe lines and in piping networks. The most common method is the method of characteristics as discussed by Streeter (37), (38), (39), or Benson (31), (32), and many others. This methods involves knowledge of the wavespeed of the pressure pulse, which makes its use in carburetor problems difficult because the wavespeed is not accurately known, especially in the channels which contain a mixture of gasoline and air. Another method of solving steady oscillatory flow in a pipe is the impedance method, as shown by Streeter (38). It is a very economical method, since the steady oscillatory solution is provided immediately, and no computer time is needed in calculating an initial transient in order to reach the steady oscillatory solution. This method requires the linearization of the governing equations, which limits the solution to small amplitudes of flow oscillation with large average flow. In other words, flow reversal cannot take place. Unfortunately, flow reversal does take place in the carburetor metering network, which makes the impedance method unsuitable for studying carburetors. However, in a most recent work by Yow (43), an impedance method has been developed which can have flow reversal. In future study of steady oscillatory flow in carburetors, this method must be considered.

-94The method ultimately used here to calculate the unsteady flow in the fuel channels is a finite difference solution based upon a spacially lumped formulation. The formulation is modified to account for compression of any gas phase (bleed air) which may be contained in each of the metering channels. The method requires the assumption of linear density distribution in space, but it does not require knowledge of the pressure-pulse wavespeed. The details of this linear-density method will be discussed later in this chapter. 4.4 Objectives of Simulation In general, the major objective of the simulation is to provide detailed flow analysis of the metering network. The pressure must be supplied at each point of the network where fuel or air enters or leaves, and the results will contain the flow at each of these points. This will be done for both steady pressures, and pressures as a function of time. Consequently, the results will contain both steady flow values and transient flow values. Since bleed-air and fuel enter and mix in the fluid network, the flow which leaves the network is a mixture of bleed-air and fuel. This complicates the mass-flow balance in that two species of flow must be balanced, as well as the entire flow. The simulation therefore, must also account for the fraction of air in the total flow on a mass basis (termed quality) and on a volume basis (termed volume quality). Even though many manufacturers use an air-bleed type of carburetor, many different fuel metering schemes do exist. Also, designers are anxious to try to improve the metering characteristics of their carburetor by modifying its metering network. Such mnodifications might include merely changing the dimensions of some of the elements

-95(i.e. perhaps an extra off-idle port). The effect of such modifications on the metering characteristics has usually been determined by building a prototype, and testing it. This becomes a very time consuming process, especially if many different alternatives are to be investigated. Therefore, another goal of this study is to provide a technique which can be used to analyze any fuel metering scheme. This means the fuel metering scheme must be represented in the input data required by the simulation program, and not built into the simulation program. To summarize the objectives, given the network configuration and the pressure forces at its boundaries, the simulation program will provide the time-steady mass flow, the transient mass flow, and the fraction of air contained by the flow. 4.5 Overall Solution Plan The problem of completing the objectives requires that the task be logically separated into smaller tasks, and that a method of solution for each smaller task be found separately. Each of the separate solutions can then be combined to achieve the simulation of the metering network. In order to ultimately achieve a transient solution to pipe flow, a good steady-state solution is required. The steady state solution will establish the initial conditions of pressure and flow for the transient solution, the friction factors for the transient solution, and quality, or fraction of air, in the flow. Therefore, the first major step of the overall solution plan is to solve the steady flows and pressures of the metering network. Once a steady-state solution has been obtained, the transient solution can be performed, It will provide the pressures as a function

of time at each interior junction as well as the transient f'low in the metering elements and at the boundary points. It will provide the dimensionless head ratios for each orifice so that the influence of the flow oscillations on the friction factors of the various orifices can be evaluated from the data of Chapter III. The steady state solution, with the new friction factors, can then again be used to find the timeaverage flow under the influence of pressure pulsation. 4.6 Describing the Fuel Metering Network In order to apply the laws of continuity and motion to a fluid metering network, it must be systematically divided into subsections, or flow elements about which detailed general knowledge of the flow characteristics are known. These flow elements in the carburetor, for example, would include the metering orifices and inter-connecting tubes. The flow elements, then comprise the fluid network by being joined to one another at junction points, or junctions. A mathematical model of the carburetor is then created by first describing the flow in the individual fluid elements with the equations of motion and continuity. The elemental equations are then related to one another by continuity at each junction, and the system of simultaneous equations which results is used to simulate the entire metering network. The accuracy of the simulation then depends upon the accuracy of the information about the flow characteristics of the elements Three types of elements were used to describe the network: 1) pipe, 2) square edged orifices, and 3) main metering orifices. Each element is assumed to have constant area; therefore, its dimensions can be described by one length and one diameter.

-97The orientation in space of each element is specified in terms of direction cosines. This requires that one end of the element be designated as the origin point or origin junction for that element in order to determine the positive direction of the orientation. This assumed positive direction is used in the flow equations to maintain the proper sign of the flow. The points at which the elements are connected to form the metering network are called junctions. Three types of junctions are needed to specify the network which are: 1) interior junctions, 2) boundary junctions exposed to Luel, and 3) boundary junctions exposed to air. In the computer program, continuity is satisfied at each interior junction, and boundary conditions of pressure are required as input data at each boundary junction. The number of elements which join together at each junction are required for each interior junction in order use the continuity relationship. Also, the number of elements which connect the boundary junction to the reference junction are needed in order to use use the boundary conditions in the steady-state solution. The reference junction is one boundary junction which is taken at zero head. For this simulation the float bowl, where the fuel enters the main channel, is always taken as the reference junction. In order to specify the fluid network to the computer, the elements and junctions must be given consecutive numbers. This is done by starting with "1" at the float bowl, and consecutively numbering the junctions. The elements are then also numbered consecutively by starting with one. The integer numbers given to each junction and element are then used to form a sequence of integers which describes the entire flow network to the simulation program.

-98R24 cr C) -q co

-99At this point, an example of a simple network will help clarify the method of describing the fluid network. Figure 41 shows a simple fluid netwoxk o.' 6 clements and 6 julc;tions. The rfc;'erence junlct;ion i.; junction #1, the boundary junctions are 1, 4, and 6, and the interior junctions are 2, 3, and 5. The scheme of specifying the sequence which represents the fuel network is developed by considering each junction. For each junction, a portion of the sequence is written, and the rule used to create its portion depends upon the type of junction. For an interior junction type, such as junction #2, the sequence rule is as follows: Junction number [(element, junction at other end of the element)] repeated for each element attached to junction. or for junction #2 2, 1, 1, 4, 6, 5, 5, 2, 3 For a boundary junction, such as junction number 6, the sequence rule is as follows: Junction number, (element, junction) along path from Ref. junction or for junction number 6: 6, 1, 2, 4, 6 However, some boundary junctions have more than one path which connects them to the reference junction, such as junction number 4. In this case, a sequence must be written for each path as follows: 4, 1, 2, 2, 3, 3, 4, 7, 1, 2, 5, 5, 6, 3, 3, 4 Notice that the second sequence does not start with a junctionnumber (there are only six junctions). The numbers which begin these portions

-100of the sequence to represent the second and succeeding paths for boundary junctions start at the number of junctions plus 1, in this case 6 + 1. Finally, the entire sequence which represents the simple network is as follows: X = 1, 1, 2, 2, 1, 1, 4, 6, 5, 5, 2, 3, 3, 2, 2, 6, 5, 3, 4, 4, 1, 2, 2, 3, 3, 4, 5, 5, 2, 6, 3, 6, 1, 2, 4, 6, 7, 1, 2, 5, 5, 6, 3, 3, 4 Notice that junction #1, the reference junction, does not follow the sequence rules, because it has no path to itself, since it is the reference junction. Lines 2 through 7 contain the information which is necessary to describe the network to the simulation program. Of course, information about the dimensions of the elements, length and diameter or L and D, are also required by the simulation. The total number of elements, NELS, is also required, which is 6 for the case of the simple network. The direction cosines, CS, for each element are given by picking a fixed set of reference coordinates, picking a positive element direction, and then by giving the cosines in the positive direction in reference to the fixed coordinate frame. The positive element direction is defined by specifying one end of the element as the origin junction. The positive direction is then away from this end. Figure 42 illustrates the direction cosines for one element, and the origin junctions and direction cosines for the simple network are:

-101POSITIVE ORIGIN JUNCTION = 1 2 DIRECTION ELEMENT IN THE NETWORK t DIRECTION COSINES m" /I~, OF THIS UNIT VECTOR yx / ARE COSINES OSF ELEMENT. z X1 FIXED REFERENCE COORDINATES CS = X1 yl,zl J= 1 Figure 42. Direction Cosines of an Element.

-102JO = 1, 2, 3, 2, 2, 5 CS = 0,1,0, O0,,0, 0O,1,0, 0,10, 0,1,0, O,1,09 The number of elements of each junction (NL) is also needed, as well as the element type (LT). For the simple network of Figure 41, the number of elements is given as: NL = 1, 4, 3, 3, 2, 2, 4, and the element types are given as: LT = 6 - 0 The integer code used to describe the element types is as follows: LT = 0: pipe LT = 1: main orifice LT = 2: square edged orifice. The element type is used for the friction factor, and a larger number of element types could be used as soon as detailed information about their pressure versus flow characteristics are known. The junction type (JT) is also needed so that the simulation can treat each junction as a boundary point exposed to air or fuel, or an interior junction. The following sequence supplies the information about the six junctions of the simple network: JT = 1,0,0,2,2,0,2, where JT = 0: interior junction JT = 1: boundary junction exposed to fuel JT = 2: boundary junction exposed to air atrameters needed for a Solution: The steady-state solution technique requires that an initial guess be made for the quality (RJ) at each junction, for the friction

-103factor of each element (FT) and for the pressure at each junction. Of course, the values used at the boundary junctions are not guesses, but known values. The following values are used for one solution of steady flow in the simple network: RJ = 0.,2x.05,l.,1.,.05, FT = 6*.5 PT = 15.,14.,13.,12.,15.,13.5 Some additional flow parameters are also needed, which are the direction of gravity (CSG, in terms of three direction cosines) the magnitude of gravity (G), the fluid temperature (T), and the fluid (NFLU). For the simple network, the following values are given: CSG = 0.,-1.,0, G = 32.2 T = 75., NFLU = 1 The parameters NFLU and T are used to atain the fluid properties of viscosity and specific gravity. The fluid number, NFLU, corresponds to a certain fuel for which the properties, as a function of temperature, are known. See the listing in Appendix C of SUBROUTINE FPROP for all of the fluids which are available for this simulation. The entire data set, which is used for a steady-state solution of the simple network of Figure 41 is now given as X = 1,1, 2 2,1,1,4,6,5,5,2,3, 3,2,2,6,5,3,4, 4,1,2,2,23,3,4, 5, 5, 2,6,3, 6,1,2,4,6, 7,1,2,5,5,6,3,33,4,

-104D = 6'.1, L = 6*1., NELS = 6, CS = 0.,1.,0.,0.,1.,0.,0.p1.0. JT = 1,0,0,2,2,0,2, NL = 1,4,3,3,2,2,4, LT = 6*0, JO = 1,2,3,2,2,6, RJ = 0.,2. 05,1., 1.,.05, PT = 6*.5, PT = 15.,14.,13.,12.,15.,13.5, CSG = 0.,-1.,0., G = 32.2, T = 75., NFLU = 1 G = 32.2, T = 75., NFLU = 1 4.7 Basic Assum ptions Each element of the carburetor, which may contain air, fuel, or a mixture of the two, is assumed to have constant dimensions. Its length and diameter are fixed. Hence, its cross-sectional area is also constant. The proportion of air and fuel, which flows through it, is also constant, and the density of the fluid varies linearly along the element length. The proportion of the flow which is air, is assumed to have a density which is isothermally dependent upon pressure, and no fuel vaporization or condensation is allowed.

-105The elements are assumed to be connected by volume less junctions or points. Therefore, these points cannot contain any mass or accumulate any mass, nor can they cause any frictional force. Perfect mixing of bleed air and fuel is also assumed to occur at each interior junction. This means that the fraction of air is equal in all the elements connected to one junction for which the flow is away from the junction. This is best illustrated by the following simple example: Fuel, 50% Air 1 LB/HE 50% Air Air, 1 LB/HR 50% Air The fraction of air is assumed to remain constant for the transient solution. 4.8 Steady State Flow Harrington (20) showed that the assumption that flow is proportional to the square root of the pressure drop is appropriate for steady flow in carburetor channels. A flow conveyance factor, R, can be introduced to create the following equation for each element: m = REL JZ2PEL (4.1) where: REL = A Jp /FT Continuity is written for each interior junction as follows: NL NL X mn = O = X REL PEL (4.2) EL= 1

The pressure drop between junction #1 and each boundary junction is written as follows for each path between 1 and j: NL Pj-P1 = L PEL N~PEL (4.3) EbL1 A set of equations is, therefore, obtained which describes the pressure drops of the network. Since the equations are non-linear, an iterative solution is used to solve the system of equations. The equations are rewritten as follows: NL 7 Interior Junction 0= L RELXEL Equation (4.2a) EL=l NL Boundary Junction DPj = t XEL XEL Equation (4.2b) EL=l where xEL = fTAP EL independent variable (4.4) XEL = ~PEL' X E_ AP from previous solution, specified initially to get solution started. (4.4a) DPj = P - P1 (4.5) For the simple network, the system of equations which results by using the information of the X vector to determine which elements connect to which junctions is as follows:

-107o=o:fP1 -R2 JP2 +0 -R4 %aP4 -R5 TAP5 +0 0=0 +3R2 p 2 -R3 %Ts3 +0 +0 +R6 NaP6 +A-PP=5P+ +ap +3+0 +0 +0 0=0 +0 +0 +0 +R5 "sP5 -R6 aP6 P6-Pi=ZkP1 +0 +0 +0 P4 +0 +0 P4-Pi-aP1 +0 + +P5 +0P6 The solution of this system of equations will then give the pressure difference for each element. Solution Technique, Steady State Initially, a guess is made for each element pressure drop, and the square root of the guess is used as a coefficient in the boundary junction equations. The coefficient of the terms in the interior junction equations are the conductances which relate flow to the square root of pressure drop for each of the adjoining elements. The values of "xEL" are found by solving the system of equations with subroutine DGELG in the scientific subroutine package (*SSP). The values are compared to the previous values, and the iterative process is terminated if the difference is small (less than TOLP). Otherwise the process continues by selecting new values of XEL according to: 1/2 (XEL)NEW = (XEL XEL) (4.6) and solving the system of equations again for the values of XEL. Next, from Equation 4.1, the flow through each of the elemen-ts is calculated according to: m = (REL) (XEL) (4. a)

-108The flow out of each boundary junction is equal to the flow of the element which leads to the junction, since each boundary is joined by only one element. The pressure gradeline at each junction is then calculated from the pressure drops. This is accomplished by adding the pressure drop for each element in the sequence specified for the boundary junction equations. This is illustrated as follows: 1 2 3 4 6 P2 = P1 +'P1 P1is known P3= P + aP2 aP's were previously calculated P4 = P3 + AP3 P5 = P4 + AP4 The pressure loss due to changes in elevation is calculated from the density of each element and the change in elevation f'or each element. The change in elevation is found by the formula: DZ = L * COS X* G. (4.7) where L = element length e = angle between element and acceleration, G G = magnitude of acceleration, normally 32.2 ft/sec.2 Therefore, the pressure difference due to changes in elevation for an element is: DPZ = RHe * DZ (4.8)

-109o The pressure due to elevation for each junction is then calculated the same as the pressure gradeline PZ2 = PZ1 + DPZ1 PZ3 = PZ2 + DPZ2, or, in general j-1 PZj PZi (4.9) i=l PZ1 is known reference, usually 0. The total pressure at each junction is then easily obtained as follows: PT = PG - PZ (4.10) 4.9 Fraction of Air: Quality As mentioned previously, some of the elements contain bleed air, some contain fuel, and some contain a mixture of the two. Since the fluid properties are based on a weighted value according to the percentage of air in the total flow, or quality, this quantity for each element and each junction must be known for the steady-state solution. Initially, the values are guessed, but calculations of steady flow are used to calculate the values of quality for successive iterations for the steady-state solution. The quality of a junction, Qj, is defined as tte mass flow of air into the junction divided by the total mass flow into the junction: ~ ma LB/HR air (4.11) r1 LB/HR total flow Perfect mixing is assumed, which means: =Qj X = X im (4.12) IN IN

-110where Qi is the quality of the junctions at the other ends of the elements which have flow towards junction J. A system of linear equations results by writing the above eguation for each interior junction as follows: E L I - ] I [ Int. I j Boundary IN IN Junction IN Points 4. 12a The right-hand side may be zero if all junctions from which fluid is flowing toward J are interior junctions. A simple example will clarify the method of solution as shown below. )Q=1 AIR, 1 LB/ER Q=O 0 0 0 J1 J2 FUEL, 1 LB/HR QJ1 (1 + 1) -0 = 0(1) + (1)(1) QJ2 (2) -Q (2) =o So: QJ1 = 0.5 QJ2 = 0.5 The flow at J1 and J2 is 50% air by mass. Subroutine QUAL contains the programming for the solution of quality.

4.10 Friction Factors Harrington (20) gives a very complete discussion of friction factors for steady flow. For the simulation performed here, the forces which are due to friction were assumed to be one of three types: 1. Wall friction factor, F, a. pipe flow (LT = 0) b. main orif'ice flow (LT = 1) c. Square orifice flow (LT = 2) 2. area change factor, FA, 3. bend loss factor, FB. As shown, the wall friction is divided into three catagories. If the element type is an orifice, the area change loss factor is already included in the coefficient of discharge. Also, area change factors are not included when more than two elements join at a junction. Bend loss factors are not included if the element is an orifice. The total friction factor, FT is taken as: FT = FA + FB+F, and this is the factor which is used in the steady and transient flow equations to give the frictional force when multiplied by the square of the velocity. Subroutine FRIC is the part of the simulation which provides the friction factors. Pipe Friction Factor: Elements which are too long to be considered as orifices are modeled by using the Moody friction factors for smooth pipe, as shown by Streeter (36). The Reynolds number is required to obtain the friction factor, and it is easily calculated from the flow, element dimensions and fluid properties. In the case of two-phase-flow, the pipe friction factor was multiplied by 4.5,

-112 - as suggested by Harrington (20). The factor of 4.5 is based on empirical data for the Ford carburetor used in this study; consequently, it may be different for other flow configurations. Frictional forces for twophase-flow are not well studied and more work on this topic should be performed. Orifice Friction Factor: As previously mentioned, the main metering orifice and other square orifices are the flow controlling elements in the fuel metering network. Consequently, orifice friction factors, or conversely, coefficients of discharge must be accurately known. This was the motivation for the study in Chapter III, the study of the influence of flow oscillation on the flow through small metering orifices. Harrington (20) used empirical data for the coefficients as follows: Cd = f (Re, L/D) Ifowcver, the study of Chapter III showed that the effect of flow osc:iillulionl on the flow coefficient can be accounted l'or by head ratio, HR, as follows: Cd = f (Re, L/D, HR) Empirical values of the coefficients of discharge are stored in SUBROUTINES CDMEAN and CDSQ. CDMEAN contains the data for the F-50 main orifice and CDSQ contains the data for the square-edged orifices. This empirical data of Appendix B is curve-fitted for Reynolds Number, and then parabolically interpolated for its dependence upon L/D and head ratio. Area Change Factors: When only two elements join at a junc-tioJ, u sually th(y are of di'fferent diameters. The re sulting area

-113 - change adds to the frictional losses of the network, and are accounted for in the following way: A1 A2 -* FLOW AREA INCREASE I FOR ELEMENT #2 A1 A2 - FLOW AREA DECREASE I' - FOR ELEMENT #2 Harrington (21) gives the formulas used in this simulation to account for area changes. Bend Loss Factors: A bend loss factor occurs when two elements are not aligned on a common axis, or when three elements form a tee section. Empirical data is used for these factors and the equations are well documented by Harrington (20). The loss which occurs for two elements is given as a function of the angle between them. This was easily calculated in the simulation from the direction cosines of the adjoining elements as follows: COSe = COSa COScx2 + COSP COSP2 + COSy COSy2 where 9 is the angle between the directed elements. The loss for tee sections was given only for 90~ tee sections, and was neglected in the simulation for tee sections other than 900. 4.11 Results of Steady-State Flow Simulation of a Simple Network Table IV shows the steady-flow results which were obtained from the simple network example of the preceding discussion. Notice that dLata is represented for two major catagories, junctions and elements. The pressures of the junctions are given as well as the flows. The sign of the flow is minus for flow into the network, and, of course, the flow for each interior junction is zero. For the elements, the

-114wO N N o N N ~ —,. r,- c- O.D i- O C O " 0 G -Y 0 0 0 -.4 0 0'- _ - C.,,...,,. OJ," ~0'0 01 C - G F r _ ~ c' 0' C 0 0 0 (.Z r.. o* o 0 o o C.4.. - 0-. 0 0D 0 6JU C, N N 41 C0 tj U *. O C O _' C C w 0 0,,-,C = O 0 ", 0 0" 0" - N U. N' 0 C - N N w3 *t 3 rU rl N uA J ~ ~: 0 C,.., u' oJ 0 w ct t O C~~~~~~~~~~~~~~~~.~ Wt -s cr\ C C0 0 C CC X e < C C < O O CJC 0C 0C; -.0 O - r,.-,ZC N,.t N - C"_ 0i C u 03 Nr N C 74 4, -' C C'' O' C C' J - C' c - N, c; N I f u - n ~ ~ ~ ~ ~. Y', 4 4 <- 0J N C UL O O O CL C" J P- N N e C, C' C C} 3 C' C.... ~~~~~~~C.. U ~ C 0 - ClN N _. IL N,-,.* r'~.. -'V' " " - U' c ~ - C' 2 _ 4N CU. N J' 0 C' Cj - H p- C-\ C'- C F 0 * U o., _J C. ~ <g; ~ ~ N-> N E\ N 0 z ~ EqD LL CN at rI F r- ( I~~~~~*C rC' " 0 _ j ~~~~~~~~~~~~~~~~~~~~'~-i"" 0 C - N'*J C' 0. C N tQ C' ac -'' GJ C', C' 4 4 C' U' -,,C C C *001 -t IC- IU C, CI C~ 0i 0; Cr C C C C Ce' C _ I' C C *. u... *,.,i O C.+ - C C; C. C Q~~~~~~~JP r 3 <: 3 r z C:,-. C: C U. C-. C" C""" u 1 C C C C c ( c c/ t.X C' C C C C_ _~^ C c@ cc * * * e e P Q / C t (r _ _3 _T _T _' - I.,.- _ _ j. _ C'~~~~~~~~~b'' tt t *** - _ - _ - ~ - L

-115dimensions are given in inches as well as the pressure loss and the flows of air and fuel. The sign of the flow for each element depends upon the chosen positive direction for each element. Plus flow is awty for the cliosen origin junction, J0. The sign of the pressure drop follows the same rule. Some unbalance of continuity can be noted due to the iterative nature of the solution. 4.12 Solution of Transient Flow: Linear Densityr Method Harrington (20) and Hosho (22) have both observed, with Iligli speed movies, the transient nature of the fluid flow out of the carburetor for an engine at a steady load and speed condition. The cause of this transient behavior can be divided into two main phenomena: that which occurs due to the pulsating nature of the pressure at the venturi and that which occurs due to the "slugging" of fuel in the fuel-air mixture which exists in the metering channels. Hosho claims that the later phenomenon is the only cause of transient fuel flow. However, the experimental studies of Chapter II showed that at wide open throttle and low engine speed, the former phenomenon is predominant. For this study, the mixture of air and fuel is assumed to be homogeneous, and the fluid properties are based on a weighted average of the two constituents. Therefore, the work that follows only considers the influence of the pressure pulsation at the venturis on the oscillations of the flow, and not the influence pulsations caused by slugging of two-phase-flow. The procedure developed is very similar to that for steady flow: that is, each individual element is described by the equations of motion and continuity, and then the equations are related by continuity at the interior junctions to form a system of simultaneous

equations. The X vector is used to specify how the equations are to be related and the solution of the system of equations at successive points in time generates the transient solution under the action of the prescribed boundary conditions (venturi, air bleed and float bowl pressures). Transient Flow in an Element: Linear Density Figure 43 shows the control volume used to analyze a flow element. Continuity is written for the control volume, which utilizes the assumption that the density varies linearly along the element length. a(pV) P (4.13) r = Pl + Ps X (4.14) [ dpl + dps t dt x = _ 1 + psx (4.15) x x ja (pv) = -| ( + x) dx (4.16) 0 2 (pv)x - (pv)1 _x x (4.16a) or 2 (pv)x = (pv)l - plX - p s (4. 16b) The linear density relationship can also be expressed in terms of the density at the downstream end, point #2. P = P2 - Ps (L-x) (4.17) L () =- - D (L-x) dx(4.1) x x

P P2 -P1! (1 —.) p -2 — V 0 V2 FLOW t it L 1J2 p(x) Figure 43. Control Volume for Transient Flow in an Element.

-118(pv)2 - (pv)x = -2 (L-x) + ps ~.2 (4.20) 2 2 (pV)x = (PV)2 + P2 (L-x) - (L-x2 (4.2oa) Now the equation of motion can be used to describe the flow at each end of the element. F pVdY + pV (V.n) dA (4.21) = F-dt (4.21) ~V A The surface forces are the pressure force at each end of the element, and the viscous shear forces on the peripheral walls, as represented by friction force per cross-sectional area. Z F = (P1-P2-Fr)A (4.22) The temporal inertial force is found by substituting the mass flux relationship found from continuity, Equation 4.16b: L d d v= d pVdY d- (PV)1 - Plx - pA dx v ~ o A L (pv)L L P12 A L L iaF (pV)1 - P 2 Ps i - (4.23) The convective inertial force is evaluated as: pV(Vn) dA =(p2V22 - p1Vl2) A (4.24) A When the three terms are combined by equation 4.21, the Constant area term is cancelled and the equation of motion is then given by: d(pV)1. P1. L3 + 2 2V1 (4.25) P~ -? -FR = T, d-t P —- PZ o~- oo- b~ (. 5

-119Instead of using (PV)x as given by equation 4.16b, (PV)x as given by equation 4.20a is now used in the temporal term of the equation of motion, equation 4.23, to give: dt pVd. = A d (pV)2 + p1 (L-x) P (dX-) o 2 3 - A d (PV)2 L + P2'L sL" A L (4.26) = A Ldt (PV)2 + P22 P2 (4.2) The equation of motion is then re-written as: Pl-P2-FR = L d (PV)2 + P2 2 + V - (4.27) dt 2 — Ps r+ p2v22 PlV12 (427) Equations 4.25 and 4.27 can now be used to solve for the rate of change of mass flux at either end of the element in terms of properties at the ends of the elements, as follows: d(pV)L = j P1-P2-FR+ P1 -+ Ps- + P V22 (4.25a) dt )2PL 2 2 (4.27a d(pv)2 P2 2 - + Ps- + P- (4 27a) Density A volume-fraction weighted-density is used to approximate the density of the mixture of fuel and air which flows in the elements. It is given as: P Pf (1-Vq) + PaVq (4.28) The fuel density, pf, and the volume quality of air, Vq, are constants for each element. Therefore, P = VqPa (4.29)

-120An isothermal rela-tionship is assumed to relate the density of the air to that of the pressure, and it is given as: P Pa -= R T = CONSTANT (4 30) Therefore, equations 4.28 and 4.29 can now be written in terms of pr essure as: P V p = pf (-vq) + RT vq (4.293a) P = RT Also, the slope of the linear density equation can be evaluated in terms of the densities at the ends of the element as follows: P2-P1 Ps = (4.31) and by substituting and differentiating pressure into equation 4.31: Ps- L (P2 -P) - (P-Pjl) (4. 32) By substituting the density-pressure relationships into the equations of motion for the element and combining terms, the following equations result: d(pV)1 = dL P1-P2-F + V3 L + 5 P2 j + Pf ( _-Vq) + V - [ Pf(l_VR) + I2 } ( 4. 25b ) d(pV)2 = P P2 -FR P2 +.5 1] + [ Pf (-Vq) +..q ] V12 Pf(l-Vq) + q ] V22 i [ Pr j iRT RT(4.27b) (,.2Tb)

LU Lv P1l P12 P13 _At 3 2 1 TIME d2P P11 - 2P1 + P13 dt2 A At F1 igure 44. Finite Difference Form of the Second Derivative.

-122The double subscript for pressure is now used to indicate position aild time, as follows: (position) (time) where a position of "1" is the upstream end, aiid of "2" is the downstrealn end. Time is indicated as first, second or third interval, with the first as current time, as shown in Figure 44. The second derivatives of pressure in equations 4.25b and 4.27b are now written in finite difference form as: p + P1-2P12 + P13 +'5 (P21- 2P22 + P23) At (4[33),0 P21-2P22 + P23 +.5 (Pll- 2P12 + P13) 2 +.5 Pl = At2 ()~.34) Ille e.lquation ofl motion for the eclemenl-t carl Ilow be wr ittsen in a lform whichil is suitable for finite difference solution aS fiollows: 1 t L VqL 2 F[ 1+-2P12+P 13+ 5P21-P22+' 5 P23 A(pV)l 1 -P1-F + 1 12 3.. 23 3RT At2 + f(l-V) + llVq ] V (pf(l-V) + R21Vq 2 L P q RT ]q RLTF 2 (4.25c) A(pV)2 =t { P -21 -F R -2P22P23+5P11P2 5P13 ] L 1 3RT At2 F L p'('v) + F - (V272 }) LPf(lq) +j V1 (Pf(NVq+ V 2 (4027c The above equations are now simplified by combining like terms of pressure to obtain the following two equations

-123L2 2 A(pV) { (1+ q- 2 v q ) P)l L 3RT At2 RT 2 v2 bR-T' 23RT P21 -) 3RT At2 v VL2 V 2 + -t (l 25d ) ( 3R RT At2 RT ( {VqL2 VqV2 - +RTt2 P21 FR 2 V L -'' -q (-2P22+P23-P12+' 5P13) 3RT At2 + Pf (1-Vq)(V12-V22) (4.27d) This concludes the analysis of a single element. Now the above equations for each element must be related by continuity at the junctions where they connect in the network. The system of simultaneous equations which results will then describe the network in terms of the conservation of rrmass and of momentum. Continuity at a Junction Since a junction, by definition, has no volume, it cannot accumulate mass. Continuity is, therefore, simply written as: j0o (4.35) Also, mnew mld + dm (4.36) Therefore, ) newj moldoLd =+ 0 fi-O (4.35a)

-124Since, ); m =0; (4.35) then dh _ O 0 (4.37) or for constant area and in finite difference form: A A(pV) = (4.38) at a junction Now, equations 4.25d or 4.27d can be substituted into the above equation for each junction of the network. This will result in a number of simultaneous equations equal to the number of junctions, or the number of unknown pressures. The equation which is used for the substitution depends upon the junction for which equation 4.38 is being written. If, in the summation, the junction is the upstream junction of the element, equation 4.25d is substituted, and if the junction is the downstream junction, equation 4.27d is substituted. The two equations can be expressed as a single equation by using a double subscript with a comma notation as follows: + Px,y which means + Px or - Py The following equation for continuity at a junction results when using the above notation: NL A v +- vq 2 ) pl L {+ (1 + q + V1l,2) P11,21 1+(1+3RT zt2 RT Aq L2 Vq 2X

-L25NL j L1{-3RT Zt2 (-2P,2 22+P13 23-P22,12+.5P23,13) 1 + pf(-Vq)(V12-V22) + FR (4.39) This equation is programmed in the simulation for each interior junction. The set of simultaneous equations which result are solved for the unknown pressures, P11 and P21. Friction Force, Fr The frictional force is based upon the square of the velocity throughi the element. The loss due to viscous friction is assumed to be equal to pF(V l2+V22) L ~R.... 4.... i' (4.40) since the velocity is varying along the length of the element. The variation is small, therefore Equation 4,.40 is a good approximation to the usual friction term for pipe flow as given by 2 F= pFV L FR 2 D Subroutine FRIC calculates the frictional factors (FL/D) for both the steady solution and the transient solution, as described in 4.10. 4.13 Checking the Linear Density Solution At this point, i-t is advisable to compare the solutions of a simple flow problem for the linear density method with the accepted method of characteristics. This was done for a 2-inch long tube with only air flowing. The wavespeed is well known for the pure air which means the results obtained from the method of characteristics must be reliable. The boundary conditions, as shown by Figure 45, are a steady pressure at one end and. a sinusoidal pressure at the opposite

-126x 2-INCH TUBE UPSTREAM DOWNSTREAM O.1-INCH DIAMETER AIR FLOWING 2200 — L_.METHOD OF CHARACTERISTICS * LINEAR DENSITY METHOD a 2000 DOWNUPSTREAM Lu I, ~~~~~~~~~~w ~~AT "x" a. 1900 DOWNSTREAM 1800 T1 TIME o 2. 1. DOWNSTREAM CJ 0 0. -1. FEigure 45. Comparisoni or Linear Density Melthod to Method of Characteristics.

end of the pipe. The results of calculated pressure at an interior point and for flow at the downstream end compare very well. A slight difference in flow is noted, which is due to a convective force term contained in the linear density solution. The results show that the linear density method does accurately simulate compressible transient flow in small, short pipes. 4.14 Simulation of' a Flord Carburetor The Ford C8AF-L two-barrel carburetor, as depicted in Figure 1 of Chapter II, was simulated by using the techniques just described for steady-flow and for oscillatory flow. Figure 46 shows the network which was needed to describe the flow path for the simulation. Notice that it contains four air bleeds, two main venturi ports, six boost venturi ports, and one connection to the float bowl. The enrichment system was blocked, since it contains the soft diaphragm of the enrichmirent valve. Softness of the channel walls is not included in the transient flow simulation, and it does greatly affect the transient behavior.. The enrichment system was in use for the complete tests of Chapter II. Separate tests were run without the enrichment system to check the transient simulation. Figure 47 shows the input data which is needed to describe the network of Figure 46, and to simulate one operation point, 1500 rpm and wide open throttle. The steady-state results for the 1500 rpm run are shown in'lblWcs V a;rd VI. The -flows in each elemen-t as well as the pressure at each junlctiorn are givun. The friction factor and Reynolds number are shown as well as the average densities. The fraction of air on a mass and on a volume basis is given as well as the separate flows of air and fuel. It is of interest to note that the flow in the idle system is shown to be reversed, which means that the idle port and

-128ty~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~C 0 co 0~ ~ ~ ~ ~ ~ ~ ~~~ r< 0 0 M 4-1 31~( g~ o4 0 0 - ~~~~~~~~~~~~~~~ C i. Z E ~.oC) e C _jO~ -C) t3c N _1 0'.,,.:" 0 ~ ~ ~ ~ ~ ~ 0 O

-129)0001A O9q-7-71 f nl7-l 1 O 09- 7-71 nnO7? I tR O-27-71 000(71 (19-77-71 ()1 0-?7-1 ()1m? Ih.nlN X-l, 1. 7.1.1.73,, 3,?,7, 3,4, 4,3,3,4,5, 5,4,4. 77, 23. 5,,13,14, 4,5,5,7W3.3.4,7. 7., A,?4,74,?,, R, 7,25, S,,Aq9, Q,A,R,.?.,.,q.In, In,s9,l 10,11, 11,10.10,312,! {.{? 14,1 5,14. IS, 15,14, 14,15,1, 117, lh,1,7,7,3,3,4,4,5,13,1414,5.15,15,1 17,14,15,17,1R, 1,1717,T19.,70,,1,1 9, 19, 1 7, 7,, 3, 3 4,4 5,, 1 3, 14, 14, I S, 1, 1 7, 17, 14, R, 19, 70,l9, 1R,20.71l,1,77, 21,1,,?,3.3,4,A,5,},1 4,,14, 15.1.17,17,17, 19,20, 0,71,?7,1,?,2,3,,3,4,4S,13,14,14,15,1,17,17,19,l 20,71,7?, 3?, 5,7,7,74,73,4, 24,?7.,2A7,7,7,24,7, 25, 7R, 4, 9. 7, 75, 24.7 97,3s,7 27,74,9, 27,1, 22,?3,3,4,4, 5,77,2,27,?4,,,?,2q, 7, 3n0, 77,?.1.2,.,3.3,4,4,5,5,4oh,7,7,.R,9,9,1,10,11,311.?R, 29,1,2,2, 3,3,4,4,5,,A,, 7,R,t9,9q, 10, 10. 1, 11 17. 1, 13, 37,27, 3O0,12,2,3,.,4,4,5,5,4,r,7,7,,l,l9,l,llll 2,13,39,35,3,,30, 31,1,2,2,3,3,4,4,5,5,,t,7,7,4,H9,9,,lO,,Ino lll.l,7,12,13,1 39,35,40,36,34,l1 32,1,22,3,3,4,4,4,5,5,A,.7,7R,,,9,9, In,, 11 II12,12,13,9q,35.4O, 3,41,37.35. 32, 33,,1.2,73,,4,4,5,5,4,4,7,7,,R,g9,9,10,,10,, 1,I, 12, 13,3,39,43.,3,4,33, 34,1,7,2,3,3,4,4,5,5.h,4,7,7,R,4,9,9,1O,10.11,11,1,,12,13,34,39,3734,, 35,39, 1,31,3A0,4n,A, 3,40,3S,34,31.,41,37, 37,35,32,47,3R.41.h, 34,43,39,47,37,4h,31, 39,4.'R,13,41.3R,A,37,34. 40,1,2?,7,3,,4,4,5,5,4,73,73,77,74,74,7%,79,?4,30,?7, 41,1,72,7,,3,4,4,5,5,4,4,7,74,74,7 5,79,74,30,77, 42,1 7, 2, 3., 4,4, 5,b 5r,4, 7,7, R., 75 5?,r29 24, 3), 27, 43,1,7,7,3,3,4,4,5,5,4,4A.7,71,4R,49,74, 3 77, 441,7,2,3,,4,4,5b,,, 7,7,,H,9,9 10,10, 11, 1,17,12, 13, 3,3q,43, 3,42,37, 35, 3?, n-.o5so,., R7n,. 1470,.?q I5*.1 5R,.70,.1n,. l4o,.OAl,.02&,, q,. 04,.042,.035,.094,.0o9,.05n,S.24, OA,3,oSna,3*7I4,.049,.02,u,*.n?, A*. 170, L-.143,.317,.975,.250,o.175,4&.750,..4o.4nh,.40nh,.930,,0q4 o. 175,.74,. 104,.loa,?.n,.nO~,.Onn,.ylr,.O2~,.?~O,. 12o,.I2O,b).O55,&.4 FtFL S-4,LFT270, C=S..,-l.,n., n.,-1.,0.,.H9Q,,44A,n,.R9R,,.434,,O, O.,l.,1O, O.,l.,()., 0r.,I,n.,.,1.,o, n.,l.,.,.,1.,.,, -.?59,.970,n., -.25q,.7Ur0., 0., l.,.,., l..0...().1,,O n.,-.9hhA,.72s, 0.,-,45h4,,0..,o0., n.-l.O. 0 1.,0.,0.,,,n.,., n.,l..n., 0,,.,0n.,.,n,,,.., n.,, O l.-O. -l.0.,0, -.5,0.,-,444,.Sn. -.R4.5,0.,.444.S.5.r...-.4. 1.0.n.0,,.5,0.,l.044..,0.,,.,o.,, n,O, -,0R, NL=,7,Z,2.4,5*3,7,3,7.4.7,3,77,3,5,3,10,l0,4*3,Q,l,13,14.l5,14,15,14, 5*3,4*10,4,.1.1,12n2, 7,7,0, R,7,0,7,,0,4*2,4*0,7*?,440,,fl1,2.,,4.5,4,7,4,q,10,lI,17,4,14,15,l,l79R,1R,l.,2U,5,4,74,9,,23,24,?5,72, |11, 13, 35, 34. 57, 34, 39 13,13, 35, 34. 3, 39. LI1O,10 TnLtlo1.;FNI{ r,n07 FRFO.Sn., PARR*14.5, PRil,l2) —.n755, -.0477,-.nl q.-Rn0,-.o070.-. o 54,-.O15h,.0725,-.0151,-.(1R7, PR(1,191)-.o755, -.047?.-o0145,-O0 S,-.07,-.O4,-,-.U754,.075,-.ol51,-.047, PR(l,2112-,57-.575 I-. - 343,-.334,-. 79?l,-.37, -.O]I5..0?2,- 04,-.39, PRIl,221 —.075S, -.0477,-.nl49,-.0h 5,-.0R?0,-.0544,-.7754,.02?5,-.0lti,-.o?7, PRII,277 —.O755, -.n477,-.n0IR,-.n0OS,-.n070,-.n05h,-.075,.o?45,-.n015,-.047, PHll1,2Rl-.0755. -.n477- 09,-.010, —.477,-,-.01J754,.Oh5,-.O151,-.47, PR( 1,?92q-.R49.-l.42,-1.277-l,-1.1,-.97?,-1*.535,.0744H,.0?9S,-.221, PR4l,30l —.R9,-l.24-l.277,-!.20-1,-.l-.97?,-.535,.n74H,.O795,-.221. PB1,311- -.P9,-1. }?,-1.77-1I.?0,-1.11,-.977,-.535,.074H,.O295,-.221, P(1,33).-.49,-1.47,-l.27,-l.20,-l.llI-.977-.535,.074H4,,0925,-,771, PlI,341 —.,Rq,-1.42,-I.27?-1.20,-1.11,-.9?7,-.535,.074H,.72q5,-.?21, NPnTN7-Io,NOnIV -sn5eN CYC., P=l14.5,14.4,14.39,144.3Re14.3714,3A14.35l4.1414.3,14.3,134 4.31,14.n,14.?79 14.31,14.31,14.4,914.14,914.33,14.4A14.?7,14.74,14.74,14.37,14.3A,14.39.14.4", 14.44,14.4.*133.7S,14.2,14.1,14.1,14.14,14.21, CS.,n.,-l.,n.,CG37.7, T-73.5,NFLII-, IsnL-i;NSPACE-50, I T TP-10 I FND A4 L I NF S p I'TFI F7igure 47. Data for Simulation of C8AF-L Carburetor.

TABLE V STEADY-FLOW RESULTS FOR THE C8AF-L CARBURETOR AT THE JUINCTIONS,ItJ r f I I T) LS r' rSc, 11o F, I /Sn-TN FL[1W, LF/Hi, I r ~-~ Hr'( ^) r lJ a t%' n JFL A I/ T )r n. 1,, -7b. % 7,.4R: ). - 4 X {s. 1 X~('~ 1,. ) 7 l *'.n) - I'. 714.l 1) 7J..4.) -',. 14 1/4 I1 -.? -( ) *. O t 1.O 3.),1. r',?0; I4 1'. 113 89" 1221; rI )3 n.fl.2 4. /7,.!t" 14.1.11' -.2?1 n.9 nl.97 n. n 0.0 1 1 * 8. t'f O 1 +.c f h.* ~ )I. 7'1. 4 *7. 0.0:53 +41 1 } 1 4. 1, 2) 1'. 1* ()2 r. r) 7,'41 7 1, 1, 3, 7 A.4 ) n } rI.* 0?, ).q*'1 1) 0. () 1 )*Q b ~I (, 1 4*1. L 1 /,. 4A 1' n.2n -2t, _. 2'?'', 0.(3 2. 1. )0 0(0 7? >* I, 57 l'1.? -4 1. on on i.o,)ru()on 1 { 1 *.) 3 7' 1 4 7''9 \7] " * ).n 4). ().0 I )0 )0o() i' 1 ). 14,'.'X r, ".l n'.?71 -).- 1).rW 7)() r).' 10+ 71)'1.'?44 1 4. 24,., C'Y4...,. V ) 0.0 ).( I.0 0i) 1 ) o ))!) I' t14/4, 14.241 ]',2t.',1 0e. lf;/r.~ 9.t1459 7 q- () 1 ),q'200)i) I9 1 4!. g 14. 4/)1 f. 20qrl.'q 2 41 1'S 9 * 1.! q714. 114' "~,r')? 1;> ~) 2.;- t. 4.9 1 )000 0''.11 7 ~'011 3 ~'1 1.0 09 0. 1. nOOC iq t,,"+. z+l, r 1/ + q. t-.!. 3. 71

-L3 1TABLE V (CONT'D) STEADY-FLOW RESULTS FOR THE C8AF-L CARBURETOR AT TIE JUNCTIONS J N 1? T rT'IlS r"' F C c,', 0 /s0-IIl FL]W,F L P / H' T" T I I:' nr tFT rAF) T & FUFL AIR/TOT'~? 14.1 1"' 14'.1 1j'.. e7),,,) " 1.* o.,) 0.() 1. 0)0)o 0 1 4. 4 c 1 4. ) r) 7 -7 * 7 t.*0 1 o 00000' I/..,f, o 1*4. J* 4. r,,?,,-' -(e.`167I - 4.l?2/C 1. 7. O00()''. 74n i'. r,)i 7.4 r, 4.4,'n. *.T:7?q4 4. 7?0r) o.'5T741 7 -,q. 7Eo 1.' c,T- o." Ir?.?. ) r,. I x,-) 7; 77 2 (7 0.nF7417 ~tl r',> - 1 1 7r". n rnq,?.';6,71,' I 778.0R8943 0 rt)57417?7 1.7:;n'.75,3 ).O3lr 2.77, 39 0.15Q+41 2.616 9 8 3n057417 37 11* tt 13J~ 7q r03.nO02??:I.74 1 nl 0.1 7?8 2.0R943 0.057417 34 1 T, 7ro 1 3. 7?3 ".3. r n 3 2.941 9q.16 Ql?. 77292 (').05741 7 -3 1 ~.,R 13. 94? r. qC)'n.n () O 0.0..0)5741 7 ^I 1 0.oI 7 13.q1.n73%? 0.r) 1.O 0. 0.0574 7417 *,7 1. 7. n r,' r,; 2 o.0 0.0 0.0,.0. i 5 "+4 17 ~ a 1 1. (' n 7. 1 n., n..n 0.0.5 74 1 7 " 1''3' 13.P'40 3.' q?.n 0..0.0 0. 10514 1 17,+, _ rn., q, _,. n O. O. I. (0')0()( 51,,, ~, _r,.n,' ) r ).n n ( 0 1 ))() 4.' 7 7,37o 00 1)n,,, _'. on -. 00 C.0,r.'*.() 0. 1.r'()0

-132TABLE VI STEADY-FLOW RESULTS FOR THE C8AF-L IN THE ELEMENTS. _r " T - " -'-T'4 ['FcC r"' II / r r rl( i N' I Ty V( LI,JL( -' T,. I rr,,.p T' rr, f t r/A / T )T N I L'4/..-f A11d ^.1 ^"7' 14.'.-'.0 n. 7',, 77. 1.1 1 7./?3'.o() * -.r, nl"o 1].,''.^, 1',.,7',-r'.q 1 33',. ".(dn77',?b.Z' i4 J.3.. 7.,}, ".,? I. n 7.' 7?.. 7T 7 17.t).?.ll / I.2?' I 1) /.,'15 ". |).0'ro3., 1 4,;4 7 " _" ],., 7,- i'r). "., ) 9 t 5.2 2' 3 ),.0. ^. *1,. 0P't; o.r,(n? 7 h 1. 2'" 7.?637 1' ).60'f, 85r. t.I /6. J 4.9963 0.911 -. l'c -~' *' n^.r A77 lth.o3 R 4 3.'.) 1 r194.?4 10(4. 40.454.? 71? 3. 930 7 (r.,C' q'.?2 a.n?1??, 7. r)tl r ".4qq,,, t6.Siqq ". )? 13 1?86. 0.37f. 2..3b' ().l949:,,.1' n.29,7,".O r)4S 1 7.744 /73 0.641 1h6.81 I,'4q 166,3T. 0.393 1. 7S7 i),9063 ", 1 1' r.?e;'> ro.q'3,7 1 7.4974 O0.9?.') 1. 7 4.r!06 2 1'34. 0.331 1. 510 0.972 1 -,7,'n.r34r, r)n917 1 7.4+7,4 9?') 16.974? h. 5r)h 12 49. 0.774 1.351)I 0.972 11 ^. 14a 0.4046i 0.09570 17.5941 1.0104 16.574 3.0915575?291. 0.517 1.19.34 0.'975 1? ".1~,~'.",q& 0.nK057'3 17.5 R41 1.0104 1.5?74 0.05L 2391. n0. 517 1.1934 0.'975 X13'5.'4>>1 X -.01079 -.1'9 4 - I)0.1I 3'4g -)."30) 1.0030'645. 3. 142 0.070.3 1.000 14 ". "?4 0,14 -.19445 -.ql', - n.1194 - ).00) 1.n0)0 1512. 1.778 0.0703 1.000) 15 I."'7 0.17' -.1517? -0.?'30 -).2?'3n;,. 1.r)0C) 2066. 1.71 1 0.0703 1.000 1 n. -.n4 n.7Q 0 n.0nOl n7.l0a1'.l!,,.0))0 l.n09) 439. 1.392 0.0703 1.000 17 I..+ 1 r. n34?7 I. I l: u ).)9) 983. 2.064 0.0703 1.000 2, 1*5 3. ".l 7-. 11f7?f-, -0.t771-?,. 1 7.: 1. ) n 2044. 1. 807 0.0703 1.000,19 ".?'tQ,o,?.1',,.3::s0; 1~.3113 0.3113 "'.0'an 1.'3301. 1?r00. 1.144 0.0)703 1.300?n II.n51'.1's 1."?719 no 13 I. -3 I 1. 000-50 10 16. 3.024 0.0703 1.00 1 X".' s, 0.100 V.02718'.14,5r ).14460 3.)nO.1. 0 133 962. 7.92? 0.0t703 1.000 32? 4.'114'.1' -*.0I -0.tq?1 -n.1?9-. -,.')00 1. 03 260. 0.144 0.0703 1.000 ) r 7, l.' )p -. r)n-00f, -0.071, -o.l I -.r)inO 1.0')00 511 4.326 0.0703 1.000 4,.,-r 7 I-n -' -. 11"': -."P-.00) 1.00 890. 3.942 0.3703 1.000 9 r. $, 7'.n-) -.0') — 057m0 -..17"? -..172 - 0.n00 1.0000 ll49. 4.0. 7 0.0703t 1.000

.'D ~ 0 C', 0 0 0 0' (7' O, O' 0" ~' 0' 0' O' 0, CY' 0~ C' ~ — ~ — ~ ~-4.-4.~ 0 0 0 0 0 0 0 0 0 0 ~ 0, —, _'-) ~ r'.- f —- ~ t".- I-.- (7' o" (:7, (:y,,.'7, o' C7 o" ~ (:7' (:7' c/'~ t.~ 0 rT' ~2_ 0 0.C'?...-4 ~ ~.....4....4.-.4 ~..~,-...4 ~.....4 t.J ~: -.~, %'"' C'~ C r:> ~ ~ ~ ~ ~ ~....4...-4......4.-...4,-,.,-"} _j L:, ~, —,,,'X', or'.3"..'t' ~ I",,4 ~ -3" r'-',~', —4 —, ~....4 ~.: 0, 0',-4 ~ f-~ ~'x,-4 0~. ~ C~ C,',' ~ ~ i ~ ~ ii ii ~ ~ ~ ~ ~ ~ ~,i ~ ~ ii ~ ii ~ i ii ~ ~ ~ tl ~ ~ ~ ~ (,111 P-~,&' -"'P ~ ~', ~' CT C' ~. ~ ~x~ u',,~, C'. ~T~ u~, Lt~ L~ LP LP C_),L-:- (' 0.:-, C C. C u", ~,r~ ~ b'" ur, ~, ~ ~' u" L.f- LP, U'.~ ~_ ~ ~ ~ r- ~- ~"- LO'~',.~ LfTM Lf' 0" u" U"', b~'- ~"~ L~ U" _F-t ~ ~ ~'.77 ~ c ~-' C' ( c_ C" C C' C ( r C, c_' C... ~........ ~ -... / ~. / ~. d ~j r- C C':.. C' nr- (,', CY I~ ~' c", — ---- ~T C'. O: 0,? C_) ~' ~l C_ 0 C' r~ I~ c~.,-, ~ I' — I~ t~ (:7' 0 C.' 0" — J (50 L: q-' ~", (- ~' "' C P~.: I"- 0,~' ~"!~, — ~-~ ~r-.,-~ t," ~r~ -~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ j H ~?;' ~'',-,-'-' "? {' (- O -.+ ~' ~: 0,1 ~ t ~ ~ ~ ~i.- I I I I CQ c~' "" —., ~c r'-,..,- ~ ~ C, C...,'t ti". ~' ~, ~,,, — C~ n{,.~ I —I ~ EH ~ —' r,-.,, —-.","',,47 o'.'.T " — C t' — C-,,L;,4.. I —.. ~ C 1' —H ~-~ ~C) ti.. r, l"x ~. ~ ~ r-'- ~ i'-, ~ ~ ~ ~,-~ t~ ~ t,, C. (-'.'~,., F-4 u..-..- ( r' ~ (' r' ~- (. t- C C' r-' r — ( — ( C ( ( [za -_,..2 [ I t I I I 1'-~ --, t' ~,~+,~ t'. ~- r'" I~..+ 1'- t' I'- I~,m t~ n. C' _,,'-' u;,.~.,~ I~' t' C' ~ I'"- -.?,,T,~+ ( C' ~, E. r'. r', r~ u ~ ~ -.t' e'. P" C,, C;' u" ~',4 ~' ~r,~,, %..: ~. j ~ ~ j ~. ",,. j.... C E- r' ~- (,,+ ~ e'.. C' 0,,t' t~ ~ ~ — t~' t. —.- I I I I I I ~ —, (',.,", ~- ~ ('x, ~- ~-,~' ~. —,.-.'F,' (,, O' C. t,,' <"','. —,.-.*'.r f', ~ ~,Z' Lf',4' Cr f"' ~ ( ~ ~' T~ u" C ~4 I'~ ( f' ~L I~- O' or,4' t,",4. Cr C 1", ~ P' f'x, LL C- I"- ~' (' C..T ~. t"x' ('~' Lr' -~' I~ 0 ~ ~ ~, — t"" (',,-~'. C ~' C ~' r,' -.1' -.- C C ~. C ~'1' (' (-2 C- ( C_ ~" ~ ~ ~ ~ ~ ~ ~ ~ ~ te ~ ~ ~ ~ ~ ~ I. (:e I I I C C? C (_, C C C ~ C_ C''~.'T (' r' (. L~'- L.r' ~' U' U" kr U' C' C. C. ( (' ~, I- ~ t', t," tF t" t",,'+ ~' Ll' kF L~ Lr L.r' C ~ C' r C ~, c~ ( r, r, rx --.- c C C- C (" ~'.,,t..I.~ -~ . -'-Z_ ~ U ~ (- c ~ ~ ( C ~ C' C C' C" C', C ~ C C'. 1" -.~ -~ -.+ L~ ~ t', ~ C'. ~ t~ ~', (' ( ~ ( ~ L, ~ L...... ~.' (.... C~ C~ (r C ~' ("% (", C,,. f"" f' (C:' ~'' L C' r ( r C,-......; r- ~-, r - ( ( r' ~ t C (: ( C ( r. f. t' ( (' I f", ~' I"' ~, 1"~ ~ ~r' I~ ~' ~ ~'" I~' ~',,.+,,.'I ~*,,.+

-1354off-idle port are functioning as air bleeds. This phenomenon was noted by Harrington, but his simulation was restricted to one flow direction. If the flow were to be reversed from the assumed direction for his simulation, it was automatically made equal to zero. Figure 48 summarizes the steady-state flow f'or four test runs at wide open throttle. Average flow is plotted as a l'unction ol' boost venturi vacuum for 1500, 2000, 2500, and 3000 rpm.'lwo fuel temperatures are shown, and its slight influence is noted. It is seen that the computer prediction compares very well with the experimental data. Figures 49 through 52 show the results for the transient pressure solution of the same four tests of Figure 48. Notice that these plots of pressure as a function of time contain curves for the air bleeds, main venturi and the boost venturi as well as the main fuel channel. These pressures were all measured with trarlsducers, and the first three listed are used as input to the simulation (they are boundary conditions). The main channel pressure is calculated by the simulation, and then plotted together with the experimental data. Very close agreement is seen to exist for the four trial runs. The simulation is, therefore, assumed to be accurately predicting the transient flow in the carburetor.

STEADY-STATE RESULTS RPM @ W.O.T. 1500 2000 2500 3000 30 O TEST DATA 20 75~F F 25 0 FORD V-8 302 CU-IN. C8AF-L 2-BARREL CARBURETOR STANDARD GASOLINE 0 L 0.5 1.0 1.5 2.0 2.5 BOOST VENTURI VACU.U PSI, TIME INTEGRATED Figure 48. Simulated Steady-State Results for C8AF-L Carburetor.

1500 RPM, W.O.T. 15 ATMOSPHERIC AIR BLEED LiJ O 14 co MAIN VENTURI 13 I I I TIME, SEC STEADY 0.01.02 STATE cL _ 15 LJ of ATMOSPHERIC C/'),_...,) w 1 i14 -- MAIN ~~Z':"14 t xx/ \ CHANNEL 2: IL: 1_BOOST VENTURI 13 12 _ X COMPUTER SIMULATION v, ~E PERIMENTAL DATA o C) r, 11l, i I TIME, SEC STEADY 0.01.02 STATE Figure 49. Simulated Transient Pressure for C8AF-L Carburetor, 1500 RPM.

-13'72000 RPM, W.O.T. 15 orr l-~ ATMOSPHERIC AIR BLEEDS MAIN VENTURI c, Lu Lu14:Z: 13 L 1 TIME, SEC 0.005.010.015 15 LLI LU ATMOSPHERIC F 12 CHANNELR SIMULATION EXERIMENTAL DATA 1- 1 1 TIME, SEC XXx Carburetor, 2000 RPM " 13 BOOST z I I ~VENTURI cls COMPUTER SIMULATION EXIERI MENTAL DATA TIME, SEC 0.005.010.015 Carburetor, 2000 RPM.

-1382500 RPM, W.O.T. 15 ATMOSPHERIC AIR BLEEDS, 14 <E w MAIN VENTURI 13 L TIME, SEC STEADY 0.0058.0016 STATE,_ m _ X COMPUTER SIMULATION 15 — MEASURED PRESSURES KLL V) I t \ ATMOSPHERIC Ci, x MAIN CHANNEL F \ I L 1 e12 DL LUC VE NTURI MAIN CHANNEL 11 L 3 | | TIME, SEC STEADY 0.0058.0116 STATE Figure 51. Simulated Transient Pressure for C8AF-L Carburetor, 2500 RPM.

3000 RPM, W.O.T. Lu Lu 14 153 STATE 0) Cl15 x COMPUTER SIMULATION Cr - EXPERIMENTAL DATA 13 Lu vjAIM,HRIC VI -' 14 " - e 12 F AMAI VENTURI 1 ___________________ TIME, SEC 1, _ S — TA DTE Fiiure 52. Sim_.lated Transient Pressure for C8A.-L Carburetor, 5000 RPM. Carburetor, 3000 R?M.

Figures 53 and 54 illustrate the transient flows coming out of the boost venturi, and the air flow going into the air bleeds. These flows were calculated by the simulation program, and are assumed to be correct since the measured fuel channel pressure compares very well with the calculated fuel channel pressure as shownl in Figures 4)-9 through 52. Also, the measured average flow compares well with tilhe calculated average flow as shown in Figure 48. Therefore, there is a great amount of confidence that the calculated flows are very close to the actual flows. It would be nearly impossible to measure the transient flows in the carburetor, therefore, the calculated flows are most valuable. It is interesting to note in Figure 53 that the air bleed flow reverses for part of the cycle. This means that during part of the cycle air is actually coming out of the air bleed, rather than going into:it. It is seen to only happen for a very short period, but the I'low reversal does Lake place. Also, it is for this reason that the impedance method could not be successfully used in simulating the carburetor network. In the same Figure, the boost venturi flows have a large flow amplitude, which means that this flow might reverse if the engine speed were sufficiently reduced (lower boost-venturi average suction). However, for the high speed run (3000 rpm) of Figure 54, no flow reversal is seen to take place at any of the boundary points. A multitude of plots could be made for flow and pressure in this me-tering network. However, the purpose here is not to study the tr'aisiernt flow in one particular carburetor, but merely to demonstrate a Inc:tlod by which the trarliclnt behavior can be accur'fately determined. The method used here can be applied to perform a detailed study of

6 5 FLOW OUT OF If BOOST VENTURI 5.7% AIR _, / \ BY MASS 3 F- 2 FLOW INTO AIR BLEEDS 100% AIR 16,19,28 0.001.002 TIME, SECONDS F'igure 53. Simulated Transient Flow for C8AFT-L Carburetor, 1500 RPM, W.O.T.

9 8 JUNCTIONS 29 FLOW OUT OF BOOST VENTURI 5.5% AIR BY 6, MASS 32,34 1_ 3\1 33 d4 O — FLOW INTO AIR 27....BLEEDS 100% AIR 0.005.010 TIME, SECONDS Figure 54. Simulated Transient Flow for C8AF-L Carburetor, 3000 RPM, W.O.T.

rany carburetor network. Pressures at each junction and flows in each element are given as a function of' time. The designer can study any or all of these points as he wishes and the information provided for each run can be given a great amount of study.

CHAPTEIt V COMMENTS AND RECOMMENDATIOQNS The programmning method of the simulation requires considerable computation time. One run for a single cycle requires up to t,en minutes on the IBM 360 Computer. Double precision is also used which makes the storage also considerable. The long computation time is necessary because very small time steps are required to insure mathematical stability (10-5 seconds). Oyama (27) also needed the same time increment for his computer work on carburetor emulsion tubes. The simpler metering network used by Harrington (20) was used in order to limit the time, but the results were poor for the transient solution for several reasons. For steady-state flow, elements of a large diameter, which have little frictional force are justifiably ignored. However, for transient flow simulation, inertia is also important, so that large elements must be included in the network. Even if a large element contains only air (low inertia) its volume becomes important because of the amount of air which call be compressed, and thereby "soften" the system. Therefore, the metering network of )43 elements and 39 junctions is needed to simulate transient flow in the Ford C8AF carburetor, as compared to the network of 25 elements used by Harrington for steady flow simulation. liowever, the cost of the computing time is still much less than would be the cost of experimentally gathering the same information. The method of solving the 39 simultaneous equations at each time increment is the Gauss elimination method (SUBROUTINE DGELG in the Scientific Subroutine Package). This method is quite wasteful

when the matrix for the solution has many zeros. (a sparse matrix) Methods do exist for solving sparse matrices as mentioned by Stoner (4-1) and this would be a logical approach -to limiting the computer time if many runs were desired. Modification of the simulation would be very simple, once a subroutine for solving sparse matrices were developed. The simulation could be greatly improved in the area of the friction factors. As mentionled earlier, the -two phase-flow friction f'actors are not well known, especially for oscillatory flow. Mor(e data should be obtained and supplied via subroutine F'RIC. It is a desirable feature of the simulation that the calculation of the friction factors is completely performed in subroutine FRIC. This makes adjustment of the friction factors easily done without disturbing the logic of the flow solution. The programming logic in FRIC is quite simple, whereas the logic of TFLOW, FLOW2, and QUAL is involved. Another improvement would be to include the friction factors and coefficients as a function of time. This would be easily (ione by calling Subroutine FRIC at each time interval. The current flows would then be used to calculate current Reynolds numbers to give quasi-steady friction factors. The orifice data of Chapter III would be of great use in this respect since it can be used to give the coefficients of discharge as a function of time, and thereby eliminate the quais-steady assumption for the orifices. The I'ord carburetor has an enrichment valve which exposes a soft' rubber diaphragm to the fuel channel. The simulation does not accoult for softness in the channel walls, hence, this unit was removed

from the carburetor in order to obtain comparable results between the simulation and the test. Including softness represents another improvement which could be made in the simulation. Such an improvement would be a major revision of subroutine TFLOW, and would be very difficult. Therefore, its advantage is in doubt since many carburetors do not have any sof't channels. l'or the simulation, it was assumed that the ratio of air and fuel in each channel remained constant during the transient flow. This, of course, is not true, but it is a good approximation if little or no flow reversal occurs. However, if a great amount of flow reverses for a large period of time, then the approximation is poor. This can be easily pictured if a condition of zero average flow is assumed. During part of the cycle, fuel will be entering the network from the float bowl, and tending to fill it. Durirng the other part of the cycle, when the pressure at the boost venturi is positive, air will be entering the network and displacing the iuel. The inertia of the network will be greatly varying during the cycle, depending upon the proportion of fuel and air which it contains at each instant. Therefore, the simulation cannot be used to study transient flow when the average flow is zero. However, the simulation could easily be made to account for this phenomenon by using Subroutine QUAL to calculate the amount of air and fuel which is contained in each elemernnt at each instant in time. Even though the simulation does contain limi-ting assumptions, it is accurate enough to closely simulate the one test carburetor for several frequencies (rpm) and average flows. It is also general enough to allow the user to specify the metering network via

-147the input data so that the simulation need not be changed in order to try different flow networks. It is, therefore, believed that the simulation can be successfully used for much further study of carburetion.

APPENDIX A ENGINE-CARBURETOR TEST EQUIPMENT AND PROCEDURE Figure 55 is a schematic of the overall test equipment arrangement which was used to run the engine to measure the pressure pulsations in the carburetor. The means of measuring the intake air flow is shown to be an orifice plate, which is the standard method used by the automotive industry. The pressure loss, which occurs across the orifice plate, is then recovered by the variable-speed air-pump so that atmospheric air pressure can be maintained at the inlet to the air cleaner. The air cleaner was in place during all tests because it probably has noticeable influence on the pressure pulsations in the carburetor. The fuel-flow measuring equipment is also shown in IF'igure 55. This operated by recording the time necessary for a known volume of' fuel to be used by the engine. An automatic stop-clock is started and stopped at the beginning and end of the known fuel-usage, and the total engine revolutions during this time is also recorded. This information is then used to calculate air flow, fuel flow, fuelto-air ratio, and engine speed. Fuel temperature is also measured, and it is used to accurately obtain the density of the fuel from prev.iously determined density-temperature relationships, which were mal,de, withl a ontrolled-temperature bath and a hydrometer. Air tempe'rat ure anLd baromeLtric p;ressure were also needed to determine the inlet air deilsity which is required to calculate the mass flow of air. Figure 56 is a photograph of this test equipment. In it the air cleansller is removed and the air cart and fuel-flow measuring device alr' nlot visibtle, but thle electrollic eqtl.ipment, whlich is used wi.tll thel -14-8 -

MICRO MA NOMETER FROM FUEL FUEL ENG REVP I NTA KE A IR SUPPLY FLOW + MEASCORF ICE PLATE VA R. AIR-FLOW CART SPEED AIR PUMP AIR TEMP. A P=O FUELTEMP. AIR CLEANER ATM. 3 PTREASS. L J PRESS. 2 3TRANS. PRESS — " MAGNETIC PICK-UP FigSur 55.J Shti ofr; EDYNAMOMETER FUEL P5inP F'igure 55. SchematiC of Engine Testing Rig.

-150 -s~~~~~~~~~~~~~~~~~~~o~~~ ~~: ~~~~~~~~~~~~~~~~~~~h.p.~ g ~~~~~~r1bZ,eB"'~"":+ vSlb 9r'-~~~~~~~~~~~~~~~~~~~~~d~~- -------- - --- ----.......... ~ ~ d I 0, l-'r,~~~~~~,4g

pressure transducers to record the instantaneous pressures in the carburetor, is shown on the shelf cart. The top shelf contains the Visicorder, or the strip recorder, which made a permanent record of the pressure traces, the throttle angle, and the engine crankshaft angle. The middle-two shelves hold the Carrier amplifiers which are used to power the pressure transducers and magnify their signal.'T'he bottom shelf contains the ampl:ifl'ier that is needed to record thel crankshaf.'t r'otationl signal which is generated by thei matnetic ptic up and the'flywheel. Figure 57 is a close-up photograph of the carburetor, on the engine, and with the pressure transducers in position. Figure 11 also shows the location of the rotational potentiometer which is used to indicate the throttle angle. The location of the transducer which measures the main orifice pressure is on the other side of the carburetor beneath the float bowl, hence, it is not visible in the figure.'fable VII summarizes all of the equipment which is used.f'or the engine-carburetor tests. Belore the engine test was performed, the tranlsducers were calibrated. This was done statically and a vacuum pump was used to provide the calibration pressures. Once a calibration pressure was reached, the pump was stopped and the pressure was measured with a mercury manometer. The corresponding inches of deflection on the strip recorder and the gain setting of the electronic amplifiers were also recorded. Several pressure points were recorded for each transducer and plotted as a l'unction of inches deflection. This information was then used in the computer program which reduced the enginecarburetor data.

"1 ~~~~~~~~~~~~~~~~a) MU'~~~~~~~~' Q i.!:':.'~~~~~~~~~v s u3~~ ~~~g~~~~~-~~~~~lii~~~~~~~~~ ~8~~~~~~!~b — ~e~ ~g~:l"~s~aL ~ ~ 98 ~ -~ ~~i~~ T~~B~~aU,~~~~" ~ ~ ~r0~ ~i,,':::~~~~~~~~~~~4 7~'~o N 0 o --— ~~~~~~~~~~~~~~~4 o N~ i,~ s~k~%~~"~HB~B B~~%~ g~II~1Bg~B~~ gh~SNk c~3 N r~~~ k~~e~~s~~tz~~ ~~ B~~B~~B~c E- ~~~l~~~~~8o~:;~~:~~:~::~i f? t ~~~k~ ~~1'~1;" k eN

TABLE VII EQUIPMENT OF ENGINE-CARBURETOR TESTS IT:EM DESCRIPTION SI,ZE,, CAP?ACITY Carburetor Ford C8AF-L 2-barrel Engine Ford V-8 302 302 cu. in. Pressure'Ilransducer Statham PM 131, +2.5 psi Ser. No. 34.146 Pressure'Tlransducer Sbatham PM 131 +5.0 psi Ser. No. 33658 Pressure Transducer Statham PM 131 +15.0 psi Ser. No. 34147 Pressure Transducer CEC 4-312-0002 +5.0 psi Ser. 34367 Rotary Potentiameter Helipot 5403 10,000 ohm Recorder Honeywell visicorder, 8 inch paper width, Model 508 12 channels Amplifier Carrier strain gage amplifier Dynamometer General Electric 26051 I'uel Flow Metler l-ewlett-Packard Model 521A Air Flow Meter General Motors Standard Air Orifice Plate Manometer Meriam Micromanometer 10 inch Model A-750

-154The test procedure is very simple. F'irst, the electronic equipment is put into operation so that it can reach stable operating conditions. The gain settings for the transducers are then recorded, and the engine is started. Once the engine reaches stable operatior, data points are taken. A set throttle angle is rmintained, while engine speed is varied from 1000 to 3000 rpm in steps of 500 rpm. For each engine speed the strip recorder is run to obtain about 50 cycles of the pulsating pressures. The throttle angle is then re-set, and the process is repeated. This is done for throttle angles of 15, 30, 45, 60, 75, and 90 degrees, where 90 degrees is wide open throttle. All of the variables, which were recorded, are shown in Table VIII.

-155TABLE VIII VARIABLES OF TEE ENGINE-CARBURETOR TESTS RANGE FOR VARIABLE WHICH MEASURED i,,,,,...,,,, - Engine Speed 1000-3000 rpm Throttle Angle 10-90 degrees 90 = wide open throt-t le Average IFuel Flow 0-65 l b/hhr Average Air l'low 0-900 lb/lhr Air Temperature 81-980 ~ Barometric Pressure 29.04-29.08 in.hg. Manifold Vacuum 0-22 in.hg. Boost-Venturi Pressure 10-15 psia Main-Venturi Pressure 12.5-15 psia Manifold Pressure 0-15 psia Main-Orifice Pressure 10-15 psia fuel Standard Regular gasoline at air temperature

APPE1\DIX B COEFFICIENTS OF DISCHARGE FOR OSCILLATING FLOW Actual Orifice Flow-Data The analysis of orifice flow for ideal conditions showed that the mean coefficient can be correlated with the velocity ratio and the mean Strouhal Number. However, the data does noL correlate well when only these two variables are taken into account. Another dimensionless number, the Reynolds Number, is used to correlate the actual coefficient of discharge, and it is defined for oscillating flow as; RE = VD/v Therefore, the actual coefficient of discharge is given by the function; CDM = f(STM, VR, RE) The data for the orifices is put into four main divisions; 1) ClM versus I'low ratio, 2) CDM versus head ratio; 3) CDA versus flow ratio, and 4) CDA versus head ratio. -156

MEAN COEFFICIENT OF DISCHARGE VERSUS FLOW RATIO REYNOLDS NUMBER=1399-1849 TEST NUi";BER 7770 ORIFICE: SQUfARE iDGED DII,iET'R: 0 05J13 in. LJTJTH: 0,3750G in. L/D: 7,2394 FLUID: MINAERAL SPIRITS TEIUP. G iiJGE:~ 88.8-89,2 F VISCOSITY RANGE: 1.179-1.176 cp SPECIFIC GRAVITY:.7786-.7788 IDEAL FLOW ST=l.0. 0.8 — | —---- L I ~ X O''. 5 1................. SYM.3OL STROUIIAL r,~~2lO RATI - AR AT.FO/STEADY STATE 0.5 1.0 1.5 2.0 2.5 FnLOW RATIO, O R ALT. FLOW'/MEAN FLOW Figure 58. Mean Coefficient of Discharge versus Tlow Ratio for L/D=7.24, RE=99-1849.

-158MEAN COEFFICIENT OF DISCHAHGE VERSUS FLOW RATIO REYNDLDS NUMBER=2910-3320 TES'T NUM- iBER 7770 ORTIFICE: SQUUARE EDsED DIIETE R: 0.051i8 in. LENiTH: o 03750 in. L/D: 7.2394 FLUID: MINERAL SPIRITS TEMIP. ~ANGE: 88.8-69,20F VISCOSITY RANGE: 1.179-1.176 cp SEOZCIFIC GRAVITY:.7786-.7788, STEADY STATE H7 I 0r; | <2 1.13_1.2 SST=2.0 i ST=i. 0,..,. x, IDEAL FLOW o LEGEND 0 o.6 SYMBOL STROUHAL NUMIBER S ST-O. 5 0 0 ~~1.13-1.27 o ~O 1.68-1.91.9-. 60 0 0o.5 1.0 1. 2.0 2.5 FLOW RATIO, TRA ALT. FLOW/MEAN FLOW Figure 59. Mean Coefficient of Discharge versus Flow Ratio for L/D=7.24, RE=2910-3320.

MI:iAU COEFI, AI'_N'NT lF D A] SCFiAI(.L, VE RZU I" FLOW RATIO REYNOLDS NUMBER=4134-4393 TEST NUMBER 7770 ORIFICE: SQUARE EDGED DIAMETER: 0.0518 in. LENGTH: 0.3750 inc. L/D: 7.2394 FLUID: MINERAL SPIRITS TEMP. RANGE: 88.8-89.2~F VISCOSITY RANGE: 1.179-1.176 cp SPECIFIC GRAVITY:.7786-.7788.j~ 10; IDEAL FLOW ~ 3 9. 4....... | O O i Fq. T 8 o-I,'UlviBER 0 }..90-144....... r._N FLOW RATIOU, QR, ALT. FLOW/MEAN FLOW o-I ) f. 2434-.9 0 0.2 0.4 0.6 0.8 FLOW RATIO, QR' ALT. FLOW/MEAN FLOW Figure oO. Mean Coefficient of Discharge versus Flow Ratio for L/D=7.24, RE-4134-4393.

-160 - MEAN COEFFICIENT OF DISCHARGE VERSUS FLOW RATIO REYN'OLDS NUMBER=5232-55 5 LTEST NUMBER 7770 ORIFICE: SQUARE EDGED DIAMETER: 0.0518 in. LENGTH: 0.3750 in. L/D: 7.2394 FLUID: MINERAL SPIRITS TEMP. RANGE: 88.8-89.20F VISCOSITY RANGE: 1.179-1.176 cp SPECIFIC GRAVITY:.7786-.7788 kcX~~~' 1i~~ IDEAL FLOW C\jA~~~~~~' -CURVES; STEADY STATE oi~~.'.~~ ~ l~Tl. zI,ST=O. 0 o - HI- | L _ (9 J o S~;`SYBC OL STROUHAL m tLNUMIBER CO-) 0 0.26- 037 0( 0.63-0.72 0 1,07-1.15 {j ~o',~.4 o.6 o.8 i, FLOW RATIO, QR, ALT. FILOW/MEAN FLOW Figure 61. Mean Coefficient of Discharge versus Flow Ratio for L/D=7.24, RE=5202-5554.

-161MEAN COEFFICIENT OF DISCHARGE VERSUS FLOW RATIO REYNOLDS NUMBER=1104-1218 TEST NUMBER 78701 ORIFICE: SQUARE EDGED DIAMETER: 0.0518 in LENGTH: 0.1880 in L/D: 3.6293 FLUID: MINERAL SPIRITS TEMPERATURE: 75.1-78.90F VISCOSITY: 1.307-1.269 cp SPECIFIC GRAVITY:.7853-.7834 bC0 I I DEAL FLOW >S ~I CU \ o RVES 0.8i " -....... m | ~ STEADY STATE \;} oO7 S _ 1 0 \<L1~JJ~ ST=, (0 SYMBOL STROUHAL \ WX ~ NUMBER o (0) 0.66-0.70 0 1.45-1.57 Q 2.35,, J5 5 0 2.0 2 5 FLOW RATIO, QR' ALT. FLOW/MEAN FLOW Figure 62. Mean Coefficient of Discharge versus Flow Ratio for L/D=3.63, RE=1104-1218.

-162MEAN COEFFICIENT OF DISCHARGE VERSUS FLOW RATIO REYNOLDS NUMBER=2349-2 6.38 TEST NUMTiER 78701 OrIFICE: SQUARE EDGED DIAiiiL'EER:.3i318 inch L'i,'GTH:.1i;d'0' nch /i: 3 629 FLUID: II~lRAL SPIRITS r,.'-r: A JE: 7T'$. VISCOSITY: 1.307-1.269 cp SP?CIFIC GRAVITY:.7853-.7834 X. i IDEAL FLOW I Co - $ i - -R UREs S T=1..., STEADY STATE \m ( i;: S f 2T=O. 0 H, LEGEND.....' -- SSYMBOL STROUHAL Fi~ ~NUMBER o 0.32-33 0.68....70 ~ 0.99-1.02 0,D2 0j} o,6 FLOW RATIO, QR' ALT. I,)OW/MEIAN, FI,A)W Figure 63. Mean Coefficient of Discharge versus'low Ratio for L/D=3.63, RE-2349-2638.

MEAN COEFFICIENT OF DISCHARGE VERSUS FLOW RATIO REYNOLDS NUMBER=3422-3751 TEST NUMBER 78701 ORIFICE: SQUARE EDGED DIAIMETER: 0.0518 inch LENGTH: 0. 1880 inch L/D: 3.6293 FLUID: MIWK ll{JAL SPIRITS TE;P-lAA iURE: 75.1-78.9~F VISCOSITY: 1.307-1.269 cp SPECIFIC GRAVITY:.7853-.7834 x 1.0 1 Dao i I DEAL FLOW C URVTE S' —' ST=. O A STEADY STATE C_O o ~,,co o,,7;0 0 u LEGEND ~, C o 6 SYMBOL STROUHAL.. NUMBER Fllo 0.21-.24 0 (.45-.51 0.70-.73 0 0.2 0.4 o,6.o FLOW RATIO, QR, ALT. FLOW/MEAN FLOW Pigur-e o4. Mean Coefficient of Discharge versus Flow Ratio for L/D=3.o3, RE=3422-3751.

MEAN COEFFICIENT OF DISCHARGE VERSUS FLOW RATIO REYNOLDS NUMBER=-4521-4751 TEST NUMBER 78701 ORIFICE: SQUARE EDGED DIAMETER: 0.0518 in LENGTH: 0.1880 In ~/D' 3. - rLUID': VihEFP.AL S: XiS TEMPERATURE: 75.1-7..9~ VISCOSITY: 1.307-1.269 cp SPECIFIC GRAVITY:.7853-.7834 — 09 Cx! r i A STEADY STATE'r' i.'' ~ IDEAL FLUv U!, 1 i 9BT=0 i. |0..................... C-) H.o!.... SYM BOL STROUHAL.-. —.- - -.:. NUMBER |' N U 0 o 037.1 0.16-.19 U 0.33-.59 )0.2 0. 4 0.6 o,4 i. FLOW RATIO, QR, ALT. FLOW/MEAN FLOW Figure 65. Mean Coefficient of Discharge versus Flow Ratio for L/D=3.63, RE=4521-4751.

MEAN COEFFICIENT OF DISCHARGE VlRSUS FLOW RATIO REYNOLDS NUlIBEBR= 1099-1198 STROUHAL NUMBER-0. 112-0.238 TEST NUiBER 78702 ORIFICE: SQUARE EDGED DIAMETER:.0 0518 inch LENGTH: 0.0319 inch L/D; 0.6158 FLUID: MINERAL SPIRITS0 TEMPEFRATURE: 75.2-75 OF SPECIFIC GRAVITY:.7852-.7850 VISCOSITY: 1.306-1.301 cp -. 1! [ S xit 0.9 0 I DEAL FLO0 _ 31 STEADY STATE 0 7 ji - -I -1 - FLOW RATIO, Q, ALT. FLOW/MEAN FLOW l, igure UU. Mean Coefficient of Discharge versus Flow Ratio for L/D=O.62, RE=1099-1198.

MEAN COEFFICIENT OF DISCHARGE VERSUS FLOgWV RATIO REYNOLDS NU\bIBER=2369-2612 STROUHAL NUMBER=O. 0514-0.1834 TEST NULT`BERH 7870' ORIFICE: SQUARE EDGED DIAXIETER: 0.0518 inch LENGTH: 0.0319 inch L/D; 0.6158 FLUID: MINERAL SPIRITS TEMPEFLATURE: 75.2-75.7 F SPECIFIC GRAVITY:.7852-.7850 VISCOSITY: 1.306-1.301 cp ti'...). {IDEALFLOW - t...... ra O-,. 7 STI'E -'V7SAT" - 0 0.2 0.4 0.6 0.8 1.0 FLOW RATIO, Q, ALT. FLOW/MEAN FLOW Figure 67. Mean Coefficient of Discharge versus Flow Ratio for L/D=O. 62, RE=2369-2612.

-167MEAN COEFFICIENT OF DISCHARGE VEiRSUS FLO'VW RATIO REYNOLDS N UBER —3R387-3713 STROUHAL NUMBER=O0.0337-0. 1313 TEST NUT,iBER 78702 ORIFICE: SQUARE EDGED DIAI~ETER: 0.0518 inch LENGTH: 0.0319 inch L/D; 0.6158 FLUID: MINERAL SPIRITS0 TEMPEFATURE: 75.2-75.7 F SPECIFIC GRAIVITY:.7852-.7850 VISCOSITY: 1.306-1.301 cp 1. 0 - iiH~~~0 2 STAD1)Y 3TATE F z 0.75 0 0.2 004 0.6 0.8 1.0,FLOW RATIO, Q' ALT. FLOW/MEAN FLOW Ratio for L/D —O.62, RE=3387-3713.

MEAN COEFFICIENT OF DISCHARGE VERSUS FLOW RATIO REYNIOLDS NUTIBEAR=4470-4721 STROUHAL NUMBER=0. 0283-0. 1044 TEST NUiIBER 7870? ORIFICE: SQUARE EDGED DIAYIETER: 0.0518 inch LENGTH: 0.0319 inch L/D; 0.6158 FLUID: MINERAL SPIRITS TEMPEFRATURE: 75.2-75.7 F SPECIFIC GRAIVITY:.7852-.7850 VISCOSITY: 1.306-1.301 cp i l l 1...1 0 o,g iaif f or L_/D= j,2 I - ST=-0 10 0.7 7 -1 7< T I-i ]T'O. 0.2 o1 0i,6 1 O 0.2 0.4 o.6 0.8 1.0 FLOW RATIO, QR, ALT. FLOW/MEAN FLOW Figure 69. Mean Coefficient of Discharge versus F1low L-1a tic f'or L/D=O. 62, P-E=4470 -h1721...

-169-'MEAN COEFFICIENT OF DISCHARGE VERSUS FLOW RATIO TEST 2470 REYNOLD S' NJviBER=18 0 - 220 ORIFICE: F-5O DIAM:.0497 in. LENGTH:.1837 in. FLUID. Mineral Spirits TEMP: 77.8-84.20F S:..'7639-.7809 VISC: 1. 20-1. 219 cp IDEAL FLOW CURVES 0,9 0 rC) * ST-1.2 m0.7 8 > LEGSEND. 6 O=rS iO \ ~3~cX -o.0 SYMROL STilOUHAL NUMBER 0 0-0.6 0l 0.6 1,2 0.2 0.4 0.6 0.8 1.0 ALT. FLOW/MEAN FLOW FLOW RATIO 1ii;uru 705. Mean Coefficient of Discharge versus Flow RX-to for 1'-50 Orifice, RE=1800-2200.

MEAN COEFFICIENT OF DISCHARGE VERSUS FLOW aRAT C TEST 2470 REYNOLDS' NUMBER=2800-3200 FRIFI GE: F-50 DIAM:.0497 in, LENGTH:.1837 in. FLUID: Miner1l Spiri t s TEMP: 77.8-84.2 OF SG:.7839-.7809 VISC: 1 280-1.219 1.0 PI 0 ~~~~~~~~~IDEAL FLOW,~; ~ ~T —XX. E-4- Ao STEADY STATE,-, 0 7, 3 3 t0.6 LEGEND S06 _YMEBOL STROUHAL NUMBER o o-o.6 o 0.6-1J0 0.5 ----- 0 0.2 d.4 0.6 0.8 1.0 ALT FLOW/MEAN FLCW FLOW RATIO t,igure 71.. Mearn Cocef'fi(ientl, of Di,-;eharg~ v_::[':.,u;', t1'Vow habf,ia) folr 1'-t,( O-r if'ice. S2 1F't()()-52O().

-1711WEi7,OlJF. ICIvIrT OF D1)I,HA-,GE VIlR. I'3U s FLO.,- tATrIO'iIST J[L7j iY'TOL0 )S' IIUl1IBER=32 -';10) OhIFICE: F-50 DIAM:.3497 in. LENGTH:.1837 in. FLUID: Mineral Spirits TEMP: 77,8-84.2 ~F SG:.7839-.7809 VISC: 1.280-1. 219 cp. 1.0 O e I o I DEAL 0 0~.~5-o715 i iTo.7 Ro f A STEOY STA=0E lil, 0-.25 [2 ].5-.715 0.5 - 0 0.2 o4 0.6m c8 1.0 ALT FLOW/MEAN FLOW FLOW RATIO l igiu~e 72.. Mean Coefficient of Discharge versus Flow IRatio for F-50 Orifice, RE=3800-4200.

MEAN COEFFICIENT OF DISCHARGE VERSUS FLOW RATIO TEST 2470 REYNOLDS' NUMBER=4800-5200 STROUHAL NUMBER=O-0.6 ORIFICE: F-50 DIAM:.0497 in. LENGTH:.1837 in, FLUID: Mineral Spirits TEMP: 77.8-84.2 ~F SG:.7839-.7809 VISC: 1.280-1.219 cp 10. o * A STEAbY LTATE FLOW o, 7 STEADY:TATE wi! 8 0,~. 2 0.5 - 0 0.2 0.4 0.6 0.8 1.0 ALT FLOW/MEAN FLOW FLO0W RATIO l"isure 3.J Me~nl Coeff:icie.lt of I)i(rhL;:'g(f. V(.:'SU8 Ji'low Ratio f'or 1,'-50 Orifice, J1IJ::(00OO-5200.

-173Coel'i'ienrts as i'unctiorns o' HIead As discussed in Chapter III, the data can be plotted as a function of head ratio instead of flow ratio. The following plots show the data of Figures 57 through 72 replotted as a function of head ratio.

-174MEAN COEFFICIENT OF DISCHARGE VERSUS HEAD RATIO REYNOLDS NUMBER=1399-1849 STROUHAL NUMBER=0.89-2.21 TEST NUMBER 7770 ORIFICE: SQUARE EDGED DIAMETER: 0.0518 in. LENGTH: 0.3750 in. L/D: 7.2394 FLUID: MINERAL SPIRITS TEMP. RANGE: 88.8-89.20F VISCOSITY RANGE: 1.179-1.1.176 cp SPECIFIC GRAVITY:.7786-.7788 1x I 0.8 i. (1,1'; or:'K H 6 2.0 2. H STEADY STATIOE HR ALT HE/MEAN HE Ratio for L/D=7.24, RE=13l99-1849.

-175MEAN COEFFICIENT OF DISCHARGE VERSUS HEAD RATIO REYNOLDS NUMBER=2910-3320 TEST NUMBER 7770 ORIFICE: SQUARE EDGED DIAMETER: 0.0518 in. LENGTH: 0.3750 inc. L/D: 7.23941 FLUID: MINERAL SPIRITS TEMP. RANGE: 88.8-89.20F VISCOSITY RANGE: 1.179-1.176 cp SPECIFIC GRAVITY:.7786-.7788 xi's 1..: CJ I i rY 0.8 Z~O STEDY STATE t' i, l_ o'i om~._..... 0....00.7 0 O6o - - L2E0GEND 1. SYMBOL STROUHAL A o NUMBER U 0 0.49-0.60 <C Q 1.13-1.91 0 0.5 1.0 1.5 2.0 2.5 HEAD RATIO, HR, ALT. HEAD/MEAN HEAD Figure 75. Mean Coefficient of Discharge versus Head Ratio for L/D=7.24, RE=2910-3320.

MEAN COEFFICIENT OF DISCHARGE VERSUS HEAD RATIO STROUHAL NUMBER=0.34-0.90 REYNOLDS NUMBER=4134-4393 TEST NUMBER 7770 ORIFICE: SQUARE EDGED DIAMETER: 0.0518 in. LENGTH: 0.3750 in. L/D: 7.2394 FLUID: MINERAL SPIRITS TEMP. RANGE: 88.8-89.20F VISCOSITY RANGE: 1.179-1.176 cp SPECIFIC GRAVITY:.7786-.7788 1*1 (1) a0X ij A 0, if i 00.8 0 D sTEAD6Y STATE H!'', 0 I i n- i 0 I H, j r H. _,, v.., 0 0.2 0.4 06 0.8 1.0 HEAD RATIO, HR, ALT. HEAD/MEAN HEAD Figure 76. Mean Coefficient of Discharge versus Head Ratio for L/D=7.24, RE=4134-4393.

MEAN COEFFICIENT OF DISCHARGE VERSUS HEAD RATIO REYNOLDS NUMBER=5202-5554 TEST NUMBER 7770 ORIFICE: SQUARE EDGED DIAMETER: 0.0518 in. LENGTH: 0.3750 in. L/D: 7.2394 FLUID: MINERAL SPIRITS TEMP. RANGE: 88.8-89.20F VISCOSITY RANGE: 1.179-1.176 cp SPECIFIC GRAVITY:.7786-.7788 1. cu 1. 0 I 0.8 A STEADY STATE [ _, I -~ o... i....... 0.7::>~.~~~ j I t LEGEND 0.6 8. |T YSYMBOL STROUTAL nz; /. ) UMBER I r i I 0. 5 LEGEND R o -! 0.26-.37 0.63-.72 E] 1.07-1.15 0 0.2 0.46 0.8 1.0 HEAD RATIO, HR, ALT. HEAD/MEAN HEAD Figure 77. Mean Coefficient of Discharge versus Jlead Ratio for L/D=7.24, RE=5202-5554.

-178MEAN COEFFICIENT OF DISCHARGE VERSUS HEAD RATIO REYNOLDS NUMBER=1104-1218 TEST NUMBER 78701 ORIFICE: SQUARE EDGED DIAMETER: 0.0518 in. LENGTH: 0.1880 in. L/D: 3.6293 FLUID: MINERAL SPIRITS TEMPERATURE: 75.1-78.90F VISCOSITY: 1.307-1.269 cp SPECIFIC GRAVITY:.7853-.7834 I 0, I 0.79 -- ci) 0.9 EGEND....... SYMBL TEADY SRTUALTE NU i: )C 1045.1.57 0 0. 5 1.0 1.5 2.0 2.5 HE ATIO, H, ALT. HEEAN HEAD TAT Figure 78. Mean Coefficient of Discharge versus Head Ratio for L/D3.63, RE=1104-1218.

-179MEAN COEFFICIENT OF DISCHARGE VERSUS HEAD RATIO REYNOLDS NUMBER=2349-2638 TEST NUMBER 78701 ORIFICE: SQUARE EDGED DIAMETER: 0.0518 in. LENGTH: 0.1880 in. L/D: 3.6293 FLUID: MINERAL SPIRITS TEMPERATURE: 75.1-78. 90F VISCOSITY: 1.307-1.269 cp SPECIFIC GRAVITY:.7853-.7834 z1.O.........0... o" i.!!| l 1: i A STEADY STATE [ 0 7, i i 6 SYMBOL STROUHAL --- NUMBER Co ) 0 32-0.33 0 O68-0. 70 0 0.99-1.02 0 0.5 1.0 1.5 2*0 2.5 HEAD RATIO, HR ALT. HEAD/MEAN HEAD Figure 79, Mean Coefficient of Discharge versus Head Ratio for L/D=3.63, RE=2349-2638.

-180MEAN COEFFICIENT OF DISCHARGE VERSUS HEAD RATIO REYNOLDS NUMBER=3422-3751 TEST NUMBER 78701 ORIFICE: SQUARE EDGED DIAMETER: 0.0518 in. LENGTH: 0.1880 L/D: 3.6293 FLUID: MINERAL SPIRITS TEMPERATURE: 75.1-78.9~0F VISCOSITY: 1.307-1.269 cp SPECIFIC GRAVITY:.7853-.7834 ~......0-; X: I, 9 0.9 1::.: i i, -- STEADY,5TATE *0*: 7 0 7.7...... -. - EH., 1. I' i. u0 0 2 oLEGE4ND FL1 0.6 - SYMBOL STROUHAL..... rIl |NUMBER c(( 0 0.21-0.24 vu O ( 0.45-0.51! z; 0.70-0.73 x 0.5 L. i ____________ 0 0.2 0.' 0.6 0.8 1.0 HEAD RATIO, HR, ALT. HEAD/MEAN HEAD Figure 80. Mean Coef'ficient of Discharge versus Head Ratio for L/D=3.Q3, Rl=3422-3'{51.

-181MEAN COEFFICIENT OF DISCHARGE VERSUS HEAD RATIO REYNOLDS NUMBER=4521-4751 TEST NUMBER 78701 ORIFICE: SQUARE EDGED DIAMETER: 0.0518 in. LENGTH: 0.1880 in. L/D: 3.6293 FLUID: MINERAL SPIRITS TEMPERATURE: 75.1-78.9~0F VISCOSITY: 1.307-1.269 cp SPECIFIC GRAVITY:.7853-.7834 c 2~.O 1,0.... STEADY STATE 0.8..... ~I — r.< ~ LEGEND H 0.6 SYMBOL STROUHAL X O.6 NUMBER 0t C[0.037 ~0,s5 A' I -~~-~ —— i — - - 4I 0 0.2 0.4 0.6 0.8 1.0 HEAD HAIO,, ALT. HEA/M HAD Figure 81. Mean Coefficient of Discharge versus Head Ratio for L/D=3.63, RE=4521-4751.

-182MEAN COEFFICIEI4T OF DISCHARGE VERSUS HEAD RATIO REYNOLDS NUMBER= 1099-1198 STROUHAL NUMBERe0.112-0.238 TEST NUMBER 78702 ORIFICE: SQUARE EDGrED DIAMviETER: 0.0518 inch LEINWTH: 0.0319 inch L/D: 0.6158 FLUID: MINERAL SPIRITS 0 TEMPERATURE: 75.2-75.7 F SPECIFIC GRAVITY:.7d52-.7b$,0 VISCOSITY: 1.306-1.301 cp "D~~~_.0' XIDEAL FLOW STrO 00 0.7 0.7 ~7O 0.4 o I ASTEADY STATE rRatio for 6/D=0. tE1099-1198. 0Q5 0 0.2 0.4 0.6 0.8 1.0 0 Ratio for L/D=O.62, tE=Kl099-1198.

-183MEAN COEFFICIEN4T OF DISCHARGE VERSUS HEAD RATIO REYNOLDS NUMBER=2369-2612 STROUHAL NUMBER=0. 0514-0, 1834 TEST NUMBER 78702 ORIFICE: SQUARE EDGED DIAIN-ETER: 0.0518 inch LEil'TTH: 0.0319 inch L/D: u.6158 FLUID: MINERAL SPIRITS TEMPERATURE: 75.2-75.7 F SPECIFIC GRAVITY:. 7652-.7b50 VISCOSITY: 1.306-1.301 cp.9 5 1 EAD RATIO, E, ALT. HEAIDEA FLOWHEAD Ratio for L/DO.62, STRE=269-2612. o STEADY STATE-j -i - 0,6.. Ratio for L/D=O.62, RE=2369-2612.

MEAN COEFFICIE1NT OF DISCHARGE VERSUS HEAD RATIO REYNOLDS NUMBER 3387-3713 STROUHAL NUMBER=0. 0337-0.1313 TEST NUMBER 78702 ORIFICE: SQUARE EDGED DIAIiETER: 0.0518 inch LEIWGTH: 0.0319 inch L/D: u.6158 FLUID: MINERAL SPIRITS TEMPERATURE: 75.2-75.7 F SPECIFIC GRAVITY:. 7?62-.7bDO VISCOSITY: 1.306-1.301 cp''ilL_ -i:. -~ 0 IDEAL F LOW 2 ST=0 0 0 _ STEADY STATIE AT HEDMAN 0,5 0 0.2 o,4 0.6 0.8 1.0 HEAD RATIO, HR, ALT. HEAD/MEAN HEAD E'igure 84. Mean Coefficient of DischarCru versus IHead. Ratio f:or L/D=O 2, R2I8-1j7(1'.3

-185MEAN COEFFICIENT OF DISCHARGE VERSUS HEAD RATIO REYNOLDS NUMBER= 4470-4721 STROUHAL NUMBER= 0.0283-0.1044 TEST NUMBER 78702 ORIFICE: SQUARE EDGED DIAMETER: 0.0518 in. LENGTH: 0.0319 in. L/D: 0.6158 FLUID: MINERAL SPIRITS TEMPERATURE: 75.2-75.70F SPECIFIC GRAVITY:.7852-.7850 VISCOSITY: 1.306-1.301 cp 00,|~~~~~~~~~~~~~~~~~~~~~~~~~.' ST=O. 0 rX 0.7.... E-e STEADY STATE E71 A:. i ~,,6 -i'.~.. 0.5 0. 02 0.6 0.68 1.0 Figure 85. Mean Coefficient of Discharge versus Head Ratio for L/D=O.62 RE —4470-4721.

MEAN COEFFICIENT OF DISCHARGE VERSUS HEAD RATIO REYNOLD $ NUMBER=1800-2200 ORIFICE: F-50 DIAM:.0497 in. LENGTH:.1837 in. FLUID: Mineral Sp;rits TEMP: 77.8-84 2 F SG: *7839-.7809 VISC: 1.280-1.219 cp 1.0'~o9l A STEADY STATE 0.5 0 0.5 10 1.5 2.0 2.-5 ALT HEAD/MAN HEAD HEAD RATIO Figure 86. Mean Coefficient of Discharge versus Head Ratio for F-50 Orifice, RE=1800-2200.

iMEAN COEFFICIENT OF DISCHARGE VERSUS HEAD RATIO TEST 2470 REYNOLDS NUMBER=2800-3200 ORIFICE: F-50 DIAM: 0497 in, LENGTH:.1837 in. FLUID: Miner'al Spirite TEMP: 77.8-4.2 SG:.7839-.7809 VISC: 1.280-1.219 cp 0 0.9 o VI) H. 1 0 8o O.7 8 ~ 07 STEADY STATE ~0.7.*6 6ESYMBOL STROUHAL NUMBER o o-.6 C.6-.8 13.947 0 0.5 1.o 1.3 2. 0 2.5 ALT HEAD /MEAN HEAD HEAD RATIO l'igulre 8'y. Meaili Coefficient of Discharge versus Head Ratio fozr F'-50 Orifice, RE=2800-3200.

-188MEAN COEFFICIENT OF DISCHARGE VERSUS HEAD RATIO TEST 2470 REYNOLDS NUMBER=3800-4200 ORIFICE: F-50 DIAM:.0497 in. LENGTH:.1837 in. FLUID: Mineral Spirits TEMP: 77.8-84.2 F SG:.7839-. 7809 VIsO: 1.280-1.219 cp 1.C --,I' i O,! P0.. o: 0 o4 * \ N- A Z% STEADY STATE j 0.7> O 0' 8 LEGEND,rf SYMBOL STROUHAL 0 o.6 NUMBER o 0-.25 oZ.25-.5.5-.715 i 0 0.5 1.0 1.5 2.0 2.5 ALT HEAD/MEAN HEAD HEAD RATIO'igure 88. Mearn Coefficient of D)ischarge versus IHead Ratio for t'-50 Orifice, rE=38300-4200.

-189MEAN COEFFICIENT OF DISCHARGE VERSUS HEAD RATIO TEST 2470 REYNOLDS NUMBER=4800-5200 STROUHAL NUMBER= 0-0.6 ORIFICE: F-50 DIAM:.0497 in. LENCITH:.1837 in. FLUID: Mineral S~11ite TEMP: 77.8-84.2UF SG:.733;-.7809 VISC: 1.219-1.280 cp 10 r0.9 O.0............ 0 ~~~~~~~~~~~x~~~~~~~~~1 f~' f rx4 i~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 0 00 E-4 A STEADY STATE - 3! 0.7 8 1.5 f~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~,: I Ix. j:' 0 0.5 1.0 1.5 2.0 2.5 ALT HEAD/MEAN HEAD HEAD RATIO 1;'iguxe 89., Mean Coefficient of Discharge versus Head. Ratio for F-50 Orifice, RE=1u800-5200.

-190Alternating Coefficient of Discharge Figures 89 through 104 show the alternating coeilficicent ol' discharge versus the velocity ratio and Figures 105 through 120 show CDA vs HR. Each curve is for a constant alternating Strouhal Numbelr, and no account is made for the Reynolds Number. That is, -tle actual alternating coefficient data is plotted in terms of the same independent variables as the ideal alternating coefficient data. Most of the actual coefficients are lower than the ideal coefficients, as shown by the solid curve in the figures. However, at low velocity ratios the actual coefficient is equal to the ideal coefficient.

-1917 o 7 - ~-.., ()ST5: = 0 I i'; I; I 0. 0 EH | ALTERNATI rIG COEFFICIENT Z; L/: OF DISC-ARGE ~HO~ ~~~ 11.!VER i S H,2 - -iFLOW RATIO W-,' i;,l,..: TEST NUMBER 7770 ORIFICE: SQUARE EDGED < 1 L/D 7.2394 H i TEMP RANGE: 88.8-89.2~F VISCOSITY RANGE: 1.179-1.176 cp SPECIFIC GRAVITY:.7786-.7788 0i 0,,5 1.0 1.5i 0 2,5 FLOW RATIO R ALT.. FLOW Ligure 90. AlternaAting Coefficient of Discharge versus Flow tio for L/D7.24, STA16

-192ALTFRNTATIN C- COEFFI CIENT OF DI SCilH.J'GE c~< 1VERSUS:2. - FLOW RATIO h0 ctJ,A,. 0 - 3 FLUD MIDERA FLOW~U2i~VCI I 1 7 9I~, 1?6'; I-A S IF ( IYTEST N78678R 7770'-r'V G 1.1 79- 1. 0 p H' J in FLOW RATIO, R' ALT. FLOW/MEAN FLOW77 low Ratio for L/D' 724, STA.7~68. FlowJ Ratio for L/D=7.2~, STA=2.68.

-193tz 7 & - I ALTERNATING COIEFFICIENT OF DI SCAlRGE * ~ VERSUS I |; VFLOW RATIO.! T 0'. 4 iO'............ ID FLO | ORIFICE: SQUAE LDED: / D!.I,iETE:R: 0.0518 in. E- LENTH' 0 3750 in <';,! L/D: 7 2 394! F-i 0,' -x-~~s:FLOW RAT0O2 Q-R ALT. FLOW/MEAN FIOW oigur 92. AlternTEMT UifBE'R 7770 8 89 2 ~F Flow EOIFICE: S.UA 78 LD-o4r FRtooL/D: = 7.2394,T= Flow Batio for L/D=7.24, ST1AZi5.22.

-194 - ALTERNATING COEFFICIENT OF DI SCHARGE VERSUS - I FLOW RATIO >' I' firi | _~..-....._~- c_...:.,. _. _.|_ _....... _., J _ s~I: IDEAL FLOW -),',.,. HiA DI jMTER. 00518 in!I HLENGTH: O 0,3750 in. J -— j-. - -— L/D: 7,2394. HS.@~ IFLUID: MlINERAL SPIRITS l~, ~ I TEIvIP. MNGE: &8o8-89o2oF VISCOSITY MGE:% 1 1.179-12176 cp SECIFIC GAVITY: 7786-.7788 G. 1.5 FLOW RATIO, QR' ALT. FLOW/MEAN FLOW Figure 93. Alternating Coefficient of Discha.rge versus Flow Ratio for L/D 7.24, STA4.28.

-195IDEAL FLOW;l, ~x ~~ i.;T....::...ST =0.7 Ojj ~A <,''. la~o~o o DIAMETER 0.0518 in.FSCR E > > VERSUS TEST NUMBERE 751-87 8001 H ORIFICE: SQUARE EDGED z l 17~~~~DIAMETER: 0.0518 in. []1 \ol'' +-t.LENGTH: 0.1880 in. POOFLUID: MINER' AL SPIRITS;TEMERATURE: 7 5.1-78. H VISCOSITY: 1. 307-1.26z9 e Figure 9)4. Alternating Coefficient of Discharge versus Flow Ratio for L/D=3.03, STA=O.87.

-196VERSJUS i' FLOW RATIO;, ~ ~ - -:! — IDEAL FLOW 0.5 i,' %I /1: STA=1 35 0.4 -: r:) G |'.:, II< A ir cii i r, X i......!..-.; L.D..:. 623. i TEPST NUERATUR 75.8701789F SP OECIFIC GRAVITY: E 7853-783GED C0' LNGTH:.10 inc10 15' FLUID' I'INER AL SPIRIT= TESTPERATURER 7871-78. OF SPECIFIC GRAVITY:.7853_.783D Figure 95. lternating Coefficien1t of Discharge versus Flow Ratio for L/D=3.63, STA=l.35.

-197/~'..... ALTERNATING COOEFFICIENT OF DISCHARGE m,LI VERSUS FLOW RATIO (\j SC:.: I 1 *; i IDELAL FLOW oX ~ t | 0 i':: 9.STAil.61:~ i 0 5 ORIFICE: SQUARE DGED E: Eq..;'I, iDIAMETER: 0.0518 inch, Eq Jo 1. - -; — — + -- -- FLUID 1II. Y.iUL SPIRIT S? 1I 1 1 l TE;;ERAi'URZ 75.1-7-..9 9 ~,, i...,* E ~ ~.~ ~ i.. ~......,...,..,.....,. FC)r, TST MR 78 <~~I1~T.t P T AT- P OA M AT VTrIi C-) Fgre~I-t: D T.0518 inch Fo R L/D: i 6293 Flow Ratio for L/D=5.615, STA=l.6l.

-1980,O7 T T-: —t —7 —'I i i ALTERNATING COEFFICIENT OF DISCHARGE, < 1 i VERSUS $, |; 0FLOW RATIO bO IDEAL FLOWI; STA 215 2II H |0 Lii..........-........! _....................X ~ ~~ E I.PEATR. 1..... 1-7....F SPEORIFICE: SQUARE EDGED 7853-7834 FLO RAO Q' INLT FLOW2 Figur VISC TY 1.071in2 chaTg v0 Flow Ratio for L/DT.6, STA=2.5. O~~~~~~~~, j~........'....,......j........-_, U~~. 5Y:t..oH z.5 c ~ ~ O~ I:F I CE SG~~~UA t~~2.0 2..

0.7'i- l i 11LlI1 I 1 I i HL II I i I i i ti j ALTERATING COEFFICIENT OF DISCHARGE L tVERSU3 S x __[. -- FLOW RATIO ~, 1TEST A=O 15 < ID - EALO FLOW; -I f - t 9 -0.5 H o -10 0.3 oO SQAR EDG i Ei: I:! ai 1t LDLD 061 0 I~~L/:0.65 0 ~i DIAE: 0 0.5021 in06.8 FL.OW RATIO, - A T.1 FLW/MEAN FLOW Flo- RaTEMPEiATURE: 7/O 2T 15.7 F'low Ratio for L/D=O.62, STA=O. 15.

-200O.7~ I, I- lL I i ~ i-11l11i- 11 —.1 1 I 1- I-. I -i.I I1L_ I I I T I I I [ ALTEt ATING COEFFICIENT OF DISCHARGE:m: | fl:tXl l-l t ERSUS i I....- -| FLOW RATIO reD!- / 1 —~ —:::DRTi! i n 0.6 _I - IDEAL FLO' ti!o~~~~~ j ill[~ r —-t —k-0 I i I i )0 0 0Hi A:>D_.. i H 2-F R f LDO, - 0.2 I..'TEST NUM4BER 78702.17 OR PIFICE: UARE EDGED 0 0.220.4 o.60.1 FLOW RATIOQTES AT.U M E 7FO 02W/A FL 0 -, 2 I o,4TER: 0 0518 inc Figure 9. AlteHrnating Coefficient of Discharge versus Flow Ratio for L/D:-0 625 8 21'-0*

0 17 -1 IIi 1.1 I I I_ l I1 i 1 I I -, i i i i 1 I I - 11 1-l_-i L- I I I I I I ALTERN4ATING COEFFICIENT OF DISCHARGE ~:.V E RSUS:FLOW RATIO 1 1+ — ~.....i4 CC ~0.61:E KK<,jS~;1IDEAL FILOW 0 o 4. o0 0.3 A I igr 1 itl iC iie io Dshr or ~ ~ ~ ~ }'o Rai:'rLD0'2'4=)2 02. TEST NUME'1BER 78702 -ORIFICE: SQUARE EDGED - DIAMETER: 0.0518 inch -....'EGH OJi LENGTH: 0.0319 inch -!:t L/D: 0 6158 FLUID: MINERAL SPIRITS0 _ TEMPERATURE: 75.2-75 F - SPECIFICE GRAVITY:. 7852-.7850 ~0 0.2 o.4 0.,6 0.8 1.0 FLOW RATIO, Q, ALT. FLOW/MEAN FLOW Figure 100. Alternating Coefficient of Discharge versus Flow Ratio for L/D=0.62, STA=0.27.

-2020 4,n~~7 ~- I 1kl —LI I111 [I J. LLL I [I -I1 ALTERNATING COEFFICIENT OF DISCHARGE - AL TRATIN L-VERSUS i — A!.Kt FLOW RATIO x 0.6 i:it- t 1 t io~'~l:- IDEAL -FLOW ~ 0 i* - - i i| 0 4 iI - — LII tI -X::1l — ElEA 527. t-I tl-F-i-t-t-tI' | TA=0.37 -- F-( 0,'ii — < At> - ORIFCE: SQUARE EDGED o- 0 _III-DIAMETER: 0 0518 inch 0,,"4 — 1 — 0 LENGTH: 0.e0319 inch i — Ai f L/D: 0.6158 11-.. t FLUID: MINERAL SPIRITS I.. TEMPE?RATURE: 75.2-75.7 F I H -: SPECIFICE GRAVITY:.7852-.7850 17K 71911 — ~VISCOSITY: 1.306-1.301 cp 0 0,2 0.4 0.6 0.8 1.0 FLOW RATIO, QR, ALT. FLOW/MEAN FLOW Figure 101. Alternating Coefficient of' Discharge vcrsus Flow Ratio for L/D=O 6.i,';'-J-'A.5.

0.7 ~... L -4 — Z 4t:- - I- Iai —'i —-+ L t —— i;..- "? 1 ".... i........ i..........I. ALTERNATIG.. COEFFICI 5NT i i ri,ll t I,-it I I I Vt lERSU iI ALTERNTINFLOW RATIOE.F: -- | / |t~ |T:TEST 2 470 i ~ — <*-;- i -t ORIFICE: F-50!..' |[:,l:~, i| ~ [1!|DIAM1:.0497 in., I' [jj LENGTH:.1837 in. I i~ Ir i! 1 t T FLUID: Mineral SDptits ~ ii I C4 0 I:: TElPERATURE: 80.0 F' 0.;qo * L t s; | L - A w t 2' -. > - _. 0 0.5 1.0 1.5 2.0 2.5 ALT. VEL. /i42A1\T VEL. FLOW RATIO "~' Filow Ratio fI:or F-5() i Orice, S'- i'..'4.

-2o4i1111!!: LiT!~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ I tFjF 4 b L t 7 K.-c- _ IDEAL FLOW; 0-~~~~ I: i 1 i<K'~c, I-t- It I I~ i j f. I I J /1._i.~.1. iFt It 0' / *~~~~~~~~~~~~~~~~~~~~~~~~~ K o r') I, t — e I j!'t i t'j t I ALTEEINATING iOEFFI T', F F O i~~~.A j G —:.i - A.: j'~...."~~~~~~~~~-! 0 0 0.~ H- i........... in VERSUS i!~ ~~~~~~~~~~~.!i+-it —'i; <11 I TEST 2470 u:Hi ~ ORIFICE: F-50 LENGTH:.1837 in. I F ~~~FLUID: Mineral Sp;rits TEMPERATURE: 84.2UF F I-iK-KSG';.7809 VISO: 1.219 cp 11iiF' J: F o0.5 1.0 1.5 2.0 2.5 ALT. VELS/MEAN VEL. FLOW RATIO Figure 103. Alternating Coefficient of Discharge versus Plow Ratio for F-50 Orifice, STA=.12.

-205I T -T-' 1, I I1 r ~i I i i lt4lt[ ~II r- -C-II ~~~~~~~~0 7', I!Il l!t{{tlll/ — t I; i IDEAL FLOW 0*5 0 ST 14.45'2 i;4 k-I~ ~~ I 1-1 1t-~-ii- /1t - i t i - E-4~~~~~~~~~~~~~~J4 40 - i-+~ -— i- - 1 1- 1 i,.iit_c 1j E-4 - i- -I —4.[-,~ —-— t - i. E-4 ~O rALTERNATING COEFFI;IENVERSUS t i-FLOW RATIO 0.2 0 I ~,lt,~.~~{~u! TEST 2470 - ti _ ORIFICE: F-50 I~I)' i -i-...-i-1........ l~~t DIAM: o497 in -i!-t' ~ii —I — - ------ LENGTH.-1837 in,-- FLUID: Mineral Spirits T EMPERAT URE: 31.3 P H i — ~ tI!....SG:i I.78- - VISC: 1.246 c,:-!i i,W''!!-tttt-!~ {-. I t i i i I i I II! i-t'i. — 0.0'~ i III t:! i i II:~ ~ ~ ~ ~ ~ L.~ VE.MA VELSS. o,L1 TMPFLO W RATIO Ii!i iTESTSC ~ L247Oi:!ri f woO 0,3 X,O DIAN: 097 in ~ F ~TEPERATUR:813 FVigure 1:04. Alternating Coefficient of Disch{rge vcr.;u8 Flow Ratio for..-50 Orif2ice,.5A=l.45

-20b S - 08 5 o]}t, IDEAL FLOW T C o 10~i-K i 1 I i 1 ii i t EC-) i. i tI:8:il| I - I-i V T t-i-t i JT 1, 96 4~~~:D O i i F RT P! i I t 1 F-A t0.2 IH i T DIAM: -0-97 -n. 4,o)I Ci:. - |I i -I i -! LENGTH:. 1837 n. |4 T -j:| 1 TEMPERATURE 77.80 F 0-1? | | [-0 t I | 1 1 T! | VISC: 1.283 cp 1 oL! 7|0I7: F 7 -- 01;", ~- j!L G.. i c ~~~ALT VERLUB. [l ~-..... F~~FLOW RATIO 0,2 TEST 24~I70 low Ratio for.-50 9Orifi 7 i n %

-207ALT-ERNATLI`G COEFFICIENT OF DISC'HARGE VERSUS HEAD RATIO o~ 0 0..:~,.5..........' 0L, 0 in 0 / Q. 0 CD.' HL TEST NUMBER 7770 E~ ORIFICE: SQUARE EDGED DIAMETER: 0.0518 in. h; LENGTH: 0. 3750 in. H- 0oi, L/D: 7.2394 4:<~~ 4 FLUID: MINERAL SPIRITS TEMP. RANGE: 88.8-89.2~F VISCOSITY RANGE: 1.179-1.176 cp SPECIFIC GRAVITY:.7786-.7788 012 3:' HEAD RATIO, HR, ALT. HEAD/MEAN HEAD I.'igure 1lO. Alternating Coefficielnt of Discharge versus. Head Ratio for L/D=7.24, STA=l.069.

-2080,.g.. ALT ERNATIN G COEFFICIENT OF DI SCHARGE ~-r.~ VERSUS x< 0.6.; |HEAD RATIO:j~0K. 7.2.... I^~~ ~i~. E MEI.7.l,..; E KU | in STA =2.' D 7' 0) r1 80 I1 1 6 o o3C) Z-; I _ L I/' i n fI!-1L/D: 7,,2394 H FLUID MI"IN RAL S?IRITS H TEIXMP IANGE: 888,.&89,20F <: VISCOSITY RAN 1.179-1.2i76 cp S3IECIFIC GRAVITY:.7786-.7788.,.... I:......_....................- -.. Ai...; 0 2 3 HEAD RATIO, HR, ALT. HEAD/MEAN HEAD i igure 107. Alternating Coefficient of Discharge versus Head Ratio for L/D=7.24, STA=2.68

-209 - ALTERN.ATING COEFFICIENT OF DISCHARGE ~ 4,VERSUS HEAD RATIO 0. o6 ~~~ i~ ~ O,:.L~ tST A a0 0. n 0' 1 T. 0 cc1 O o 5 1 x; *. t O 0 U ( km TEST NUMBER 7770 ELENGTH: 0.375.0 in. Z i.: H /I 0.2.D 7,..... vTEST NUMBER 7770 ~O /.~H ORIFICE: SQUARE EDGED /HI DIAMETER: 0.0518 in. Li;LENGTH: 0.3750 in. <; 4 L/D: 7.2394 tl; OO_FLUID: MINERAL SPIRITS TEMP. RANGE: 88.8-89.2~F ~'}. VISCOSITY RANGE: 1.179-1.176 cp SPECIFIC GRAVITY:.7786-.7788 2 3i HEAD RATIO, HR, ALT. HEAD/MEAN HEAD l1'igu3'e 108. Alternating Coefficient of Discharge verstus Head Ratio for L/D=7.24, STA=3.21.

-2100~o 7 - - t -... ALTERNATWING COEFFICIENT OF DISCHARGE VERSUS HEAD RATIO (-\]1~4 -,-;oO t- ~ ^| II:C ) H 0 030 TEMP. RANGE: 8818-8;..F 8C, i TEST NUMBER 7770 ~,,~ {SPORIFICE: SQUARE EDGED HED A DIAMETER: 0.0518 in L/D: 7.2394 1, +FLUID: MINERAL SPIRITS: CTEMP. RANGE: 88.8-89.2~F VISCOSITY RANGE: 1.179-1.176 cp SPECIFIC GRAVITY:.7786-.7788 U 3 HEAD RATIO, HR, ALT. HEAD/MEAN HEAD 1~igure 109. Alternating Coefficient of Discharge vexsus Head Ratio for L/D=7.24, STA=4.29

ALTERNATING C OEFFICIENT OF DI SOHARGE VERSUS HEAD RATIO x'I: ~=. I' a -. 0...5 [o5 0,ST0' Co V2 (3, I DIAMETVR: 0.0518 in. 3,3LENGTH.188 n. -4 L/D 3.6293 sl TFS'r NITEMPERATURE: 775.1-7890F OR1 VISCOSITYCE: SUAR1.307-1.269 pE LENGTH: 01880 in. E-41 /0 3. 6293 O 1 2 3 L HEAD RATIO, HR ALT. HEAD/MEAN HEAD V'igure 110, Alternating Coeff'icienlt of DisChtl;a'e vtr;u Head Ratio for L/D=3.t), S'I'A=o.83y.

-212ALTERNATING COEFFICIENT OF DISCHARGE VERSUS i,A ~HEAD RATIO ST =1.35 c-) K0-3 L ~ Fr> L 3 359 E-4 TEST NUMBER 78701 o ORIFICE: SQUARE EDGED [-' LENGTH: 0.1880 in nVISCOSITY: 1.307-1.269 cp SPECIFIC GRAVITY:.7853-.7834 9 Oo1 3 3 4 D ATIO, HR, ALT. IED/MAN EAD Head Ratio for L/D=5.65, STA=i.L5.

-213ALTERNATTNG COEFFICIENT OF DISCHARGE VERSUS:~,. HEAD RA'TIO Uo $ C\C 0W~~. -0' 0 02 > t i ro.I........... ot! STEST NUMBER 78701 HDIAMETER: 0.0518 in r; C 1 LENGTH: 0.1880 in. VISCOSITY: 1.307-1.269 cp SPECIFIC GRAVITY:.7853-.783,;0) i 2 3 -HEAD RATIO, H ALT. HEAD/MEAN HEAD Figure 11 Alternat0.1880 ing vV.8U Hea L/D 3.6293, Sr.1. Head Ratio for L;/D=3.63, STA:::i. 01.

-214ALTERNATING COEFFICIENT OF DISCHARGE VERSUS SI~ ~JU:| -o,6 -.i —— |- HEAD RATIO h0 I I: E-i ~j.';' i FX IOI -— I —t —-A < o o tLENGTH: 0.1880 in. 0.3 3 o J O O 0v0. / / TEST NUMBER 78701, J VISCOSORIFICE: SQUARE EDGED I DIAMETER: 0.0518 in. LENGTH: 0.1880 in.'~ o "''L/D: 3.6293 FLUID: MINERAL SPIRITS TEMPERATURE: 75.1-78. 90F ~-: VISCOSITY: 1.307-1.269 cp SPECIFIC GRAVITY:.7853-.7834 02 1 2 3 41 5 HEAD RATIO, HR, ALT. HEAD/MEAN HEAD Figure 11. Alternating Coefficient of Discharge versus Head Ratio for L/D=3.63, STA-2.15.

0.7_I i j ii i Ii I i I I I I I I 1 i IN VERSUS 1-1. — HEAD RATIO H 1l — 1 -} |<17 1 - - KS R -- — 1 —- --- -- I p.5 H - - - -- -- - 1.6- <- ST =0*15 ")! (!2 -- - - - 1 - ii I -t - ---- I —l 5t1 I i.... 0 8 + L!.I,- V.- -.i.... i r.. f-' 1 00.3~DME 0 24 JtKc I lLG:31 Ic I-I rrr - j1 —c-,L 0,61K8 TEMP VAU 72750 0 -t ti t I TEST NUBER6 78702 ORIFICE: SQUARE EDGED II0.!~.. I LENGTH: 0.0319 inch E__t.~... L/D: O.6158' K I FLUID: MINERAL SPIRITS K — i: f ST:ECIFICE GRAVITY:.7352-. 7850._ VISCOSITY: 1.306-1.301 cp 0 02 0.4'o.6 0.8 1.0 HEAD RATiO, HR, ALT. HEAD/MEAN HEAD Figure ll4. Alternating Coefficient of Discharge versus Head Ratio for L/D=O.62, STA=0.15.

-21t - 7 -t - - _- I',, i i i - [ I I I I I I I i i i I i I j 0.7 -1 ALTERNATING COEFFICIENT OF DISCHARGE! t I I { VERSUS 4It HEAD RATIO aX 0 -. t rN> 0 2 | ~'.... t - -'1 t _ tti j- -. t I__ -!. j ~ I T - - iA0 5 i i | L - — if-.-. - KI — ST m0o 23 I P3 VKK1IYIY 7.:4{ I-4 —— L. -,r-j —I -:.3 cp _ TIL 0 0.4 o H LI I i i-i -, — i01 v >ATIO, HF LG 031 i HNh HE 0....... _ _ _-i-.. ——, iHj-i K,1 FCORIFICE: SQUARE EDGED 0 _'!' LG'0 in c 0 0i —2 —i o.k c. 0.8.0 eaIRal L._":r'.i L/D=. u2, 2j. 0~~~~~~~~~~~~~~~~ 1 0. 0.4c 0. 0-..8 1.0 ~~~~HA R A T IO HR ALT H E D MA HEAD] — i~iue15 lentn officieto Dishrevsu }f~.~ ]: t?-~t-i' f'-,r 1./lh — 4' -0ql.Lo

-2170.7 I I I ALTERNATING COEFFICIENT OF DISCHARGE Z i I l - -~ — — I tVERSUS — 1 -: —HEAD RATIO 06 _ _' *L I r_ Si~<1 11 m 053..ST...,.7 -' -:- i ~iUI-/ —-! -l —ORIFICEi SQUARE EDGED rx LD: -,61i8 o | 1 1_._1-._- u' — 1 --;:8 I II j-I I|0 ||- L R;FLUID: MIN;,RAL sPI[RITS I ~ I I I /-1 1 I 1-1 I { I I- I I I I- TZi::PZRATURE: 75 2- 75.70F I o 03'~ 1: 1:l- lORIFIC E: SQUARE EDGED C ODIAMETER 0. 051 i0 nch.:I 0 e LENGTH: 0.0319 in cha r- Head Ratio toLL/D. O 6158 -TEMPERA TURE 75.2-75. 70F SPE CIFICE GRAVITY:.7852-.7850 0 0.2 0.Li~ c.6 0.8 1.0 Figure 11u. Alternating Coefficient of Discharge versus Head Ratio for L/D=O.62, STA=O.27.

-2180 7 ALTERNATING COEFFICIENT OF DISCHARGE -bK-l 3 f-1 —: VERSUS HEAD RATIO 3~ t t 0 -- - I r.. -T - STA7O8 L7 0 D i — i.18 -1- I -PERATURE: 75 2-7570 ~o.3 H i=0, i:-.> L DIAMETER: V In,h ~ LENGTH: 0039-. inch F:4FT- j- i:%-I i -I r 0 ~ I -iI O.DIA~ETER: 000.18 cnch r~l Il....HEA LERTIO,GTH A 0HA03/9 MnchEA Figure 117. Alternating Coefficient of Discharge versus Head Ratio for L/D=O.62, STA=Q.37.

0,7..: o 0.6 o M 3 | H~ 5 3=0~'0 H *0 4T|OO74 rr 0.'-4 2- O 8 /0 ALTERNATING COOFFICIMiIT O - 403 O OF DISCHARGE ~-4 VERSUS HEAD RATIO' V TEST 2470.~C 5 ORIFICE: F-50 ~f~~ 0.2z ~DIAM:.0497 in. E-H4~~~ ~LENGTH:.1837 in. 4c'~~~ ~FLUID: Minersl Sor1its TEMPERATURE: 80.Q F SG:.7829 VISC: 1.258 op 0.1 0 1.0 2.0 3.0 4.0 5.0 HEAD RATIO Figure 118. Alternating Coefficient of Discharge versus Head Ratio for i'-50 Orif'ice, STA=O. 74.

0.7 0.6 0 0 o A o 0 0v5 / - rr T EST= 1.412 w H X 4o o s 0.2| "' ALTHI:i.A1'8Ii OQFFIGIENT E-4 ~co~~~~~ 9 /OF DISCHARGE X <* 3 VE -. SUS >~- j Fw~ I WHEAD RATIO 0. 7 w I TEST 4 473 H o ORIFICE: F-50 DIAIt:.OL97 ln. 0 d O. 2 LENGTH:.1837 in, 4 H IFLUID: Mineral Spbrite 0: TEMPERATURE: 84.2 F 7z~~P=~ @()jp~ 8~G.7809 fr3i: VISC: 1.219 cp 0 0 1.0 2.0 3.0 4.0 5. 0 ALT. HkEAD/MEAN HIUAD HJEAD RATIO Figure 119. Alternating Coefficient of Discharge versus Head Ratio for F-50 Orifice, STA=1. 12.

-221o t A~~~~~~~~ E-4 z _ — O ttl dC g<~~~~Ta= 1 45 O rM4 E-4 Hz 0 3 2kLIJ i1 ATI G OEFFICI ENT > rt`(~~ 8 OF DI SCARGE:J [,VERSUS -3 Or Q. HEAD RATIO C1 | |TEST 2470 o 0o2 | w; }>2~ CRIFICE: F-50 E-4 DIAM: 0497 in, ~~~~~~~~~c~~~~~~~~' -1.1<~ E-~ |LENGTH:.1837 in, gM~ ~ | FLUID: Minernl Sp;rits TEMPERATURE: 81..3 F o i| SG:.7822 cC< v. ~~~VI SC: 1,246 cp 1V 2..0?.o l. ~ ~.o ALT. HEAD/"OEAN HEAD HEAD RATIO ]t'iLgurc 1X20. AlternatiIlg Coeffi'ieint of DischaXre versus llead Ratio l'or:'-50 Orifice, SOlA=l 45.

-2220.7 0.6 0O 0.5 rx, 4T= ST 1.96 H H o ) ALTERNATING COEFFICIENT oC o~. fOF DISCHARGE zH ~ SVERSUS H HEAD RATIO 00.22 TEST 2470 E H - L-4Q~~~ ~ORIFICE: F-50 DIAX:.0497 in. LENGTH:.1837 in FLUID: Mineral Spirits iC. 1 TEIPERATURE: 77.8~F SG;.7839 VISC: 1.283 cp 0 1.0 2.0 3.0 4.0 5.0 ALT. HEAD/MEAN HEAD HEAD RATIO Figure 121. Alternating Coefficient of Dischar;ge versus Head Ratio for F-50 Orif'ice,?:'T'A:-1.63.

,JNJ'FK S I I Y tJ- A4I(t-CiIGAN ALi —tiAA,'-JICLAL ELNGINLEU-IlN, I I) 1'.iL}AL -1- IE.I 3_ 1'Ii[,L - I S L t A Fi L t CU t: -F I C I L r S -jR i LjSC ILL TOY F L L --. S 1~E{L& J 1-2A4 -- -E i h [ U jU-M EiER= 2 4 70-) 1I,N: F. AL I IS 4T TEMPLR ATU4L!iF 7 7. 8 SPLCiL'IC GRAVIIY=.739 VI St(SIfTY, CENTISTOKES 1. 280.... aHElI L Au I I A?FIL; _a.... _ _ 7 /!I F IF F L ENGTH I 4 INC IF3= D.1837 )F. IFIfL LENGTH/DIAMETER=. 69, 2 CAij 1 Jl P A_ACFMF- N T =.0740 )i 0 i 4.57 MAR 31, 1970 t',', L. 3 U H, L'):]-:,1 f', L LF: CLIF t f'K,u.'v;Al t' CJ FFE I'/H-tJ, CI S,t I A Ac t A l) ALI' tt AN RAI' U 1.215 1.215 l. t) J )J0.0J444 0.09) 3.4 39 18. 7 0. 7 7 91 1-.l'5 4.H93 l. )54,9 0~605 0.2 2490,).)32 19.o u.81dS2 2.il 9t.5i3...224 041 1l 33333 D,i/, 3-1 2 _1 ~8..5 843,.275 14.423'!.158 0.455 0.4193 0.1,)85 19.1 0.8692 3. 7 b 1 3). 93 d 4 0. 1 o4.4 5'- 0 4695 J. 938 18 9.3 0. 8636,2. A73 23.u) 1').12:).34Lq 0.5710. 0786 1 3.9 0.9363 3.A,Uo 2.48 61.1. 0a 0.)472 3.6210 0./S)76J 19.9;.9170 4. 13'4 33.416 o.125:).)+0 7 0.6565 I.0111 19.6 *0.847 3..664 31. ).. i.. J9 71; 9 7 ). 7 _A_:_ _ _. 3.5 /4t i3. 4o4.o8 1.) 0492 0. 7 9 7 1 29)1 ) 7. 94 77? 3.b ( 5). *3) J ) 71 J. J 15 0. 803' ).3 558.! 3 J.9448 3. 5>7 2.,) 44 1. 75'). 1 1 3 73 7.7 334 42 ).. 7594 -. 1,':, o.6:3'). Jl. ). )026 0. )245?2 0.4183 43.1 0. 7499,.L,l t7 1 1 1.6:*5 1. )f3, ). 1044.33 3. t11 4 3.9. ) 1 J5.'32 1 L.2r1 i-.'), t/ J. 3.IO43 0.4284 0. 24 35 43. 9 0. 8381',.: i 4 ). 1 0. J1).}5125,).?)1.) t. I 0.:t'446 3 >}), < 3 ) 3 ii J 7 * ) 4 L t. ) * )' ), 4* (J 1 J.500' 34.41' 3.216 J. OO J.I)tWS K).)1S / 4.t9 u. 9245'. (51 ~.S 3').26') ). 1)64. 7164'). 14"+ 44.7 70. 13 iU 0.316 41.154 I u. 2 0.lJu u.1551 Jl 3.141. 4' 4. J 0.889Z i ).779 49.1 9.21 1.,) 4 0.8314. 1 2 6 44.1 0. 33 ) 1. W.t3 1.1 6 6. 12 0. 1499.?'DU74 1.9615 63.1 0. 5552 9.~ 4 4. lob 1.7 15. 1522 v.23') 7 3.69) 4. J) 3. ~379 1uJ. 3 3S d5. t 1155 o. 19t5 0.3356 d.'456 62.9 2 u. b83 1i.4I 3.71 ).84 J. 1 5j4: J.4235'3.3 u50 63.2.90111 1. 533 19.591.O4/t J.I151..5.., _3.3151 i..i.5__.. 1 3. 4K 1. 7 36. 565 J. 151 ). 5171.2 26 66.2 J. 9341 1.3. 4 F 3:.2- ).). +2o I. 152Z 0.064o4 ) 2.355'- O.t O J089o1 1,,, 377.',) ).).3 7 b.3. 1.412':j. h6 I45. )1..9. 58

-224 - TABLE IX (CONT'D) F-50 ORIFICE DATA UNIVl RS I TY JF M ICH1I(-,AAJ MECHANICAL ENGINEE RING DUUIOR. AL TitESIS'I,-IICE DISCHAR G CUL EFFIC I'T F] [.R S I LL A T: Y t- L j........... TF P - F N _J __iS.I_...................... TESIl tUM3Etk= 24 7'fI N ~k:'\L SP I i.ITS Ai T E~[ P A t.: l t: 7 7. SPECIFIC GRAVI Y =.783)' V COS 5I I Y, C ENTI STO KES i. _QRIE_1L-L LDIALTE R...IN _.INCHLS=. H4L)1 LR IFICt LE:NGTH 1JN INCHLSt - 0.],i tR I F I C L L. L ENGT 1-/i) 1 A 11it fL r 3 = CAA D I SPLA(;E,',4T =.(. L74.?)O C A:.`,t I:) 7I L A 31 1 9 7 J PK LR U. RE DEU? LLb,S.. rRL...L. E F1 NCHF S WATIf-k Fi (O TET/HJk US ALT MNEAN RRA T IMA. ALT MEAN <ATI 1) i s. Q)1: 44.214 ).317 3. 147 0.73)89 JO. i 3 2. ) 0. 875' 1i. ~h6 43.5j1;D. 342. 15)5 0. 3 9 ). 7 99; t. 2. 9208r 6. 7J5 6:3.7h66.2 3 _ 14 85 __,1.I___. _ j7 13.1 3 1 2.834 4.t33.). 1944 u.12. 251 1.554 31.;3 i ).5852 13. ui1 7.501 1. 735. 18'75 0.2455 ). 7o35 1 i.8. 7uo2 I_.729 91 7 8 1.496 9).1911 0.3170., )3,. ).4+ ). 8242 1 3. 79 17.663 J.777.15 30 0.4354 ).:2,:4 r.812 1/+. 44 28.596 )504.1o5{3 0.524'3 0. 3154 b. 5. 772".16,, 13 9 1 30...I.. 521 7 J.__4 6 b13 3'..1 19_..._0....:J i 5 "5 9'i 1 1. 17 A2,.. 2)1,' 55.6 )Lt84 0.6643 J.. 25 35) J. J3 ) 39244 I 8.. ()4 4.l 3.8 48 t.'+ 1 2 0.1 7 1.9 ().7494 ). d, (..": 3 / 8ij. 1.: 1.') )16 47 3f*.)8,.. 3(7 9J. I"'s 0.":135 2, 2J.14., TI l.: ).9()59 1.3'9 5 J.4:) j. J ). 1'. 1417 ).2)1 1'. 0. (907 2J.'t39 3.6)(.57 ) 2 0.910 2. J [.1 1 ).I 3,9 2' 7).671 9, 7 3 2 t)9'i 2 22,L ( * 314. ). 1.3',t 94, 3, 1 i 7 t. i 18.82C) 1.29 )22't 0.Lt 4U 1 01. i.,,.3 0.74 Z ic:.:320 7,: 1 7. 7. L 2L1 (.1). 4 74 +t J.;,.6. 4.) 3 0 8 8,;- 1.41 7 1.419 1.3 0.2267.51 i' ).+41)8 i.4 4.'..83t) 3 S3. 1 j 8 1.,2. 817 0. 22 77 (..6251 3. 1,+2 )8 0. 79 797 2:.2,?2 44.631 0.844 u.?23) 2 2 ).662b4 9. 3.-?3 9)' 4.2 ),896P.3. 25 6! 45 4 1) J.'1 7 (J.22, t t 0. 7351 7 ).3 82 5:'. 3,. 859.4 31.7 39 4.9`5 0.723 U.22 1.lu 3. 22 7)1.9 3.9 ) u 3.557 6,17. 52-7 J.527 0.22') 3.8f.)39 ).2818',. 3.7 77 6

-225TABLE I (CONT'D) F-50 ORIFICE DA TA UO,I1VLE I 1' Y {IF ilCVilGA\, L C1t A. C 1CAL E NG IN L, t. I N iJuCIT P. AL IH.T SI. S.1}I[ I" t CI -r1'\ V C' 6EFf-IC I E:CI S l-u' )&1LLAT-:,Y FLCC S I E PLELLJ~_Dt. L_. —-- -'t,SK- 1 T - S1 NUM 3tR= 2470 rl k:AL S P IR 1, I A1 TTi - UPE'P AT;TIJ L-;3F 1i I 3 C. LCIt IC G RAV IT Y =. 7b22? v I S L S I' Y, CENTI STOKES i. i Jr. 1 t- t U i A;', L T L i. I i't., L -. 0 ft 9 7;S I FI C L LL F-Jl -T IT I I 1 N GIS ) 13.' h I I J,1Fi1( [1 L F'NU T t! / O I A ML1 I L. k = 3 e.), L (C f 1~ t; I P,) L A C F 1". q T =. l ( (!.~ f') t)'4 4u.'! 7 MAR 1, 191){'. S i............... Li..LLLL.. I:'t.J-.L v4T- ATl- CdJ F EL' /t,fi Ui CPS \L T1 IL tL A A I I, AL T Hi EANL RAT I 0.21 7 5.60 p.3'~ 3 i 47 2 0.2 2.l b t 1 4.7- L., I 5 8.73 8. 5 D ). )17.04 3 1 0.2992 +. 14 z+t 2 3. 4 C.) 8) 1 3.b 3 15 7 1 5.3l.. -.. _ 4_1 4.. 3IL _I3. O 2 l.3.1.)4 19. I 7. 15t,.'3 J4C07 ).4777.4) 85 12.7 0. 415 3. 7 J2 23.4 4.34 7. )425 J.C 521 ).,f 1') 13.2 3 ). U72 3. o,33 1. 1. [,tI I I. i,5.t) 33 L ).O 12.5.9 T)38928 7. 1 1 5 3. 3'. )4. 4 2 7 9.6 2) 4 i.o i 1 3. 3 92 1 3. ~)1 ~.'3,'. J)4. 242 ).7419:..J'T0h 1 3.. 935.,.'3.0,9 46g.u/-o d,.i'u/2 0.U'Z/ U7954 J3i.'o,' 13 I...3,~224.,*'~3.,k"t A.',')),..).' 1.?- -')., )'lT, 1.? ). 179?2 (. 1,.i 9:s 3. 1 it 21. 12Z5 ).27)9 9. J -.))i 3 8.1 3.'J 2124 J.,! 1~~.!,,; )*.5 9t. 1~0')'. 597,.'. A*i );o) ) t )",I 3 l., 1'. 7?1 [o(:,';) Lr).4't )./,11 0. llZ4!.g-/b5 t. 30't 3. a ). fJ. lo3i /J. /.',,,, t( 3 /t. 3'_) L i Z) 0)5490 ).?ti2 3 1.3 3 9. 89 7,j.K-,]1 ).125 J..2' o.j)j9 12'Z'd.2L69I11.).17:. 37, 2. 3. 91B51.,361 337.3 a.o' ). 120~ J:.J)70&JI ). L T' - 7.4. - 53 1). uZ 3 7.o, 7;. 0.12.2 i.7425 0.J 9 3.3 0.3 7 5 i) 1 7 1 l. 1 t)t 2. 1 5 ).? ~t 0. 12 2, 9. 7792 ). 1 8. ) 3'. 0 C).930 1 3. 55 5 ). 9.24 12 lb 0.6 504 i) 0143'2. 3 7.9 3. 9( 7 1I) o;.'~ 5 5 b D.2 3 I Io o _ 0 2 1 3) 5 5. 7 1 n4 12.tb I I'.... l.7_l 3?? l_3J._3__ ____.! 13o505 3l.5 95.. t 4. 1775.4 o t) 4j.37 1 55.3 (.7994 14. 7 3 19. 745 ). 74o 1.83J3 U. 5iu42 ) 3576 7 6. 1 U 8:93 3 -i.'.;16. 25 7,-8)! )'). )ll 1'i 7 J 53 38 i 1 q1' 5 5 aI 0. 4 1 /. ~,, 1(., - 71.;. 9 9).1771) 0.6158 3.23. —3, 55.4 0.6 21 1. /l.o A1.V".":) ). 5 7 u. 1 7': 0. 6441 23. 27') 7 t4. 0 I).- 8.,3 1. ot Y''t *. 0,2 ) ~. 4 2 3..., 3__J293 L _ 8 749 ~i.dt a * 11 0 3. 1 73 4 0.77 9 ) o 54 2 ) J 22 4?/X).~?]..b'5 /4 4'.379 0., 173, 08272 u. 2091 5+4,.3 0.8758 1'S. L_: _'1.t3 2.., Z.3~..~2_ 2_J.230~ZC O.*2 ~4;)9J.99:)02 71.5 0. oq 5ts29

-226TA;BLE IX (CONT'D) F-50 ORIFICE DATA UNI VLRS II Y l-,IIC.HICIN EC l HAf,ICAL A NGINLERiN DUCTCJRAL T i EIS!J.~ i f- I C [ 1._~) I Sf, C, Cfj E F F I C i E T S F,F'P tj SC I L L iA 1 j r Y -F I L., w............... S I_JtEN_...E i. E.___ LL'-Li'......................................... r.. S NUME:.-= 2470t I, it,t P\L SPli ITS Ai TIt MPFRATJIt: -!F: 81.3 SP'CIFIC 1<aGAVI'>'~=.7622 VIS(I-SIdTY, CENTISTOKES 1. 24t I F I A 1M TE R 1TIN_ LNCHE H =,,it I 9 UkI F-ICE- LEN,;TH I, INCHLS= ). 1'i 37 Ui~ 1 F I C L NG J H / IA L A M E T E 3-. 3:'+.')? 7MAP 31, 1970 PPLS r j. kF Jkt)PV - - _ TLQ t6 CL L CUt F INi(;UE S TV. LP: CU FEE l/t/tOUR CPS AI.T MEA N tA r It1 AL r ANt RA r I 19. 3 4 9.8k3 1." -J:3.Z314 J.292 0J.7:Jo?2.) J..7335 1. 1 C 1 1 7. J5 L.2,. 2 5 1, 3 94/ J.5? 7 ) ) 7 4. 5 4 2..6 ) 1? *7.49.3-5 4935_4 /5 71 3. J. 744 1. 635,?.4b,,)~. 1I 81'J.2351.5603 ).41 7 13.?2,. 4414 2.u57 Z 9. 7,t.7 3. j 2344 2. (.622 3) 2.3(49.9. 9 9 2. 58i) 3b.-4 3 >- 1. 2'3 2 0.6do 1 3 3 415 7* 1 ).86"5 2J..)2 43.115 ).'5' ). 23 7376.3 17' 7 2.) 884 2i.'J328 52.9'39., 7 3 2.237o. 7 916 ). -)2', i3 14.'. H53 " * 7' 4. 20 4 2.') 3,B:.23 D) 8 5 0.)7 D.2 1 4 7 1 t 9()8 2. 17 1 47.. 4 5514;5. 324 I. 2 3,1' 4 1.''t) 3.. 4 ). _865 "t)..21 7 23..1:) 1 i.2 5,i. 2)31.;581'1 U). 7".'U?'9. 5.. 1'1)72 2*. U 2 i'4.7',: 5.,'2 + J. 3'32,.643;).'+3 J/.4 *'. 971.5,.> t I.1,i.4f74(,'2, t,' O.. 4 9 7 1 -3). ~)12 3t.i''2 1.')1':0 ) 2 3 1 4,3.6169,,) /t 37 9 5 ) 7 lt 35. 89/)'!3.U,9r:, 3 6 9.!' 3133't/329:.).,'_.z):1> J 5.3 87u' 5-). 124 44.523 7.r: ) ). 31/ +4 ) 0.'7td z )6'. 3)91'i..'7 4..8 J21i 5o.1,9 Ui. 1 i3 1.' 7 ).t 1 4. 3 1'.9'.'3 CA:') 11L tt PLA.I OLNT =.U2::8),' 4. 57 MAP 31, 1 7U fpF', RF 1Ew F. _..: _ f:.j). E-O,_.............. ( J w $.......F.._ ". f C, S F.L F f: I fCHLO, S AAT E CU.) FE-ET /J.UR CPS L] 7L MEAN / A 1) AL F fiLAIN' 1 3.9 c20 3.929 1 459'),3. 37 0. 4931 J.o,.3 3 1.5'). 792.,_, 3'/.157 29.714..25i; ). 33.;).5621':3.5"-9%. 31.3 ).8,1048 39 3 1. 7 2 i9) )7 1 4*.'3). 2 )59 ( 3 41. 1 * j 4 5 -3 & i ii5 ). 4.53') )/ 4 3 2 3)2.8<) 3 4...- ~ 5~.)4. 1;.81 5.11 ) ) I. ) _',. 1185),. 11 I I 4/.3 ) 7z t,,'o,. i'2 d'3.4 -s 7J.' ) * (') 2')' 3. 1 (). *? ~ j,-,.9. 19')- I /,.' 1I:?.)1 1 7t.. I1 {S. S +/+! t').,'.J..'. 2'. J * )J * 1 ). 1 /"'

-227TABLE IX (CONT'D) -- F-50 ORIFICE DATA UTTIVERSITY OF MICHIGAN r1:(I.t-Ar.IIaL L.LNG L?FIRI,',Ij 3LCVf.UAL TH.ESIS ~i..F [ t.,f- I,[ Y:( 1,-,Ft.,. CJL[_'tF-IC, lLf4S F["'~ [":C.,LLAI~I;Y F-LiJ SI'-P fi L N J. _ D li. i I A, UM Lh'= 2413J M! NIA.-t- SI PI' F- I t. I. I TLfP F' A fUll If" t4. N1'L CI f 1 C 6UR#V II Yv'=. * 0( V(I LITY, CENTISTOKES L. 12 Ui,<!1FI! L. L UI A"LI L2( 1-i- I!: INCALS=.. J,. UF-IFI(_L LtF:.N(,i IN I IN(]HtES= )..:.831 0i,',1t f-LI c L LE:.NO-[H/ULAMLILR= 3.b962 CA1 1I SPLAC(.TE I_ ii T Ci= 1 2 9; )C t';,zu.57 MAR 31, 1970 1KLSt I k L U.RL -D_i~.u2 _..L iu __ _..S__ ~ ___.C..___....' F r', F C) ~' F FF INCHLS A T TFt< CU -FEJTi/HUR CPS ALT MEAN,: f IU ALT FtIEAAN Rt AI J ).719 4.1 2 4 O,.'.15u 4.LJ 653 b J.1935 3Z7 15.3..737 2.Th2 8.476 J. 2.8'). 661 0.29?? I.2256d 15.9 0.8O04H, NJI 1o.'~I i.).2'-J 5b 8..:3:...J. i.J L3. 7 7 JH 5 2.2 18 1 8.5. 17, J.5571').4+L33 ). 12o L3.8 0.8986 4.~1.2 3 4. 7:,, 4 5,,',,"J7 1.,.,. ).,)"!)'7 ['.J 1 3 14.' *t. 12& i 294 ~. 146 9.351 3,f~14 3.94 14.3 3j. 3t~33 o. 7,',) q_.).(,,'4 o,i. [IN J. 353. ). (5:I,, I.0( 12.8 0.?ht 9. (.4'i 4 L'.2' )J 1~[.'55/,'.,)',9 3). )4 T 1. 0.-,1' ).Ode 51.0) 1,05 4 J.35i.8'/ J.J6ZL2 1 13.2 7.9' L, C 5.8u0? 5.,', I. 5)')) ). 1451'.)J o ).)3.') 3..f I 79 3.2,4 11.5 - i 10 U. 1ct5: J.3.1) 3 1 J. 4' 4 i3.J3 0. 723V ). 1,' 3 1J..1 3l ).12,, 4j. o 9. IfO v] 2.-.,:5'-,"t'3 1.64 1. [125 0.4t62,.3533,'I._..8550 I':I. e5 2.:4 ~5.') 7.56-. 1726 0. 56 2 3.3. ]6 41 7 0.8738 I'1.BL i~'~t 1AL'.I_/,'g _"____Z..2_L_7Z( 0.5?ZL_,'_,Z.._J.6 13_ _ _I4. 1t 15b.754 3,8:.4s, ).4 13.17 82 6.6"'+',J.2)5 i+ 3.. h671 I 1 o. ~Z 3 3 i~.1~5!_r:?. c41 It 17, 17 ) O.i 73 89 J. 2 J 1 41. —I -0._9 3 i in.! 2~ 5S.;~5'., ).z~l~ 4 0.1'70'5 0.7/,99 ~.).253[3 f 41.i3 D.93 9 0 6' 1 9. 3.'-,.7 - 9.397.156 9. 1'93.7? _34.),+4. 8 0. 8927 1'4.07 5.: 2. I 4 249.2;9Z 0.2 093 L. ~ 0.1 1.9721 1 7.717 3 12.t6(8 i, " ).2544 931q6 ).7:)b6 6.4 9. 7.33 0.i__'7._ 1V _/%... 115i_02 5 5 7 J0~ ~IJ5 1. O-753.- -...... ZZ.? 711 3.6dI 2.93 2 3.2557 ).494,.3l 1 71 o.1. 7( 5;5.G:C+8'31.6'-5'.'! 1). 25 7 0.5592.).453'7 ol.2.'7'3 2'4. 75, 32.0!,' 7. 17~'). 2 14 J.,221. 3).413 o2. 1:.8 I, 4. J.2' -J~...',4 J.259't I. 15 J',. 3.6 1 o2.6 uJ. 8o,_ 2.i.,4, 4,,.. -..2521 ).1) 9. J. 1 o 3842 3 28..5.6 3 b 1. Z'J2:.5..>_J9 (~,'ZS__Z..k_F.L'Ji_9 4.2L d i...l_l...Lt_3_ I....w3",UL - - -, _ J.,- 2 5,_'.0,z 3_. - 7. 12 ).259o...54., ). 3) u.. 952.7:: 14.",3.. o ).331b 0.3118 1.'63 8d0 0.6337 3*5.3f- 17.528 1.951 7 3).336. 4 ).434 I 9:35) 81.7 30.7605

-228TABLE ix (CONT'D) F-50 ORIFICE DATA U N I VtEz I Y 1.F FlICHI (GA MAECHA NICA L E NG I EiERING DUCTL-AL T_AESIS I V[F I t C 3 I S c Ak Gt C U F F- I C I EJ S F L L \TJY -L -— SL. I. PHti fN, I.,)i-FR7 F 7 1 i NSK...' ST`IUMB Lt - 2470 i'1 iP, AL SPR I 1 S AT 1I'EMPVP ATij->`J-')' B. SPCIF IC GRAVITY=.78~9 VI SCLI I Y, CENTISTOKES I.?bS.............. LJ:.. L, i A T1.rI'-1._ _........_. Oit I Il t-C L ENT'; T 1 t INCHFS= J.1.'3 7 UKI FlI C IF LLNJOTH/i) [AMETLP.= 3, c', 2 C/' MI,) IP L A C [t E ix 1 =N. 0 C' 7t).. i 0':.~5' 7 MAP 31, 1970 PiL. i' E. i_P. P _ Hs FLS _._ ~ FF_ t-} _ __. __ I 1 Cd.F S't,, lREk CU FE T/HJUR C" S AL T MEA\N \ RAT [ AL T MEAN RAT I J,.. 783 6.8uv: ). 717 u.ldu 0J.2240 J.b52 J 1.6 ).67 )Eb8 J5.5t() 9.1.93 6.i4 ":. I 101 9.3,)12'. 3674 1 7. 3 1119,.C,'5 i 12.98 _ 9b l.7). I bo.,3_._92Z...J...Zu 6 1 7.2 _ 59_...6. 42 1 9.h'9:.. 7t., ). 4 H 2 ). 3 ). P? 279 1 7.2 9.85 1 b.,'i,2_,._: )..u j.I 15 9. b',.9. t I 22 I.3 (4 3.I1'~. _)~.t L 2.tf,' ).Zq'~.). 1 )'):,t.clJO ). 1!24!.: ~.'l )..~!t,,. 50 b. J.4. ).. 30 i..)'J5t 0.6582 ). 1:.1 1.. 1'. iI5,87 I).zIT s2..4 J..2l6 J.? ))6965 ()0.7J)37 I).1 i 7 1 ).3'9.851 4 I. *ou 42. SJ J. 5 9 J.i I.0 3_4 ti.1jI 1 ) 2. 3).3. 3855 D s<,. 3?,b.*.). I. 1 l 0 8 1 6. I I I t I 9 o )) 15. 135 $. %'t.f.16?,).)_,.). ] i 33 1 1 tt. J.5 2 4' 96 ]. sts(); 143.')7 14 L 6.? 715 5 U'',8i ).I:,''t 5 3. 6 41 3 2 1. 5jo 53 L 3 1.j 9 2 35 ) 9.44o 9 J.6 2 2 3.2. 1 7 64 3. 2 1 L6 4. 43 3. )271) 9:3.4 744 5 7 1 3 52. 3 ). 7523 L+*. 753. 32 3... L_5___.6 t6 8i3O_ 5 -_ s... J C4 4.i)2__ _.'h2 7 342 2 2.3-) 4 u. o4-* *8 Z. 3 62 39 3.? 4'-,.- ),-i. 8,5 ~-9. /I`3 t1. 3 o. 120 J.273J4 6.690 ) 7 U.4.31. 4-. 8461 32...t') 41.7 45.o' ).I 439.746 ).J5 79l'+4. 1 0. 9559.?.2.4t) 4;.3 e,9,.667').27j) O0.70b7 J.3)'3d!,+3..8CJ 23` I2.''' 6'2.;, ). 621'7. 743 7').7627 J. );)'. -!, 84i)~: (-Sf. 7441 t ) 4' J.24.:. D J.3 j.'3353' tJ.3.J. / 7.951 2') 1.:;,~''',': 1:'.. *', S'). 5") 1.: 1.'"86? ~."'.) [I t:,.'.1 r'. I, I, a,,.,', [.244 1. t J./t)').'3L "J4.3 8 1. s'.. 1 l.55' t I* 1 2< 1*1 ('+ L4/ r J t'.(4!,1* 1,).71 72 I: ( 1. (/ 1. j!.3, )l,..l9 9. 71 i:j.s. i, 44'.9'1, i.'7..7. u512 5.,_1.777 1 4 L. 3 544 (,U? 1 ". * 1 3 7,3 37;1,6 7153 0). 2 9.) t 0. 8(, 1, I.:) 4 J? 4 6.-, ). o:).36 - 7 25 1 J.5 ) i. 4.8 4 1 2 4.),&'I-9 51.21 4 3.855 )3 11.8059 4'~1~ 3. t38b 6

TABLE IX (CONT'D) F-50 ORIFICE DATA UNIVLRS [Y UF AICiHIGAA, MLCtHA-f ICAL LNGINEE-_ItN DIUJ CTUfL RAL TIDUtilS.. OR9IFICE [D[SLHARGF CUE;FFIC, IE,'\[S FJi'" USCILLATOkY FLLW S T FPHF N j rF):-RF 7 1 N SKI ILST L 1Ul kE K- 47. AINEA.L SPI.[ 1 T Al Ti FMPFp ATURE LJF JF d,). SPL C I F It ( kiA.LT Y =. 782 ) ViS'tiKS'fY, CENTrSTOKES 1.. 54',l I ( L L)I A,f-l.L", 1- L,` It IN C HESH O * /t'~! Iti'1:'l (I.- L' [N 1GTt I N IN, tL: S ).1 I 1I Jt I Flt I f' L T 1,iH/t' I A,`1F T.ki. C 1'P l, 1 PLA. Ct: L- lN' )'7 J0,..,t',''..> /) MAF', Jl, t lO7 i t. i.J t. L,i t1...........i.......... iA tr..I Iitiut: S AT[ fE- CU F l E T/HJt)UJk CPS AL l' FA J, A 1I I A L T,.,N r ATi 4 3 0 f t) ) 7 9 7 3 73 cj; 1) 4t), t _ 3 5 79 1 it I. ) i 4 5 2 A 7. H' l 4 7 ). 4 IC) I - 2. 5 3'1.8 J, 6454 4 3.12 1 1.23 3.J 5 7:.'4779 ).2 3?2) 1. 6 94 7 5. 0. 6633 _;.b * 5(.6 2,.( *2 S %J. 3; 7 I)3. 46 78 3) 3728 1. 2 5 4 7 3.9 0.625 4')! 7 3 2 6.21 "7 1.73,5'.4791 0.45-(38 1.C.'+2' -75.7 0.o7', 7_ 5 s. 161 s.34.:1)+ 1. 4 3. -.). 48 \: t.. -4 7 7 7.2. 7061 5 *7 CQ5 43*. 1 5 4 J./. 4813,6 4, 2. 751"-)'16 1 r). 7615.. 4.u 471.u') 1.234..4 4737 3.3 f3i7 )3 7 J91 75. 6. 723`'5-,.078 U 7.4. 7i., 1 74 ).4 73.4:u. _ C.)..6.. i 8' _.J7934'5 3.,', 1 55.6:,+' I *1 4,2 7).4'7 7412 J. 6459- 15.6 ). 7Z2 (7, 1.~4'.,4 ).;.554 U,.4c3.)8 0( 2(..53()3/') 7 1.3. T75'"

-230TABLE X ORIFICE DATA, L/D = 7.23 UNIVERSllY CF IC -ICAN IECHPNLCAL ENGMi&LEEK L~CCTCR-AL THESIS OPIf-ICE OISCHARCE CCFFICIENIS FCR OSCILLATORY fLGW SI FP.t-Lf J. LERPF INSKI r lEST RLtI EEP= 177C,IINERAL SPIRITS 1 l TEPPERAIURE OF 89. 1,FECIFIC GRtVTTY=.7 7'P, VISCOSITY, CENTISTOKES 1.177 CR FICF rIAPE TF[ I1.C N 1NFCI. -F=,,'j51 C I F ICE LE CTF IP I C -ES=. 374.5 CRIFICt LENGTH/L 1 tETEF= 7 229 7 CAM U ISPLACEENT=I-.CC75OC 11:41*.5 JLL 30, Ic7C.FT.hSLRIL......F L ___ _. _ F i r k S _ ERLQ LF ___ P INfCt-ELS tATER CL FEET/HOUR CPS L T MEAN RATIC FLl EAf RATIO E.L.3_95.....5,36. C_-2C.e3.C..2392 C810t8 8r.&5.,_7. 4 Q7..4. 2.E. C5 21.O 4 1.243 C*.19S C.4Ec7 C.4021 81.7 0.7708 3 6. C 63.701 1 CE 6 C. 1 14 GC 515,. 215 87.7 C). 186 4 4. 6. 738 C 6 3 C.21C4 C.e8426 C.2497 87.3!0.7454 L,101 5,29 2 C,fi4129 C,Clt 17 C*,271 C,271211 1 5.6 0 7131t.4 21.C1C 72.26 C.C622 C.4596 L. 1363 26.1 0.7236.227 1.070 C.200 C.C64C C.I 6? 0.996J) 26.5 i.751 3',.47E 62.71S C.151..Z 1 C0.ECC C.0798 26.6 0.7334 C 2 4 5 7 1.34 4 C, I C.24 3 C. 5 1 5 3 54. 4 0. 67 29 S. 3 E 21.826 C 0.44 2. 1. 3 2 C. 4 4 2 2 75 51 5 5. 3. 7 4 1 1,.26E 41.551.C 295 O. 1342 C.6:4Cb C.Z2 16 55.7 u.7250 1 i 5. 1 6C. 314 0. 25; 3 C. 1 3 7C 228 0. 165 5o6. 9 0. 7657 CAM C ISpLAEA-PF t T.C 1( Ot:' 11:41.53 JUL 20, l' 1C t F LC L S..L-E.E............................................... - _ _l. INChFS AITER CL FEEW/F.OUR CPS LlT PEAN RATIC ALl TP N P ATI1C 4* * 4 4 *+';0* *Xs 4* **4* 4C**;' ***** 3.t24 4E,-53 C. -lE C.C1e1 C.21C 9 a j832 2...7 7. 1 -3 ~ * E I. E 7 2. 44c C.C839 C.449l C, 186 26.1 751 1 _E. L7 40.621 _2C3i C 83C C.44EO C.]268 26. 0j,-734 1. 5 66 6,170 C 194 C3.' 8 C.F28.C 1)38 25. C. 7133 12.7-3 2 378.C C3 C... C 2288 0.8020 55.S 1.C491 I *t icb 2 2.57 6 C CE C. 1836 C*4661 U, 3939 5 711 O, 7090 17,643 39F.175.45C C 18C1 C0, 4 6 C*2786 56.1 0 7466 2.2 t2 t:6.765 C.3C3 C,181 Ce142 G,0.2234 56.6 C. 7202 3.184 12.418 3.z477 C.2865 C.2231 1.28, 42 8S.2 0,.4576 4t.26S 21.S13 2.112 C.28=6 C.4774 0.5940 88.3 (-.7371 c1~.' 7 i 4_,46 _.1.217 C.._2_-3,.536 C. 4335 82 O. 712z t 5(.(~C 67.541 C.2S C.S C152 C.4'.&4i (. 1. t c34.' 12?4

-231TABLE X (CONT'D) ORIFICE DATA, L/D = 7.2-3 LNIVE S IS lY CF ICt- ICAN,tECtH ICAL ENGIltRI~ lG CCCTCR&L THESIS C'IlFILE LISCHAK L CUEFFICI[Ehl FUR CSCILLATORY FLCW S - __ STFPFF J. [L FRF IThNSKT lEST hNLVBEF= =7C I[Nk PL SP I PI T S tl I EMPFR ATJR F P. PF CI 1 I CRtV I I =.77L7 ISC(iJSI1Y, CENTISTOKES 1.'1f PIf-ILL LI/P.LILt irb IhL)-LS=.*01d (1, I fE 1: L NC I -F 1I INC- l.CES= C.3 18 CkitlItt LtENOCT/L.IAPETE= 1.229-7 i':4'1.3 JUtL 30, 1 7C FF. L E CF'L _: _..F..._..S __ _ LL_.S_FR C-...... INCFES kATEk CL F[El/F{]UR CPS aLl MEAN P A It L ALT F N RAT I _........ 4$ 4 4 4* 4*.:':.. 4'4*4* **4 *** 4**'?'.& t 6. ~ 7 L'.5 C. C c.2715 C < 3303,2_3C3, _c77565 c. 1 2 2.271 ",.418 C.CE49 C.4 6 0.18 19 22.0.7147 _ 5 t1I 3.32 C.. 2 C 5. C. LIE6. 1 -2 2 1 9 0. 8225_ iC.22C C6.9H7 C.1 C. 1 C.C: I C4 C.'-)bo 21.6 0.'/56 1?. 3 2 4.2i 2.136 C.19t; 3 C,. 282 0i.6 559 5J. 7. 799 1 I t- t~.136 C1,. E 1 C.1l4'C C.4618 C.4201 50.3 C.7?)9' 17.Y24 3 5.5q C. ~.48 L.118 C t 4 C.2967 49.8 C. 7631 1C.(F C 4.55 1.296 C.lg12 (.tC 1 C.23b2?- 49.6.-7282 5C.1 I 11.tE1 4i.338 C.2 37C C.24&2 1.3518 871.4 0.524(; e. t "~t:.C ISC4,., L 2.tl r4 4 1 C. 4 F' C. -V) 8 i 8 b.2'.I 4 Sb 1 (f. Z.:. ~. 1."i', 1.SO1.3z,4 l 7 C.441 tC.S 366.t,.? u7 8.3 LL? ~. ~ t,4 4E 9 1 1. 4 77 j.3 5 _.F. 2 17 C. * 1. J CS." 5) ('PaM i,I tSFLACI CtIV: =.(. 1ICO 11;41..2_ JLL 0, 1S7C....._ Et'-,L FF 1f1 CS f:l F(: S -FQ CLLE ___ INCES AAITtr CL FE[ T/FOJUR CPS ALT P EF AN p R IC PL1._Fh.- Pi'... __AII O4 444 4 4 -*4 * *4 *4*t* **** **4* $4.9C2 12.1 3 t.Ei, C.42 4 C.2.A44. 2.15. 1 86L_.54lCt.C5S 27.tC 5..131 C.1(7 C.C.18 C.9325 83.7 U.7126 ( C. ___S.... _. 51; 1 7 5 f 7 8. 1 _ __ _ lC,.51. E 5.21 71 1-c 18 C.5 2 3 C.e2 70 C.6316 85.6'.7968 1. t8 1 IC.4C, 1.275 C.1 72 C.2Et2 C.0'12 28.7 3.3 6 r 4 L 4 7.529. 2 0.17 7 C. t 7cC. /1, 2.l (". 71'.) ~ -.~6 1 7.2,C. C.3. 0 9 - -L3:_.L.2~.C... 4__2_. lA 1Ugt3 24.-i1,47 ci 2.6C1 0.3320O C.27f l 1.1)31 54.4 4. (b29 tc. 1 2C.6I5, 1.' 34 C.3414, C. i44.13 732 55.9 C.J 13d * 4 75 4.5 5 C. 2 C.3 4 1 C. 6 6 i9 C. 5 1,: 7 5 6. 0. 69 38 42.42C t7.1Io7 3.322 C.1384 C.8116.41 69 55.4 c. 7158

-232TADI3:, XI ORII,ICi DATA. L/D UNIV SFISC I ICt-. I /N ~ ISC AL GIYNLL 1T CECTCOKES 1L THL.3 S13 OR If ICE C<RHAFICE CEN Gh 1t ICES I FCP CSCI LAi t=Y.-LUW STIfPtC-F I. f3FRF7NKC-= f_ __ _2I_TEST LMLEft iL7Cl i teE RAL SPIRI I 5 tT I tM PERA T U k CF 75.:3 P E C I f I C G C I T=.A 7 T Y 74 vISCGCSI1Y# CENTISTOKES 1 323 CfRIFICL I AiETt iTF TN(;F S=.518 - CRIFICE LENGIf IN\ INCHS<= 2.168u C IF I C E L E N C T F / U I A P E T E R= 3.6293 CAM CISPLACE'NIVTI=.CC75,C 11:41.53 JLL 3C, 1 7C _f.PF FSStc. IF EF- _FS F [WS' _fl _A _ C(iFF _'F t( CFES WATER CL FE El/f-OUR CPS L t T I"EIN.IC AL 1 F LAN RAT IU *44*4 *4*4* 4*4* 44*4*9 4*$'*4*4* 444 *44* * 2.'s(c 4.2Jq (.5 6 C.C 14 C. 1>84 C.3261 2D.5,.664 3 39 t 1 1. g96- C 2EF3 C.C6 1 C3 4(C r6 C 153 1 25.4 ).7786.t4_3 21.549.3 c..C.4 C _. 5' 5? i_.C_ 1_22 4 _;. * 93 4__, ___ t t, 54 C.C19 0.117 C.6 1 2 C. 7&45 C.C 37 25. 4 C.G 5 H', (AM CISFPLACE8ENT=.CC750O 11:41.53 JUL 30, 1c7C.... lLE__.-R[LPS f l (hS F< FkF il Q (: f: f-F _ IRNChLS %ATEP CL FEEl/HOUR CP' Al I t,N R/ATI L ALl FE AIN RAIIC $44 4 4 *4* 4*o** * 44* 4*4*4 4444* 44* 44*44.47 -/ 4.026 1.6C7. 12S3 C.IE 4 0.6d663 53.7 0.6815 ta.5 1 5.~d4 C.*53E C.12 Ee C.4C(28i L3 16 5 i 3 7'.73 3,.. _...C.... 1._______... 2 1_ 5_C._ r C _ 0.1 7 d. 1 2 cd J.453 (C.677 (C.l'C %:C C.C56 I C 32;$2i.3 7.734" c.141,, 5"5C C.;26.1944 C. 1110 r.252k 3. 7!.7649 CAM C I SPLAC EtlK T=. C 1.SCC 11'41.53 JLL.30, 1S7C.F..FRFSI, RF [HrOCPS t S __....... (c1]F- F INCh-ES hATER CL FEET/HOUR;PS LT IV EAN RATIC ALT fP A N RATIO 5.765 5.048 1.143 C.1467 C 1942 0.7)53 2 7.1 0.6273:.c~= 13.641 C.647 C.14Ei C.4C75 C.3635 24.9 77S5 C 1.3C. C. 1. 15 C. )1 7 r,7as C.35.'. 75 ___ 1E.5CE.1.3C C0.36C C.1519 C.7E88 0.1)23 25.5 9.7996 1'.204 4.346 3.i72E C.8 l]E C c.i923 1.t58C 53.6 3.6694 3.4 t 1 7.86 1.3' C..3168 C.4C t6 C.7 75 53.3 t.7 7 13 r7.2 1 33.330.6E19 C.31S2 C0.SE99 C.5i 30 5. 0, 1530'.4 4 2. 4 1 C. C.5 3CL C. 7 C.7cZ3 J.tH32/ S, 9f. (1 rr 794 f. 6C 54.461 1.48: C,;3DL C 8rL4 C'L. 1 4,.91 J.'.7uz

TABLE XI (CONT'D) ORIFICE DATA, L/D = 3.63 ttLNItPSI1Y CF FC Ft I C PN frLC NPhICAL ENGINELFIbG CLCICR/tL THESIS H IFICE LI CHARCt CU(EFFICIE IS FUR CSCILLAT CRY -L~W........ _ _. _. SEPF EIN.J. [FRF1 hS<I IE ST NI'v LEEF= 1_? -I.. IINEILtL SPIRITS tT TEMPERATURE CF 77.5 -PLCIF IC GtRL II-V=.l 41 ISCCSI1Y, CENTISTOKES 1.283 -f. ELE U ~ LUL lA l TA _iE ITn- h _ S-35 1 8 _ C(PIFICt LENGTI- IN IN(t..-.ES=.18d80 C F IC L EC'T - /C I E ER= 3.6293 (AM I SF LACLtPENT =.(C 2CC ll:1'.53 JLL Ct, l7C t, L1..EI. f LE ILP_S.LLLS -—........ LL A.. —f-. LNChikE 1AT[t CL FEt1/FtUU CPS, L T E,AN FT I L aLl FEa tN RATI U 3.5SS.C 421. 7 C4 C CC,CC C.IS17 C.51u9 25.4 0.6771 c5.: 12.549 C.462 C.CS 1 C.4ClCC;.2476 20.7 u.806r.... 1_l...5 _.26 C,103 C. i c....16I 2.6 7.2722 _ 1C. J5 4E.56j,.2C7 C.1C75 C.7766 C.1384 27.* J tb883 S,CoC 3.926 2,302 C.2C7i C,1923 1.LtJb9 513.8 0.7030 13.(C4 11.104 C. l4 C.21E2 C.4182 0.5218 56.b6 0.7333 13.043 9.-413 C.443 C.19 3 C.57=19 0.3360 50,2.77C2 2C.15C 51.(,47 0.395 02CSC C.7829 C.2617; 54.2 0.7947 22,.2 1...~ 11 2z.391C A i L. Cii.i.A6.i....,1d 19U1_ i. SLU263 3S.4,i 31 2.l18.16L C.OC'3 C.t613 0.4t3898 78.9 * 6.7748 4~3. 4;.!38 (.cS12 C.]1C9 C.EC19 C*3678 80.?1.8230 (APt [I I SFLA C E E rlNT =.C I j C C l1:4l.b3 JL> {0, 1c7C - L_L....liL S __....L...hSf.. F I 7/LE t- I\NH S hATEt CL FEEI/FOUR CPS AtT E"[AN,ATIL ALl,PEAsN RATl *4** 4 4 *44* * 4*$*4 4*4**. lU2 5.C1P C.b 3 C.C 73 C,2C29 C.4302 27.2 0.6509 4i.374 16.714 C.262 C. 8 4 C.4333 C.2017 27.,2 C. 16 83.,_>5Y2__3_OL._.I...l52. CC..C9 C..t14t8 0.1446 27.1 I.8117 t 9;t 3q. 2 (,, 1 tC *C7 7 I 7 C. 7 $ 11 C. 1 0 7 2 24. 8.786 3 9.;;Q;.4t 1.815 C.18 77 (.1927 C.S74 3 -5.-4 C.5s66 14.I 3 17.-32 L.C28,.1E64 C.4393 C.4244 580 0, 7521 2C.i755 3 4.349 C.604 C.1945 C.6161 0.3147 62..5 0.7646 1.&t 2 54.79 C(.356 Co1Et7 C07666 t.2436 58.1 0.7511 1Ci.'t? 5.1C df(L.C C LlLL7.5.71 4 42C~_5 9 5_ _ 71. 73 1.'5 1.800 C.2721 C.42F6 C.67348 84.7 1. C.78-. 1 4 2C.ct 15.1 55 C.2827 C.6246 C.4526 88.0 0.8155,.(t, (.4 7 2 C.6 4 C.21 5 C. 765 0.3633 86.7 Cl. 7965

-234TABLE XII ORIPICE DATA, L/D = 0.62 UNIVt-HSI Y CF ICf-IGAN IECFA-C[lCAL EthCINEELI1C LCCILKAL IHESIS CHIF ICE DISCHARCE CGEFFII EN1 S FCR OSCILLATUsY FL(lN _ SIT-PI-FIN 1J IVFF!F7 lhS KIT _ __ _ t... 1 51 I E ER~ _- 7e02 INEI EAL SPIRITIS 1 1E, PPERATURE OF 75.2 SPUlIF IC CRtu TvIY.7?F2 \ISCC[IlYt CENTISTOKES I.3t ______ (f'IFICF rIlhFTER It thNF F. S-,5l8_ _ Ck IFICE LENtTt II INCI-ES= 0.0319 C -IFICE LENCGTh/LlALT I IR= 0.6158 CUM L ISPFLCEPENT= I.C(-Ci5C 11:41*,3 J6L ]3, 1lc7. e f1. S, F E C e _i........ LD _ImS_............................k_~.....C_................ IhNCFE-< WATE!t CL FEET/FOt0UfR (PS ALT 1EAPN krTIC LI EPh RAT IO x**4* 4 *** ***ft* ***44 * *** **4** *8* t*t'* 2.,71'.S9 t Ie2 C.C2. 2 0.I222 1q.13 1 2 6. 1. 74' L4' 4' 2O.,;; 7,( 71 C C6'7 C.476 ). l,2t4?2'5 0? 7216 t ~2. 7. t,5 C. 1.. ~L -..' CL.i. 0 2. 4 1...__ 1C.73 - 3, 32 C. Io CJ.C' C.eCqO [.b 2 1 2 7,6. 1378. 251.2 5 1 1/COC; 1277 C2LZCT 2.6Z22 b3.O j.5J5-1., 2 4 5 1 4.5 q 4 C.5a 5 C. i225 C.406O'. 1 7 5C.8 C. 7 713 10.tcc 4.C17U J.2t6 C. 12 7 C.l 1 C7.256 52.8 0.7094 1 4. 1 t5:.t e9 0.24S C. 126 0C.717( 1 C.1o2 / 52. 4 g. 7348 i S. 1 4,.7 7 3 L 4 C. C(3 C.- 4 1 C_ _. 5J2I3_L _ 5. 6 0. 5 8 7 3 5.c7L 4CA.446 C.5SE C.2CS2 C.~223 C.33o2 86,8 0.6853 J4.7'$2 tA.',776 C,5C4 C.21C3 C.7781 C.2702 87.3 0 b800 (tM C I SF LAC EMIN T', 1C I C CCC 11:'41.3 JLL I3' 1.7C __ES,L_ L.. _ _LLS_..... T.L.L.. INCFE S /TATL CL. FEF /F)UR ( P S ALT1'E/N kAIJIC aL 1?EAN RATIL L. it: 4 4 2 4 2 C. 12 C 7 1 C. I 5 5 I 79 -3 1 ) 2:. 6 4 7 1 c.:4 I.$ c 4eC c c;1 C.,C' J I4 7).'% tXC,1;.C 1,...6.. ~.1C;.IL13 J! Z5.., O,7L'4 I %.~2_.564La 1('5,t20 0. 168 tC C.C8191 C,11 Gt3 I.' 3 25.3,. 412.7:3 1 6i. l 1.Ct.C C. l(~: C.242 J.6W84 5.6 2. (1387 i.435 1 7. 19.c4 S. 1 7 2 C. 421 C. 24 55.8'J. 7294 15A7d2 3A, CC4 L.403 Lt. 1C2 C.6C7 C.296C 56.1. 7074 1.C 75 5. 876 C.3 2 C. 176E C.7640 C. 2314 55.n i. 7166 LS.; 4f q 57 C tC._C_2 L i]14 C f.L78d 0.372 H,Ljj3 Z 596f-_ 41.15f 6:E8.49S.tl~C C.277q (.77c12 C.;3512 86.5.6' 3t

TABLE XII (CONT'D ORIFICE DATA, L/D = O. 62 LNY [VERS!I LF [IC- N16N ECFPNICAL LtCN\ILLNt1C LCClERAL THESI- IS UkI F IC: C1Ct-.RKCE (CEFFICIEN!S FOR CSCILLATTCPY FLCA _T_F d_ t-PtF J;FRF?Ins <I TEST LdEtLR-= i~7C2 INE AL P I P I T S IT T E MPP A T U R F 7. 5!PLC If I CR \ llV =. E 1 TSC C SI1Y CENTISTOKES 1. 33C IfICL LFNCIF IN INCHE S= C.031 LIFILCL LENCTIF/IHCtEILP= 0.c158 L/ d?; )IC 1F LAC t- ~E f T= -. 1 &(e. 11:41.~3 JLL 3L, l'U C.....L. L. A:-.F " LL.S L 1._..._ L LaJ~._.........E....Li.I.L.LiT:_ INCI-ES t,ATEk CL tI E/FHOUR C pS A/LT PIV E T PTIL /PLI FtAhN RAI IG *4 t 4 * 8 447*' 4 4 * * *44 4t** 4 4 * * o.E.t 17.44 CW.&e4 C,15E8 C.1CJ 0.8)11 2 6.17.55 9'i 12.i b 2 1.CUtu C CC7 C 14E5 C.4274 3) 3474 25.0 r,.6758 i.5% 4 C.te35 6.38 t."14' C. 317 0.22 15 24.2 0,.7174 __ _ ie. 57 5-4.L i6 C.3 C7 C.15C4 C7.E39 C.)19?5.3 C1. 769 it~4.1 71 1 1,0'2' I2 5 Co1 17 C. 1539 19 6 7 1 2, 4 0 g 23 8 2;2.5C 25.C,4 C. E 6 C.13 C.4111 0.7743 53.f6 ).5853 2.2dI S C.c55 C.i2 C.I i C.t' 0. 5355 53.4 C. 71 7 1 3 4.4 i t.1( 4 9. 3 6 C.7' 3 1 C. 4 3 4 1 56.5 0.617 ~~'i7_..;.-4_'77 1LL *....C,.C.1C3 C L.3. C-:..12_9.. 8.5 2 _ C.5.24 74 71?.t ~3. 4'-i,L (f..&57 C.t0(26 C.'77E C.6'455 84.6 G.t bl4 (eAi 1, I PL ACL EN T=..C 1C, iCC 11:41.b JLL 3C, 1 7C Pf cL.S L6._Fi_... L L. C.P_............... __C_............ _ -S INlCES AI[Tt CL FEET/FOUR CPS A LT PEAN 8AT IC L 1 EAt t RAfIC 84*t* * 4* * *4 **4 **4* 4 44 4 4 4*4* * ** t:27 5.275 C. 725 C 72 C 1SE4 C.49 00 25.2 0.6267 E.71C 1 8I E 8 C.461 C.CC c C.41 C9 C.23 E 4 25.4 0.6861.2(;..~7.114 C 5 SC C.C L'C 75 C4 Cs 583 25.7 1 7450 12.144 55.899 C.'28 0.CSf5 C.7745 C.1245 25.0 (*.75i7 1c.(tl 7.592 1.5& C C 272 C *148 C 1394 7.0 C. 5131 1S. t1 1.q 1 C,3 C C.2 4 C.4G483 0.6555 68.8 0.!635"5 1. 3 4.t 7 C. 7 CC C.2 7 2 7 C.6CC 4 5 39 7 0..7. 4 5 35. t. t- S c.52 C. 5 2 C 26 7 C. 7 5 C.336 63.9 0. 7 i4 C. C 5 2. 1i6 C. E 5 C.5 0 5 C.C42 C.58C5 2 9Z? 9. D 37.. -.. 7 1i. 724 6t,2c C. 1 7 C. 4 10 C.75e7 C.457 3 9C.0O 0.6730

APPENDIX C LISTING OF' MAIN PROGRAM AND SUBROUTINES MAIN FLOW2 Steady-State Solution TF'OW Transient Solution FRIC Friction l,actors OVAL Quality of' Fluid iIl Each.I'le,merlmt CDMIAN Coefficient of Discharge,.I.'-0O Orifice CDSQ Coefficient of Disclharge, Square-Edged Orifices for Pulsating Head CDSS Coefficient of Discharge, SquareEdged Orifices for Steady Flow FPROP Fluid Properties CI Parabolic Interpolation of Tabular Points

-237Ern Tl! TI r l CIM! FW'A^N 10-Y-7 1 11:57.1 4 PAGE 000 T' T r n yT -r'r., ", -III' r'F p p r.I S[I j4 VI VI SHF,ICS.P'.,,P',P7,RJ,).,FL,C H,CSJ, PI)KIJP, 1 eI t, /, JA/, F, F., r C', /, q?, tP P),F ""!^. t~'t _ ) r!'r SI'. 1, A, RLD,I i,A,L f,R[,F VRS,,VISC, t f, I)P,D, ~' 1 L r.~ t ~"~' ^''' Vl /'t'r',t[ b ),')(,,'-;, (,.t,^l,), )'), 4' ( j -! 4,,'(),,V; l.]'~rq'~l,r'q(,,g.~),l. T',;.V "VI sr ( r, f'( ),''t L ),'(t5 (, It, FL,,A,'(' O I,"*JUNC,~"" 1 T A TtroL II'Tl.'r- t 1 I f. - 1 I~"~'? Rf-/q )(r,'h. ) It -'$'tP? F.) —.T "t'')' " r 7 P F 1)'IT =, N FNO= 99) n"'' ",';,( 1,,itP ) = A I(: 4. ~h.' —'', rhf'r 7 1 -1I, r:.111.".(' ","', 1. I t1(1)l, C, t') rji -T..... ('I I 1 1 I: I I,T ~) A^ p.'' f( J ) -.f! ~ N!), [ 14 7111p I'' I r i pi-, A Li r r FP I) Tti' F JT[ "ICT Il3NS,T THE ENID S 3F EACH ELE'E.AT "";~' IF(..TtJ).*:F.,") i')J TJ U0.'r n -, ^," 1 F t $ = F.'T t (.I 1 ) K tt IM I I) L....r J I L r" I Jt= _'i A *')K) 1'C l ~ rT -J"f I +'"': I I" J2(I )j T + I1; *.7 n~~~~~'1 1, cf'''1 Vt I

-238-,, t,-, \ u q r~;, I "A T, l| - - t71 1l1: 7. 14 PAG( ()Ou, - aI f "..',, I L' T - () ^."/, ~, p,-j qr f =c I ^. F r,t I 7, f'&(1? _ t* " "-? V' F -1V 11 C 1. T - r'' v,t ( I =V) ( 1.. I II'"> r i} I r t I t } ~ Z { | I /' L t Pf I ()-T f I ),'l'.. I C.- ( (1)r'F * O) )'(11 = ( p1 (T - or (fl) I!= -.-),, r 7;,, - t ~ { t * 1 J'C ( 1 * Tt'f L 9;( I).u'F.(,) L ) +CS(, I).(;S 3, L L )''... > t F/ - I If4 tV/ 1'. ~,' "I f','-:.c' r t.r(I 1 )'J'1,J )r.%.)S L I "'', I1( II (.1 L).I ). ~,,z!? T(.J= T P ( 1J PT JT ) I, 14'., C. AIL F'Li,2?( ni,pT,PT,FI,T.P, p'",FL,II1,VISCA,VISCF} I' I'Fr( " 7 14) z r I If t.F. ) Tr.I r+''?,Ff) *t az t 1 ( 11t1,' 3',, JIj. )CTINS' "' I. t.' l rT I',., 1) r "'77 lIr, r r'Q' AT( l ",( X,''RF S'iIRE, LFI/S)- iI',I 8 X,'FL(, L,/-tP' ^1, Fr;'AT2vY'gi,,X, A 1TTAL,,''.')F,.,X,,lF ),, IX, I T At- 6 X, AI,," F'.'',' I, I'[ /Titl T) t 1'. Ar^ \T t H>,' >I T F' T!T INS I Frl'., l? APl-'I4), 1 1n!5 X I vJ= I I N,\J'!J,~, ~ ~ ~ ~ ~ (J'?n; 1...... -!.r ) 14,: T, (F 1) \!<'; 8.................................) IF (.J F., ^) WQ I T E, 15,*...........P1V( J, )3 =n)( J r "~'a 1,,:1 A=,J( J)!,I=It T....+' FIF=(Il.'J-(J))!l f.... I =: r ( J ) / 14/,'* *. P'~:'~/I ) / 1 //,. 1"!'r, lr',,1;,) I,'~1, - r, r4, LIT r l, r F I J J,.,,"1 I' *-,. l( 1 1,,1 v., f' 1..' t )

-239-.: rT A tV r ",: ll' V'ATN-J n-71 11:57.14 PAGE 000 1 C 7 I 1 X I 1 1 y 4'' 21 2l_ 211 r~f 4 1 ( ~, CFJ 4 * C, C.,, >'/ >,';<,.,'X T )ITAL' i, I, 1', y * 1 1 T / r'r' X,'NU A' ) 1X I L /CU- f', 4 X,' RAT I,) r, rx 1 X I > r, > r. J - I; 1-fl T~~~~_) JC t I wt -'1 5 f( 1.1'1" \' ". I j r 1' 1 ( r1 A I I T I PI ( J ) I b'1 f r r( 11 7 JI 1''(.J}'' — +\/' (\) }t 11 $. ~ l - i, 1 "'. -) r. ), 1 7, j ) - 12'.3' "),I y!.'(.J )1 t,,'! Tr1(, P1,I.,' W"! r. T., I I1 I (1 1,,?,1,' 41 r - Ct I)'''' T ) I.' l (, ) I) I A T I C I C "71 2' I (:!',' t ~ -'~ f I)'' 1'>. "!1'='-( 7.-" i.') 7 -! T (' I T 1 "F(!.!,'<,? E( L:h.,,N'),t.". X,1F.4,F7.3,FZ. 4, -/. A 1, 7., Y; ).,t,- 1T. 1 7.' F+' 37 F TI,Fn T, T T - 2;rL 5 A R4 T F S

-240FOiilRAN LV J COMP~ LEh;LOW2 09-25-71 12:0d. 31 PAGE OOQ Oc. 1 SUbL, JLr 5L[L FLOLu 2 (L',, P,l,,, L, iJ, PL,OP,[L, Il 1I,.VISCA, VISCF) 00n2 IAl1c.Et X O, H8ZAL * L 0004 DOUULEI PLdECISION D,A,IiLL,,,,FT,CS,iR HO,RiOA, VR,VISC, uiLOf',DP,DZ, 1 E, E H, TOL' 00 05 mJJidLtt PL' uC~LIJ. Pi(~3,?J,B,, AA, EP,A Ak,A J,PZj,DR,SUi'l,'LOIN C (,J'JOL;~ r('$ L~ l.;~ ii Ec i. IN ct J, I,P,rL, J, FDOi,h L, Vi bCA, V1SCf' 0007 uLi[Ei, Si t',; (50),i~i' (JO),~5L' ~0lt, it)),FL{50), Z (5O),RL t50), 0COd C('t[,ZL A (~0),L([!)\),~ (10;,A (bU),&l~D (50),E (5),f'T (50),JT(50), 1 J( (50), C3 (,, ), L ( ), ( 3,, A t S), ( 50),,V (50), 2VriC (50),RIFuf,D( i50,L' (bO),I' Lu (50),h (J ),Ti, NELS, AA (2500),NJU1lC (d'C) Ct&aL C1/0A'Ii'Li, IL,L,, i L'li 1 0(J 11 0 L'' V-i:,L-O 0. I 1 1 C 16~0.V 1,LUil 0)12 Lt; 5 1 1- 1,2500 OC1 S A (1 1) =0. 0 14 b; 6 I1=1,50 COl1 i 1 (11)=-. O0 lo i',L.f =l'lItk+ 1 0 L 17 i k =0 C C CALCULATE Ti DilJI3 S COITY AND VIISCOSIY IN EACH OF THE ELEMENTS 0013 18 4 0019 D0 130 II=2, NJUNC O r 3' N U&i LIS=;JL (I1) G0L I IF(JI (II ).NE.0) GO TO 130 0022 LO 129 J=1,NUMLS 0023 LNUE.=X (I-1+2*J) 0024 JATOE=X (I+2*J) 0025 fk ESC=2000. 0026!&' (IV.Er. 1) PDBOP (LNUM) =PG (JAT]GE) -fG (II) 0027 [tiOA (LNU.I) =PRESS/ (53. 34T*32. 1 7 4) 0028 RL (LNU,1) =l<J (1I) 002,) 11.' (f (JAIC E). ('I. P(; (I1) ) R1L (LNlUM) = (J (JATOh;) 0) 30 Vt (LNU M) = L (LgNUM) * f{HCF/ (ihL (LNUlM) *+i{Of' ilUtO A (LNUUM) * (1.-L (LNUM) ) 0031 t41lO (LNUM) htlJ A (L.IJM) * V (LN(JM) + (1 -. Vi (Lt.U1) ) )*HOt' 0U32 V1SC (LNUM) VR (LN1) * VISA + ( 1. -VY. (LUh) ) *V iSC 0033 D PL (L;JUti) =-iitO (LN UM) * L 2 (LNU M) 0034 129 CChNIIU E 00)35 130 I=I+ I +* NJL c S1:T UP TilE YATitlX OF E~UA'II0NS FOh COtiTINUITY AT EACii INTEdIOa JUI C036 1=4 OC37 DC 20 J=I,NELS 00 38 (J) =P ( + 1) 0 39 NUtL.iE=L (J+1) C;(,LC DC 1~V LL= 1,NI'LL5 0C4l1 (.3J,LL)=O. ",.;r! 1.~ = 17,J 1,-, U i J0-, 3 / l,U, [- X i I~-1+.I 1

u0'I A N IV G; CO(iL'ILE L kLoW2 09-25-71 12:0.31 PAGE 000, 0 01(4 1 t ( I (.NI.L 1J t) L(i'~O 17 00 4 5 J' (I.;- (I *+, 1) 0 f 9 (J, 1.L);-L i'r (A1)AS S(1L(-l (LL))) 0047 ( x ( + +2 * 1). J E.G(L, LJM M) R (J,1L) -B (J,LL) 0048 1'k (J1(J+1l).-E.O) GO TC 16 0049 I' (F1 (LUMt).G''T. 100.) F'1 (LN UI) =1;)0. 0050 ~ (J, I.) -AA (LMJM) *i,.S3R (LAi3 (S2. *L,X,0 (LNLUM) /FI (LNUMU)) (;051 IF (JtLULM). -'.JI E (6,LL) =-a (J,LL)'00 EC.2 16 J 1 =NUM.LS 0053 17 CCNI,NIJL 0054 19 AA (I L- 1) *ELS +) = R (,LL) 0055. 20 1=i I1+2*NULS C C C SCLVr TiH' 1:AThlX O8 lIhEi ILL-MENr Pi{ESSURE DliOPS C ****+** ********* **#**** **** $******* ****4 *****+ 0056 CCNS=.00O60001 O 0C57 CALL L Gl;LG (b,AA, NJELS, 1,CC ENS,IE [) 005 6 O 30 LL-L1,LN.S 0059 EP=LAIUJ (P'DRhO' (LL)) -VAIU! (5 (LL) *B (Ll.)) 0060 1E If L.GT.ICLL?) l of= 1 0061 30 PL[O LL) (LLL) 0 (L) *D1JS 1 (LABS (PLD)bO (LL))) C C C SCLVE FOiU fL()oS THRCUGH ELLtENT':J A/lD OUT OF JUNC'TIUNS C ****4*******************#***44********************** 0C62 1=4 0(C' 3 DO 4C I1=2,NJUNC jt h? I-'L = WL (II) 0C65 It (J'1 (11).GT. 0) GO IC 40 C0066 L; 4 1 J= 1, NIU&LLS 0067 LNUM=X (I- 1+2*J) 0068 A= 1. OCb'9 I i (J (LNUM).. Q II) AX=-1. OC 70 E Lu (;NJ *) = AX*R (I;- 1, LU&L) *S (L NUA) 0 7 1 F (FLO(iLNUi).EQ.C.) D.) Ci( (LINUM) =0. 007 2 4 1 C IC I U 0C73 40 l=I+1+2*UMtLS C C C CALCULATE lti; PiEiSUE1 Al EACIi JUt CTIC?i C * *++ *4*+*** ********* t****4*$ *4C******4* 0C74 L&U'=X(2) OC 7 5 F (1) =-LALS(FLO(INUM)) OL76:-4 0077 L0 5C 1=Z,eNJUNC OC7 dtL.-:L ( {~I) 0079 1 (J{ (11).zo.0) GO IC 50 OCc) E-GJ= PG (1 ) O0E 1 PLJ=C. 00)2 DC 49 J-lt,h.U,LS OCO 3 z. lJ:m=X ( I- 1+Z'j) CCu J A'i'C: A ( +* J) C (:' A: 1. Ob,,o 1[ (]C (LUNLI l). E. JATOE) AX=-1.

FOI{lRAN IV d COMIILilb FLOW2 9-25-7 1 12:08. 31 PAGE 000 UOCH7, (JA'0E) - PI + A X 1Z (L h UiJ) 0 C 8 i J - = Z (J Ii CL L) 0 } I (J. E. NU iLS) GO TO 48 Ot 10 Pk; (JA1U) = iGJ+ AX*PiiOF (LNUM) 0691 P'I (JA Oti) = P (JAOL,) -PZ (JAIUE) CC9 2 E -, or= (JA'1CE) OCL3 CC 1i 4) 03Cu;48 PUL (J A I') E) =P'T (JATOr:) + Pi (JAlUE) 00 9 5 L i (Z i) =b U ( J AlU t),- ( 1) OC t96;L (Ja'rE) =- AXi* LC (LNtNU ) CC9 7 49 C 1 L 009d 50 I:=I+ 1+2*NUML C C CALCULaTl' Tthi Alii Tu EuFiL iATIO AT ACtki OF THE JUNCTIUNS 0C99 CALL UAL (J) ) 0100 I (1t i.EQ.0) IV-Li M+1 3iO 1000 CONTINUE 0102 6fiETIU[ E 01C3 iND ICIAL MEMOtY REQ)UIIEM.tNTS 005F5E LYfES

-243rPTr T l Iv r, C"It' ILFr 1FL,4 10 - 7 -1 C9:t4, 1 4 PAGE 0001' -~'"1 %,I'>';'," Y l!': r I fL Il ( rJ''N r,'') Iv,NICY tFRFQt I TP N4SPAC E').'~/. ( f"rlJ t ~)' rC C,[I D, J, T.LrIa t-), F T,I C S T H r, RH3A VKRH, V I SC,RH P,;FDP DZ, 1 rl Ft t:1 n'~-tn f'.,.,~: X.e^{~ 7 "z), r1 ( -i'!, ), ~~"; A), -,,),),' I F)I'. 5J,PI' )(FIX. 7, FJ (-) )I I1( P,'( I - %' Il, -,' f 1 ) -' I f -''\( ) ), f'4L. ( I V; 5!?"t99 t r t V t 1 V! C( 5),'',"I,I'7(': R.S ) 1 (, L S,AA(2':D, JUNC "!8"1 or) 1 A 1 T "I0-1 I r, C; 3 C f - n r 4 2 T ( SU DI. f I ) ) n-.~14', ^ a Fr"' A 1'F,''"'T( (, %* Ft'", L'/H'!'",: lOFIO.5) q~l~' F? F:,'1lA I T, )[F:TTOt -'CF,%IA=' [C.' I0.%)'- l7 F. r -_.'F lp QPC'= 1.,/F'' l /: 1n CI n I ('.Ir -/ LJ l V m,C C r I —?q.~',/ ( 1 q'+ 1.* I =. i 7' 4/T * r,' PI N= Nl) L'(1 T+ 1 "n -2 P- ~F. 1"'0,I F l,1)J r "~?3' I ~r.:) I'1 I_1,r= l J11'4 9~~, r~'~a qn 1q. 1=1 (flJfpj ~,'',~ 1 Ir [ T.(C.'.'.cLS) GI TF (1'~.. FF~r- ( f ):- n T,~0')27 " C( I =! I )L ( I ) rn.1 t) 1.(rT * r7 ) h I ) ) C, t - I )=VC)( I;r.'C,tl C ( I ) %97 );-~:V(,) l 1 -1 [ / I( I) IT- T 6 3 rTF: r I \'I)F'n'. NI N' J:N t N T 2'5"" Iu ( I )='"'; TJ nl1t/' C; 91 CrQ!!F T r' r-) ) ^ " Ir(.1t) (C,..( I ), T:,% -LSj

nPTFPA', IV rG CIMPFI.LEP IFL9W 19-08-71 09:14. 14 PAGE 0002 ITr-(6,w"') (!) t=!,NFLS)' O':.!} ~ WRITE 7,,,'ri ) I, IT r))r., W, TTF,,?C?) ( A I, I I,",ELS ) rV'; WRT T TF(',?(n ) ( V( I 1 ,t r, NIF S) On 54 I T F (, r) ( V (VI I,2), I=,NJF LS} n'-'r W'Q I TF,,TTt(,' l' ) I'V( I,1, 1=1, rLS} r' -,.7 Wt, ITF F- J(,,?') f'T (,11), 1=, ).', C)JJ C -VA T 4 L CJ G.; TX-);.::,., -,',,~n~,. 1;( I T.f!',! T=,q. rl'~ i~~T=T+nT'Ci nFT'EUI,.IN'F THI- NrW lltJN')A!RY PR FSSIJIf S C n,-'r,f nn 1 4.1=1,'J J-' On f 1 PT J, I)=PTIJ,?) 4, P'T (TJ,2)=OT(J t3) o",'. ITFF(.JT(J).FQ.O) f,) Tf11 4 n ro,m'.. PT (,J, 3) =C I ( T, P, Xq rF, PF, NP 1, 50, J) a0(7 14 (CfNT!TI)E C C CALCUtI. AIF TI-I: FRICTI 3N FnRC,F TFRM DE, 16 J=J,NF LS p,~;,o FF l- F ( I ) 7F F ),J ):=.? 5' rf.I C ( I )*RV( J, 1) DA P,S( VI J, 1 ) +PV (J,2L*0 tIS(V(J, 2 ) FP(J)=FIFf (J)-FF I )*F,C T+FF( J) rnn r I' Il ri'P. FQ. 1.* &'). I T. (O. 1 ) F J ( J) FF( J) nO3 1 1, C (liT I [IIF r C SFT UJp T!.F C rlFFFIC NINTS rlF THF I'FJFPEND1FiAT VAR A I_ES C At,)'F T'E RI GHT S I E rlF THE fEQUJAT IO1N S qq Dz.oil Is J=l,NTNTJ? 1 7 1ci AA I J ) = O 17 rnl?03 Jl,'L,JJNIC,nT 7 1~- I q ( J) (nn,~ r' q ( It )=Ic. r. nt I DL=I J)(1 = T I J + I r )-) I N T rJ fL r=:N. ( J) nqR Dnr 1 K =1]N,NLtLt ~r~ 9/+ l1t t~ r!ttI = X ( t - I + Ki', S I l =J[ (t, 1) I'. )'",tYJATqr-=Y I +2~K) 7r,rIr..I T! r ).. - )U = T R.J +.I ( RJ)ArT=)T TE) -I ). I JTJ.... IlJ,.['). ~,F ) r" 11' I': r L " I, I, rq THf J!JN CT IqN

:'OpT:?'t tv r, tC,'CPII fl fFl-rlW 10-r)0-71 09:14.14 PAGE 0003 I F ( J T ( 1 ) C. ); C r - Cl CA'JL ATE T4E C.1FFI CI TI S!,,(V nC, C )-.,, A T, i- T. 11 1 1' ([(1 I- ( J" T)( I -AT P:F ) "Jt C,N) VL) 1 11 C. CAI7ILArF TIF CUC;- rFFICIFNTS 01,,-,, 3 t'-p -l C ( 7 te?[ )!',;-l.') /C. L N Cf 1, f1. ) ) -( U M VL' 2 L) )t ( V ( L*UM1 ) UM2 ( 7 t17 A I F I ) A A /I ( I I, L: )./3 C 6 ( L NU C 5 (L NUI ) V ( L NUM, t lA, DAS (VI I ( L Nu, l ) I C l D/:1 S (V (L',JUF, 1.!1 C CALCrl!ATE THF R IGHT HAND SI DE C 1 +.5*CA(LNU`4)*-(4./3.*PT( 11,2 )-2./3.*PT(I1,1,7'rf,a,"IF T( jT"r).rT.,)) (,, T'l 19'~n lc7 t,.(I)l! ) ( II) J-PT(J T'3IF ) (CS L U -C6 L NUM )/6. C LNU )*VILNUM, 2 I *.UAB t ( V( L NUMt ) ) C C CAtLC'I.TF THF PESSRS T THE I NTERIR J I NS C'C1"'/, ~R ACA Cr.'i t, CY AJN'C JTJ, [,CIN, I ER) Areq!.. 11) I 4 )="'.,jJ\)C Il'V,A, IF(JT ().I..9' 1" r Ti, 45 J= T ( I)'~ ~,~,p',r\ (,' I ) ) I d I 4]A, S, / (b l' fA, F 1\ )! C C C. fI.)t lr' T~lr [ "l';.hr',T,R' S'.'t-SS FI.UX IX EACH ELFMENT ^1>4 ~ ~' ct ^C.,, X,JJ..tS18

'nr TR P J ITV, C.~t LLED TFLlW l-)i-71 0: 14.14 PAGLE 000 C'1 I 7 I = J I f L'11. I'*} n11 3 P tfT (,t l, J, 1) (C 4 l N'I 9) *+ C U I-5 U' IT( I,3 ))/(. (L NIJ' 0 11 4 RHn r T LNI' t',? I = ( C 4 ( L'l: I' ) + C i ( L "' ) PT ( I 1 ) CS( L NJXl PI q =C 7 {'(I (;v) (-PT( (T'I ), )- F I l''II ) i/C ( l L ).r l 1~ 7PW X: ( I ( (tl, l ) -' V (.t1,! J +{V( L M, + }~, ~,\,;' V { L N(J'~,! ) ) J -t}ril'I( L'J,7I. R* W'l! P.V(_,"'',.?)'/(L'",Iv,,'+ I + Pi'- I tI L" LU'~) C( I.C ~ C)'/!'.~(C.:Pr( 1[2,3 }-4. 1 <:''T( TT2,? (9.:Dl(!',1 "'(I l.:;, )1 - -2.,' Pr( I L,2 )+'1( l,1 ) ) r 1?. \( ['!1C, | 2) =? I V ( L,,' J', 21) /,-:.!I,*f/.."',? | 1 C 1 O 1= tIt'J t'1 ~" I.)r )~, t - I,I!.I.% L(1) 1FtT~/TTP4tIP-Tr) L~2,97,1)3 t? 9 J 1( t ), r'l f PVC' r I:<1=DAT,) P{ (l1,?- P T{ I.)-t, I )'" ~,, 4 F (I r'.-.FC.I.a~i,). T.- )lp I t:lT/Y I n~ )? pTFy?I.:.{ JJ ) 1 fp T )F'"A X, 0 T, YI, T,'Y Y2) 01' W^ o,,( [ ):-AMT (I ('I TP?Y P t PT,. Y ) P'1'!1 w*Tr ( r t / IC T (1, 3-) 1'I,?11PJs 1.,149? 7 W,I T (,'2) r,. TI T "T I I r T / I. 31 144.'~3 P4 r)Tl r,7)-PT..( I I/ I1'.C PVC V, l;\V t 1,2/ I,3?. /) nl^~~ 1~,?~r 0t4 f R (T ) —F rq f I 4 [/ t, 1~, 7o,'rIT I rf:I F ) IIr V( T,1 ) I=I, IF FLS) n I~',) WR TF6,I.TF 3) V( I,2), I -I,'FLS!: -1 Wr;T( A,. T f (( [4*(*,2. ), I: I IFLS) " -,2 Wk'I r r:( F, 2(''> ) (P IT( t, 3 )I [ 1 o,JJ i W) ~)1'* 3 C'RITCFI (-(,, l f,W) IF!'( F ) I:I, r-FF LSN 44'Pz, p9 9 I l:,r,J I l.C 1_ IF F(t).F:.) I. ) r Tr 93 ~.1, 7 qV(! IT():V( ( T1 (, )V ( I]J I )=oV ( [ )! 1 t, PV( I T - V ( t 2 )(2 2. 2 36' -. - ( 1 ) )I r, 1 I,! n cnN TJ r T TI) "1:!': 3w,':"'I TI -' I " ) L/ { " r(T OF TIF Pf "R )A) r ~L A-' *:. - 0:$ $ * $ +**.) 1 45 1,1 5 1? =Pt tI,': L S II: )~~~~~~~~~~~~~~~~ ffr

-247~CRIR AN 1 G CC['PllFIP F'IC o09-29-71 13:47.C7 PA6E COcI C~i1 5t ISPI LI INi f'C (I -, f I!,V r cr:, CIr,Ht.,VI CF,F) CC L It hlA.4 L CCC3 lICt- R X CCC4 LCLBLL PHLCIS 1It F,FA,F,V,ARtCE,C,A,PLE,RE,FT,CS,tRC,RFCA, 1VR,v1IS C,RCF,IP,CZ,FLC,HR,AX,AIN,CULT,CC,h,/,iNG,Al,A2,tA3 CCO5 LZCL!eL PRICIICN Al,RL,VISCF,F2 CCCL Cl1E - [1CN F ( — C ),-A( I ),AU3 (.C),V(5C),AR(5C),CC(5C),RL(5C) CC07 CCI/VCh X ( 7C ),L ( SC ),(50),A(5C),RLC(5C),RE(SC),FT(5C),JT(5C), IJC(5C),CS(3,5C),L1({5C),RFC(5C)},RtCA5C),NL(5C),VR (5C), 2VISC(SC ),FCF,UP (C ] ),C(C),FLC(5C)6 FR(5C),TR,N.ELS,AA(25CO ),NJ.UNC CCCe CC 1 Il,Nt~LS CCCO v(I)=C. CClC IF(A(1).EC.C..CR.RF-C(I).EC.C.) GC TC. 2 CCOI V (I )=CEIS (FLC ( I )/(( I )RFC ( ) ) CC12 2 HE(I)=C. CCl3 1F(VISC( I).c.C.) CC TC 3 CC14 RE( I )=V( I }) E ( I )/VI $C I ) CC15 4 F(I)=C. CC16 FT(I)=C. CC17 FA(I)=C. CCIC F ( I)::C. CC15 CC(I)=C. CC2C 1 R I ): l.O C C AREA CF-ANCE LCSS FACICRS,- FA CC21 I=4 CC22 L L X ( 2 } CC23 IF (L.1 ( LNUF ).EC.C) FA (LNU" )=.5 CC24 CC 1C I 1=2,NJLNC CC25 NLULS=L( II ) CC26 IFJT(I I ).NE.C ) GC TC 5.CC27 lF(NLF LS.NE.2) GC TC 1C CC28 IF(JT( I ).NEC) GC TC 5 CC2S CC S LL=,NLL"LS CC3C LNL=MX(I-142*LL) CC31 IF(LTC(LKLV).NE.C) CC C 1C CC32 AX=..CC33 IF(JC(LNL ) EC. I I A =-1. CC34 IF(AY*FLL (LNL?).GT.C.) AIN=A(LNUF) CC35 IF (AX*FLC (LNL).LE.C. ) ACLT=A(LNLtP) CC3 9 IF ({AX4*FLC (.LNLt ).LE.C. ) LEF=LNLd CC37 R(lI1)=l. CC3E IF(ACLT.EC.C.) GC TC e CC3S aR(11)=AIN/PCLL CC4C IF(R( 1 I )-1. ), 7,E CC41 7 CC=.61E+.C *(AIR( II )+.6)**5 CC42 IF(CC.CT.I.) CC=l. CC43 FA(LRFF )= (I./CC-I.) (./CC-1. ) CC44 C-C TC 1C CC, 5 FA ( LRF )(R ( 11 )-1. )* ( AR2 ( I 1)-1.) CC4 6 C TC 1C CC47 S LL'>= ([-l2 ~4NL1LES)

-248FCRTRAN IV G CCWPILER FRIC Cg-29-71 13:47.C7 PAGE C002 C048 IF(LT(LNU! ).NE.C) CC TC 1C CC4S AX= 1. CC5C IF(JC(LkLFi).EC. II) A=- 1. CC51 IF({AXFLO(LKL).LE.C. ) FA(LNUM)=0.5 CC52 IC 1=I*142*NLPLS CC53 I=4 C C C EENC LCES FACTLKS, Fe CC54 CC 2C II=2,NJLNC CC55 KUPL:SK=NL( I CC5E IF(JT(II).\E.~.) CC TC 20 ~CC57 IF(NrLLS-3) 12,13,2C C C C ELECIS C,4,4~,4, CC5E' 12 LI=X(141) CC5 L2=X(1 3 ) ~CCC X 1. CC61 IF JC (LI).LC.JL (L2) AX=-1. CC62 kz(CS( I,L 1 )*4 ( 1, L )CS(,LI )*CS(2,L2 )+CS( 3.L )*CS 3,L2 ) )*X CC63 L=CSCRT(DA( I.-h*l ) CC64 ANC=C= ES 57.24*LATAN2(U,) ) C065 IF(ANC.LT.1C.) ANG=C. CC6f LREF=L CC67 AX= 1 CC6E IF(JC(LI).NE.II) X=- 1. CC,S IF(/AXFLCI(LRF).LE.C. ) LREF=L2 CCOC FO(LREF)=.C lT2*ANC C071 GC TC 2C C C C TEES C **** CC12 13 LI=XII+I) CC73 L2ZX( I-3! CC74 L3=X(+5 ) CC75 IF(FLCE(L1).EC.C.) GC TC 2C CC I IF (FLC (L2 ).EC.C.) CC TC 2C CC77 IF(FLC(L3).EC.C.) CC TC 20 CC7? al=l. CC7S 2E I. CC8C 3=1. CC8 1 IF (JC i L I ).NE. I =- 1. CC82 IF(JC(L2).NE.1) 42=-1. CCe3 IF(JCIL3i).NE. Il) A.=- l. CCd4 N FCI=hA1*FLC(Ll)/C S(A*FLC(L) ) CC85 h2=A2*FLC(L2I/LAeS(20FLC(L2 )) CCU6 N3=A3*FLC (L )/CAS(*FLC (L3) ) CC_7 IF(N1-n2) 14, 15, 14 CC%E 14 lF(k2-N3)1,17,16 CCes 15 LSI=LI CC4C LS2=L2

-CRTRN, IV C- CCIPLER FfRIC (-2q-1 13:4o.C7 PAGE 0(C03 CC9 1 LC=L3CC s 2 C N CC93 C-C 1C 18 CC94 16 LSI=L1 CC95 LS2=L3 CC96 LC=L2 CC97 NC=N2 CCSE C C 1C 1I CCgS 17 LS1=L2 C1CC LS2tL 3 CIC1 LCL1I CIC2 C=N I C103 1 A1= 1. C1C5 =({CS( 1,L1 )*CS(I,LC )+CS(2,LS1 )CS(2,LC)+CS(3,LSI)*CS(3,LC))*A1 C107 L'=CSCl (CABS(17.-2:Th) ) C 107 NC- 1= L A C S ( 7?. 2*CA. AN Z ( L, ) C 1C IF(ANC1.L I.lC.) ANC I =C. C1CS,2=1. CllC IF(JC(Lt).LC.JC(LS2)) A2=-1. Clll t=(CS( 1 LS2)4CS(I,LC)+CS(2,LS2)*CS(2,LC)+CS3L,LS2)*CS(3,LC ))*A2 0112 C=CSCRI (CAtS (L.- I ) ) 011 3 ANC2=CA S( 7.2Ca TAN2 (, L,)) Cll4 IF(ANC2.LI1C.I) ANC{2=C. C115 IF(AIG.E C.SC..AN. h NG2.GEC.90. ) FB(LC)=1.8 0116'IF(Fe(LC).EC.1.e) CC Te 2C C117 F8(LS1 )=.C1 222*ANC1+F LSl) c11e F8(LS2 )=.CI222*NG24+F(LS2) C11 2C I=I+1+ 2 N L L C C FRICTICNAL LCSS FACTCRS, PIPE ANC CRIFICES, F C LT=C; FIPE C LT=; P IN PEETERI1NG CRIFICE C L. T=2; SCL/RE ECGEE CIF ICE 012C CC 1CC I=,hEL5S C121 IF(LT i)- 1)- 11C,12C,12C C122 11l F(I)(.64-.CC64*(RE( I )-CC. ) )*RLC(I) C123 IF( E(I ).LE.ICC.) C C 1C CC C124 F( I)=.3164/(( I )*.25 ) C12-5 IFIE ( I ).L. l11.3 Z2) FI)=64./RE(I) C 126 F( I )=F (I ) *LC I ) C127 IF(VRII).LE..CLCC.HR.VR(I).GT..SSS9) GC T0 1CO C12E F(I)=F2*F(i) C129 GC TC 1CC C13C 12C RX=E ( I ) C131 FX=FR(I) C 132 IF(LT( I -1 ) 130,13C,14C C133 13C CC( I )=CCMEAN ( RX, HX) 01 34 GC TC 15C C135 14C RLCX=tLE( ) C13 CC ( I )=CCSC(S X,F-X,RLC) C137 15C IF(CE(I).Lt.L.) CC(I)=.05 C132 F( ) I./ (CC()*CC I ) )

-250FCRTRAN IV G CCIPILER FRIC C9-?9-71 13:47.C7 PAGE CC04 C139 I CC FT (I )=F A() +F( I )+F ( I) C14C HETURN C 14 1 EfIE TCTAL IEI:CRY RE CaLIREM,ENIS CC 12B4 BtTES

-251ORTRAN IV G COYPiL~Ah AUAL 09-25-71 12:Ob.38 PAGE 0001 0001 SU0JhOU~lNE [JUAL () 3002 ~I iC-t i( X OC EthAI*8 L 0004 V()U'LE PdELCISIJN D A,BLi, L,FT,CS ihO,RHOA, VR, VISC, BEHOF',I,P DI., 1FI.O, k',TCLP, AA, FLO C,, L,CCNS 0005 OlMII1NSl,JN ('O(),13t0),I'n (50) 0600 Cotl(.h( X (h(O),Li5)),: ('.,),C A(50 ), CL (5 K 0) (),F'T(50),J1(50) VIJ;C (SJ),iti.,LPL (5J),[_ (3(.),'LO (5tU),t,ii (50),'TR,lJEL, AA (2590),NJUNC u007 C:L N. b,OC (j ( )U')() 000 1 OCo C 1;LJ SO= 0 0C09 0o 5 J=1,NJUNC 0010 11 ( ( I(J). t.O) GC; TO 5 CO 0 1 1 N1, I J- t4IiNJd+ 1 00 12 It (J) N INIJ OC13 5 CcL11UMJL 0014 JC 6 I=1,NINTJ 0015 b (I)-=O. 0016 DO: J=1,NIN~J 0017 6 AA (I (J-1) i4 NTJ) =0. 0018 I=4 0019 DC 10 J= 2, JUNC 0020 Ik (J1 (J).NE.0) GO ~O 10 0021 iJ=IP (3) 0022 NUFMLL=NL (J) 3023 DC 20 I=11,NULS 0024 JATCE=X (I+*1 1) u02 - L NU.- X (1-1+2.11) 00. ILU= -LA3S (. LO (LNUM)) 3027 iL (JCi(LitU,t).EV.J. ANoD. iL 0(LNlM).T.0.) GO 10 20 0028 lI (J(' (iNU;I).NE.J. 4 N)D.LC (LNUM).LZ.O.) GO 10 20 0029 II' (dJ' (JA'~C). NZi. O) GO'C 18 0030 LI 1 (,J A L:) i )J11 AA(IJ+ (Ii-1) *NINIJ) =-ELCLi 30 2 GO IG 19 0033 18 il (J'l (JATCI). L(E. 1) GC'O 19 D303 Bl LJ) = (IJ) +FLOW 0035 19 AA (IJ+ (IJ-1) *NINTJ) A (lJ+ (J-1) * INT'J) +FLOW 0030 20 CCN2I1 JUE 3037 10 =1+ 1+Z*NL (J) * 3038 CALL L GELd (, AA, Ni dIJ, 1,CONS, IEA) 003 ) -=4 30O4 CC 20 J=2,hJUNC J041 LEL- L= L (J) 3042 Lr JI (J).NE.9) GC'TO 30 3043 fl=I ({J) (J) =-: (IJ) 0,Ci Z, Zi II1=1l,h aMLS 304 o J Ar= X (I + 2 1) 3047 ii ('i (JAir'). Ei.O) GC'IC 28 )04d L'.U iL-A (1- 1+ -* 1) )J4) (..::J.JC(i rti U). AND. ILC(L NU.i).LT.O.) GO) I0 29;,G_)0 1':. (J d:)..AND. Ef I LNU), r2.0.). GO i 2) L ~ ~ ~ ~ L2

-252EiTB AN IV. G COMPXILEL CUAL 09-25-71 12:08.38 PAGE 0002 )053 29 11- AJX (JAIOE. EV.,) Q (JA'IU'')=l. 3054 I1, (J'l {JTTCr). Ey. 1) Q (JAIO.) 0. )0' 28 CUNIINJE )05o 30 =I+'I1+2*NUELS )057 tiTUBiN T,C58 Et3 TCTAL MEd'ORY hE.jtliZMIENTS OCu95'C bYii

-253 -:nPTRAN IV G COMPIL ER CD?EAN 09-13-71 14:54.09 PAGE 0001 O001 FUNQTIN CMr E \"lkF,I i) 00o2 nDI HENSIO", C( l,.+, (1, 1, XPR( 11 ), XH( 1 1 ),C: ( 4, l1,CH( 1,6), XCH( 6) 00on3 DATI C/. 7 3,~. )?,,.-, r 71',5,. 70, 1.732, 7i2,.670, 6,. 36 9, 794,. 329,.d 50,. 860,. 855, 2.845,..'H,.85I,. 7.,.7'54,.72z,. 620,.880,.910, 3.915,. 91 1,. C?,, R5,. 16,.835,.805,. 7 7 3,. 4. RS'],. 92',.9)+'),. 9 7',.'3'),. 7 75,. 720(, 60 5,. 61 0, 5.5, C / /'.,..,,.- 3;,.!:;I::),.' q'),.B",.O 7 3 t 6. 7),'. z / 1>)., J-)., ").C.,4(),)). 76(-r:)., t,.)I., 0;)0 ).,9,)0., 1 ) ))./,X/0.,.125.25 8.37'5,. 3 -f 9.,''.2''I I) I. 1. 125, 1. 25/ XC/ (Y1. ) ). q 200(, )., - ) O., i,),; ) 1,'K) ]O. / 0004 R=A'V ( F ) n,on5 H=A~ S(1lI n) (n6 IrF(.l..01 ) T.' T1) 1 )0 000(7 If {R.uT. 00' ).' )1. 00(38 IF(H.(, 1.1.? ) H= 1.2 ) 0009 CH ( 1 ) -O. COlO DO0 10 I=,4 00 1.1 nrl 9 J-l,ll 0012 9 C)( [I,J)=C(J, I) O 01 3 K=I + 2 0014 10 CH( I,K) =C( I(i,C),. 1 22, L.25,11 4,l,I 0015 CH{ (1,)=CH(11, 3)' -.9+43 0C16 Y:(T, I t R CH I 1C 0,C, 0 0 53.,500L. 96,1 1 1) no17 GO TO 200. 0018 1 0O IF(R. T.10000) R=: 100O. 00119 Y=CI {R,CS,IO0O.,1000)0. 1, 1 1) OC020 200 IF (Y.F.0.) Y=.05 C021 IF(Y.GT..) Y=1. Onr22 C [;E ANj=Y 002 3 RE T'J R 02?4 FND TOTAL vE MRY RE'.)t.QIPE'EN T 11S 000(586 BYTES

-254AN' IV G CrMPIL. ER COSQ 00-16-70 01:54. 18 PASF 0001 FUNCTION CPSQ(XI,X?,X3) ) I N!M_r. I 4," "I R I t~ t C f) tC[ tCO[ 5 IF(H. GT. 1.) I H=l. R'=ABS(X.) YLO= ABS (X3) 1 1625.,3115.,47b7., 07. 7.3,,,7,. 2 9,., 2.2 47 I,." 2, 215, 62 I, I I l l~, I/. 25, -i -A; ) 4, o26,.265,.2 2 3e. 5 5 4',. 2 lJ- 1 / C 7 ~ 7- 77,.,. 7 7;,. 7,. 7;-6, 7 7,.,. 7 5 7 3.7 5. 7 5 4/, Lqj/.0lq.51 r9,'~.t, 7. 3'4/ I CZLF I 7 0) T 4 C I'So= C r'S s, vl 9 ) GC, TO 7(,) 4 LI2=3 L 71 3 D_r( 5 L0=1,3 IF(iYt.~ bT. L. Dr(I I)) )C.[ Tn r5 L nt~= LDI-1 L 1)1=LD)-....LI)2"LD...... —..-....-. L )=3 5 CONTIlNUE IF (1f1.f-0,.9) 1r)j= _ Of"; tO Li)=LDtI,102 DO 10 12=1,5 IF(12..-Q.5) G() TO 30 IF-(R.GT.Ff I( I,L))) GOil TO 10 IF(12.F(.1) G` TO 20 I1=12-1 Do) 40 J=l 1,2 40 r) (j ) =-A ( J,LI)*(H-B ( J,LD) )*(H-B(J,L )+C( J,LO SLOPF=3. IF(RE(I2,LD).EQ. RI(I,LD)) G[I TO 41 SLCPE=( C ) ( I2 C ) ( I 1) P,L ( IC2, L I)(? t))-RF(ii- L0 I. LD.. 41 C[l {Lr)=SLOPE* (-PF(I1,L })n+C1J(Il)' I2=5 G1 TO 1= 20 XLL=PrLO(L}). CD{SS1="]SS(R, XL) - XP=E(i19LO) C)SS2=-OSS(XR,XLD) CL)(i)=-A( 1,LD )*(H-P.( 1,LD) )*(H-B( 1,LD)) I+C( 1,LD) CI)1 (LU) =C., ( [ ) *CI)SS 1/CSS2 I2=5 GO TO 13 30 CD1[(LD)=-A(4,LD)* (-(4,pLD))*(HH-B(4,LD +C(,LD __s_ 10 CO"ITIN!IF IF ( LD(L 02).[Q.PLhI(I.' t )I GO Tf' 69-, St DPL= (C -;IU t2 )?-C'}l(.O1l) )t/I LO LU2 -RLD( L01) 69 C:-)S(=Cr'I ( L 011 +S1,LC't', YL [ -P4LM Li;ll) 70 I ( L).SQ.[ T.O.) C,)(,=)..r[(f:S',GT 1 )I rs-1 ___ _,"_ tr j r,

PR1 (,AN IV G CCMI' I [t Cf)SS 09-13-11 l6:30.3i PAct 0001 0300) 1) FUNCTI r ON C )SS(R:, L ) 00m2 In f EN,Il[ Y 1? 1 ),l Y 1, 21 ) Y3(l, 21),Y4(/121 030 3 DAT'& YI 1/,:.- 62., 66:) 65, 645 64 1.639,. 636,. 635r3, 3.33,. 3 2,. 631,.63 9 63, 6. 6 3/, 2Y2/0.,.682,.72,.685,.675,.698,.685,.675,.675,.67,.68,.70, - 3. 68 585, 685. 7 7/, Y 3/O., 3 * 6,7 72 7,5,. 7,.7,.?6... 7 7.... 4.78,.7,33,.785,.786,.787,.798,.788,.739,.789, % 5*. 7 /, t'.i /(;,.,.. 5'.),. 9,. 9 7Z,. 7 3 5,. 74,. 7 4,.7+, 742, 7?45 t 6.74%,.'14,,.753,. 753,.755,. 757,.758,.759,. 76, 7..75 / 000 V4 XV=,1SV ( F ) CO r5 IV A=S (RLL)) 00-Of, IF(XV. LT. 500. ) GO T l 80 00)7 IF(ZV.LE...) GO T 30 Or0Q IF Z V.L..615) G0 11 4I 0 0,'?:TM ff'(v.l['.-S3V. 6 F.O 1.3 50 O~1() IF (ZV.LF. 7.??5t)',( 1I0 o().0011 GO T 70 0 I/ 3 0 C [)S" -C I (X V,Y,b)O., lo0; )o., 21, 1, ) 0) 1 3 kf 1 IJ I rN (OO14 40 Cl =C I ( XV,YI, b );)., 10()00. * [ 1, l ) nnr, I i) -C I' =' IXV X Y? t 5C. 1I (.)( O. t I I I 3 1 0010 C2=C([XV,Y3,50().,l()()0.,?l,1,1) 00I20, Cl)SS=C?-(.636-RLl))*(C2-C! ) *.332 n021 RETUJRN 02() I2 50 C 1 =C I ( X V, 50., 10000.,1,, 11 I ) 023 C2 =C I ( XV, Y,00., 10000., 2It 1 ) 0024 Cns=C2- 7.225637-RLD)( C2-Cl)*.33 278 002 TUNSS=C2-7-RLD) On26 70 Cr1AX=.827-.CC85*RLD n 27 CM 71 ECI (XV,Y4,500., 10000.,21, 1,1 ) 00 28 CDSS=CvMX *C"l 7 RE- 1.314 O0: -)'0 R E TUN. 00n0 80 IF( V.GT. 1.) GO TO 90 0031 CDSS=.C5 On 32 RF TU RN OC33 90 CMAX=.?27-.C85-ZV 0034 F ( ZV.LT.2.) CtAX=. 7 +.045VZV 0035 IF(ZV.tT.1.) C'AX=.6+. 17?5ZV 0036 C= I. /CAX +20./XV*(1. +2.25*ZV)-.05*1V/( 1.+7.5*AL (.0001 5*XV ) n('3 7 CUSS= 1./ C035 FETI)JRN O0 39 E tND rT(TAL "['[11RY REJ1 RI -tNTS CC0504 BYTES

-2L — I ~ G_CCP..~ EF..___......._F.PRCP. O-_ZO_. - _.? 162 L 2 P...........I.... PAGE__O.0)... SLBROUTINE FPROP(FLUhCt TE!Pt SG, VISC) I IF(FLUNC.NE.G.0! GC 1C 2 IS OCT SC=0.7219-C.CCC43826*TEIP ISO OCT vISC=-O.437e+213.34k2/(TEMP+200.O) ISO OCT A ETURN 2 I F( FLUI%C.NE.l.C'GC fC C 3 STD REG SC224720.0/(TEtPPf27C.0)-.3. 172 STD REG VISC=135.79/ TEPP- 132.5)-0. 0830 STD REG RETURN 3 IF(FLUN.NE.2.0) CC TC 4 WATER S_ C =1.O-C.0001 33*.T E P WATER. V ISC=-C.157041+ 2.C/ (1EMP+20C.O) WATER RETURN 4 IF(FLUIC.NE.3.C) CC TC 5 ETH ALC SG-O.830-C.OC034,*TE P ETH ALC V.SC=-O.C8904346.C/(TEPP+190.O) ETH ALC RETURN ~5 IF( FL UI.NE.4C) C IC 6 SHELL SG=0.7839- 0.CCO4C047 22*EP SHELL ISCO. i 710-0.CC244C*TEMP SHELL RETURN IF(FLUNM.NEo.O5. GC IC 7 CLARK SC:0.7480-0. CC40*O T EFP CLARK V I SC0',6 7 4 0 - C.00 0 1 C 3I 3 - T ECF C LARK REIURN 7 IF(FLUNO.NE.6.C) CC TC 8 MAR'ON SG-2328.56812/(TEtPP*1.8+32.0-2074.7644)+2.03898 MAR'ON VISC=118.12441/(TEPP*1.8+32.0+77.16928)-0.07321 MAR'ON RETURN 8 IF(FLU-LC.NE.7.0) GC TC9 - MIN SP IR -SG=.064CS+41.88/( E lEP+215. O) MIN SPIR.ISC=-0.1250+201.C/(/ITEIP+65.3) MIN'SPIR RETURN 9 -IF(FLUNO.NE.8.O) GC IC 10 AIR SG=0.6360/ (TEMP+459.6), AIR ~ lSC=12.0774+4.642*TEMP/1 O0.0O AIR RETURN 10 -.RITE(6,1v) 11 FORMAT('NO FLUIC FRCPERTIES LISTED IN FUNCTION FOR GIVEN CODE NU iMeERS) RETURN MEMCRYRELEIDENTS 000 C M;E-McR-Y REC:L'PEM'ENTs... 00J5-5C' B'~TES

FtlK'CTTON CI(Y(,VYrDX9XMAX9TMAX) DTYMENSTO' Y(1O) XSPAN IMAX*)X-DX XZF O=XAXX-XSPAN X- ( YX-XZER;) /rx +l. I "X IF( X-XmAX+DX) 1,,2 It=IMAX-1 1 F F( XX-X7ERPO-X ) 3,4,4 3 I 2 4 XH= (XY-XZEDO-( I-I )*r*x)/DX CTY(! )+,S*XH*(Y(+1)-Y(I-1 )+XH*(Y( 1+1)+Y(-1 )-2*Y( R FT IRt I E ND

BIBLIOGRAPIIY Meterinj of Oscillating Flow withl Orifices 1. Bailey, N. P., "Pulsating Air Velocity Measurement", ASMVE Trans., Vol. 61, 1939, pp. 301-308. 2. Beitler, S. R., "The Effect of Pulsations on Orii'ice 1Flow Meters", ASME Trans., Vol. 61, 1969, pp. 309-313. 3. Beitler, S. R., E. J. Lindahl and H. B. McNichols, "Development in the Measuring of Pulsating Flows with Inferential IIead Meters", ASME Trans. Vol. 65, 1943, pp. 353-35b. 4. Benson, R. S. and H. M. F1. Shafie, "Non-Steady Flow Through a Square Ed.ged Orifice in a Pipe", Journal of Mecil. Eng. Science Vol. 7, No. 4, 1965. 5. Daneshyar, H., "Development of Unsteady Laminar I:'low of an Incompressible Fluid in a Long Circular Pipe", International Journal of Mechanical Science, Pergamon Press, 1970, Vol. 12, pp 4135-445. U. De Mestre, N. J. and Guiney, D. C., "Low Reynolds Number Oscillation Flow Through a Hole in a Wall", Journal of Fluid Mechanics (1971), Vol. 47, Part 4, pp. 657-666. 7. Earles, S. W. E. and Zarek, J. M., "Use of Sharp-Edged Orifices for Metering Pulsative Flow", Proc. of Inst. of Mech. Engr., Vol. 177, No. 37, 1963, pp 997-1012. 8. Hodgson, J. L., "Commercial Metering of Air, Gas, and Steam", Proc. I.C.E., Vol. 104, 1916, 1917, Part 2, pp. 108-193. 9. Jeffery, B. J., "Pulsating l'low Through Orifices", Ph.D. thesis in the Faculty of Engineering, Kings College, rUniversity of Lorndon, 19b5. 10. Moseley, D. S., "Measurement Error in the Orifice Meter on Pulsa-ting Water Flow",'low Measurement Symposiutm, ALM,E,,pt. )'t-20I 1190)G, pp. 103-123. 11. Oppenheim, A.K. anld GI,:. G. Chilton, "Pulsating l'low Measurement - A Literature Survey", Trans. ASIME, Feb. 1955, pp. 231-248. 12. Sparks, C. R., "A Study of Pulsation Effects on Orifice Metering of Compressible Flow", ASME Flow Measurement Symposium, ASME, N. Y., Sept. 26-28, 1966, pp. 124-138. 13. Williams, T. J., "Pulsation Errors in Manometer Gages?", ASME paper, 55-A-92, No. 1955. _2've _

-25914. Zarek, J. M., "The Neglected Parameters in Pulsating Flow Measurement", Flow Measurement Symposium, ASME, N. Y., 1966. iFuel Metering and Induction Srstems 15. Blair, G. P., and Goulburn, J. R., "The Pressure-Time History in the Exhaust System of a High-Speed Reciprocating Internal Combustion Engine", SAE A,paer 6,70477, 1967. 16. Bolt, J. A., Derezinski, S. J. and Harrington, D. L., "The Influence of Fuel Properties on Metering in Carburetors", SAE paper 710207, 1971. 17. Brandstetter, Walter, "Der Gemischbild ungsvorgang im Ansaugsystem der Verbrennungskraftmaschine bei periodisch-instationaven Stromungen", (The Mixture Formation in the Induction System of the Internal Combustion Engine with Periodic Fluid Flow), Sonderdruck aus AI, Ausgabe 4 vom 25. November 1966, 11 Janhrgang, Vogel-Verlag Wurzburg. 18. Brandstetter, W. R., "Theoretical Analysis of Unsteady Flow Phenomena in Single-Cyclinder Four-Stroke Engines with Intake and Exhaust Pipes", Geineral Motors Research Publication (GMR-884, June 17, 1969. 19. Goyal, M., G. Scharpf, and G. Borman, "The Simulation of Single Cylinder Intake and Exhaust Systems", SAE paper No. 670478, may 15-19, 1967. - N 20. Harrington, D. L., "Analysis and Digital Simulation of Carburetor Metering", Ph.D. Thesis, University of Michigan, 1968. Also see SAE paper 700082. 21. Hosho, Yukio, "The Mixture Ratio Regulating Effect of the Air Bleed in Simplified Carburetors", Hitachi Review, Feb. 1963, pp. 36-42. 22. Hosho, Yukio, "Flow Quantities of Air Introduced Through Air Bleeds into Carburetors and Pulsating Fuel Jet Phenomena", Iitachi Review, Vol. 16, No. 4, 1967, pp. 173-178. 23. lluber', P. 1and1 Irown, J., "Computation of Instan-tanleous Air Fl.'ow arld Volumetlric Ef.L'iciency", SAE paper 812B, 1964. 24. Kastll(cr, L. J., "An Investigation of the Air Box Method of Measurin the Air Consumption of Internal Combustion Engines", Inst. of' Mech. E`ngr. Proceedings, Vol. 157, 1947, pp. 387-404. 25. Kastner, L. J., and T. J. Williams, "Pulsating Flow Measurement by Viscous Meters, with Particular Reference to the Air Supply of Internal Combustion Engines", Inst. of Mech. Eng. Proceedings, Vol. 169, 1955, PP. 419-432.

-26026. Klecka, M. E. and Oubre, C. L., "Mathematical Simulation of Automotive Fuel Systems", SAE paper 680436, 1)683. 27. Oyama, Y., Tejima, T., and Hosho, Y., "Transient P]?low of Carburetor Fuel Systems", Hitachi Review, Vol. 183 (1Ci)0), No. )I, pp. 162-167. 28. Prien, Walter F., "A Study of the Efifect of Air I lsationls on the Operation of a Simple Carburetor", Thesis l'or Bachelor o1' Science Degree, M.I.T., May 1954. 29. Shinoda, K., Koide, H., and Yii, A., "Analysis and Experimenrts on Carburetor Metering at the Transition Region to the Main System", SAE paper 710206, 1971. 30. Taylor, C. F., Livengood, J. C. and D. H. Tsai, "Dynamics of the Inlet System of a Four-Stroke Single-Cylinder Engine", Trans. ASME, Oct. 1955, pp. 1133-1145. Transient Flow Analysis and Simulation 31. Benson, R. S., "Some Recent Research on Non-Steady Flow Problems", P]'low Measurement Symposium, ASE, Sept. 26-28, 1966, pp. 80-102. 32'. Iellson, R. S., R. D. Garbg, and D. Woollatt, "A Numerical Solution to Unst eady l'low Problems", Int' 1 Journal of' Mech. Science, Pergamon Press. Ltd., 19)V4, Vol. 6, pp. 1(/'/-144.' 33. Carnahan, B., H. A. Luther, and J. O. Wilkes, Applied Numerical Methods, John Wiley and Sons, 1969. 34. Chaudhry, M. H., "Resonance in Pressurized Piping Systems", Journal of the Hydraulics Division, ASCE, Sept. 1970, pp. 18191839. 35. Streeter, V. L., "Computer Solution of Surge Problems", Symposium on Surges in Pipe Lines, Part I. Inst. of Mech. Eng., London, Nov. 1965. 36. Streeter, V. L., Fluid Mechanics, McGraw-Hill Book Company, 1958. 37. Streeter, V. L., "Water-Hammer Analysis of Distribution Systems", Journial of' the Hydraulics Division, ASCE, Sept, 19(07, pp. 18>-201. 38.?Dtreeter, V. L., I1ydraulic Transients, McGraw-li1i:l. BIook Co., 196gr.,re.e ti;er V. I,., and Wylie. B "Ntul.a I.i.p.ea39. i t,en Ls"AIEi4, papr "P.1I'. >J,, 19). 40. Stoner, M. A., "Steady-State Analysis of Gas Prodluctionl, Tlrismission, and Distribution Systems", AIME paper SPE 2554, 1969.

-2, 1)11. t,jLoer, M. A., "ACLe:itivitLy rialysis Applied to Steady Statce Mocdel o h iaitural C!s.'Transportation 1Systems", AIME1 paper SPE 3056, 1970. 42. Wylie, E. B., Stoner, M. A., and Streeter, V. L., "Network System Transient Calculations by Implicit Method", AIME paper SPE 2963, 1970. 43. Yow, W., "Analysis and Control of Transient Flow in Natural Gas Piping Systems", Ph.D. thesis, University of Michigan, 1971.

UNIVERSITY OF MICHIGAN 3 901 5 02519 6299 11111 3 9015 02519 6299