ENGN UMR0003 THE UNIVERSITY OF M IC H I GAN ENGINEERING INDUSTRY COLLEGE PROGRAM Effect of Initial Velocity Distribution on Heat Transfer in Smooth Tubes PETER HERMAN ABBRECHT September 1956 1 P -180 ANN ARBOR

THE UNIVERSITY OF MICHIGAN INDUSTRY PROGRAM OF THE COLLEGE OF ENGINEERING EFFECT OF INITIAL VELOCITY DISTRIBUTION ON HEAT TRANSFER IN SMOOTH TUBES Peter Herman Abbrecht This dissertation was submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy in the University of Michigan, 1956. September, 1956 IP-180

ACKNOWLEDGEMENT We wish to express our appreciation to the author for permission to give this thesis limited distribution under the Industry Program of the College of Engineering.

ACKNOWLEDGEMENTS The author wishes to express his sincere appreciation to a number of individuals for their assistance during the course of this work and in particular to the following: Associate Professor S. W. Churchill, chairman of the doctoral committee, for his continuous interest, encouragement, suggestions, and advice. Professors D. L. Katz, A. M. Kuethe, H. A. Ohlgren, and Alex Weir for their suggestions and assistance. Miss Anne Lampman for her assistance in the computational work. The Department of Aeronautical Engineering of the University of Michigan for the use of their facilities for, construction of hotwire anemometers. The Horace H. Rackham School of Graduate Studies of the University of Michigan for their grants ofUniversity Fellowships for the years 1952-54 and a tuition grant in 1955. The Visking Corporation for their generous fellowship grant for the year 1954-55. iii

TABLE OF CONTENTS Page ACKNOWLEDGEMENT....................... ii AUTHOR'S ACKNOWLEDGEMENTS................. iii LIST OF TABLES........................ vi LIST OF FIGURES....................... vii NOMENCL ATURE......................... x ABSTRACT..........................xiii I. INTRODUCTION...................1.... 1 II. SURVEY OF PREVIOUS WORK................ 9 Empirical Correlations................ 9 Experimental Investigations of Thermal Entry Length.. 10 Velocity Distributions. 11 Eddy Diffusivities................... 12 Analytical Solutions for Heat Transfer in Pipes..... 16 III. APPARATUS.............. 21 Hydrodynamic Entrances............... 24 Heating Sections.................. 27 Calorimeter..... 32 Exhaust Section and Gross Flow Measurement....... 36 Pressure Measurement.................. 31 The Temperature-Velocity Probe and Traversing Mechanism........................ 37 IV. EXPERIMENTAL AND CALCULATION PROCEDURES...... 43 Velocity Profiles................. 43 Temperature Profiles.................. 47 Location of Hot-Wire with Respect to the Wall. 51 Experimental Procedure............... 53 Physical Properties of Air.............. * 54 V. DISCUSSION OF RESULTS.................. 55 Pressure Drop...................... -56 Point Heat Fluxes................... 63 Velocity Profiles.............. 68 Temperature Profiles............. ~ 75 Eddy Diffusivities.................. 87 Radial Heat Flux................ 94 iv

TABLE OF CONTENTS (CONT.) Page CONCLUSIONS....................... 97 APPENDIX A.......................99 APPENDIXB... 106 BIBLIOGRAPHY.......... 128

LIST OF TABLES Table Page I Gross Values for Heat Transfer Runs........ 107 II Point Values for Temperature and Velocity Traverses.................... 108 III Momentum Terms in the Entrance Region....... 126 vi

LIST OF FIGURES Figure Page 1 The Hydrodynamic Boundary Layer in the Inlet Length of a Circular Tube. 3 2 The Thermal Boundary Layer After a Step Change in Temperature................ 4 3 Portion of Turbulent Velocity Profile Showing Mixing Length................... 14 4 Experimental Apparatus with Long Tube Entrance... 22 5 Experimental Apparatus with Bellmouth Entrance.. 22 6 Flow Diagram of Apparatus............. 23 7 Test Section Assembly............... 29 8 Detail of Calorimeter............... 33 9 Velocity-Temperature Probe........... 38 10 Traversing Mechanism............... 41 11 Hot Wire Circuit:................. 45 12 Temperature Corrections for.3 mil Platinum Wire.0482 inches long............... 50 13 Dimensions of Hot-Wire Probe............ 52 14 Pressure Gradient in the Inlet Region after Bellmouth Entrance for Re = 15,000......... 57 15 Pressure Gradient in the Inlet Region after Bellmouth Entrance for Re = 65,000..58 16 Friction Factor in Inlet Region after Bellmouth Entrance. Re = 15,000.............. 62 17 Heat Flux Correction for Calorimeter Measurements as Function of Wall to Room Temperature Difference. 64 18 Variation with Length of Point Nusselt Number for Long Tube Entrance............... 66 19 Variation with Length of Point Nusselt Number for Bellmouth Entrance.. 67 vii

LIST OF FIGURES (CONT.) Figure Page 20 Variation with Flow Rate of Reduced Velocity Distribution for Long Tube Entrance........ 69 21 Velocity Deficiency after Long Tube Entrance for Re = 65,000................ 71 22 Universal Velocity Distribution for Long Tube Entrance.................. 72 23 Comparison of Velocity Profiles near a Pipe Wall.. 73 24 Dimensionless Velocity Distribution after Bellmouth Entrance. Re = 15,000........ 76 2~5 Dimensionless Velocity Distribution after Bellmouth Entrance. Re = 65,000......... 77 26 Dimensionless Temperature Distribution for Long Tube Entrance. Re = 15,000.......... 78 27 Dimensionless Temperature Distribution for Long Tube Entrance. Re = 65,000........... 79 28 Dimensionless Temperature Distribution for Bellmouth Entrance. Re = 15,000.......... 80 29 Dimensionless Temperature Distribution for Bellmouth Entrance. Re = 65,000......... 81 30 Longitudinal Temperature Distribution for Long Tube Entrance with Re = 15,000.......... 82 31 Variation with Length of Longitudinal Temperature Gradient for Long Tube Entrance.......... 84 32 Variation with Radial Distance of Longitudinal Temperature Gradient for Long Tube Entrance. Re = 15,000................... 85 33 Graphical Differentiation of Radial Temperature Distribution for Run 4. 86 34 Longitudinal Velocity Gradient 1.5 Diameters After Bellmouth Entrance for Re = 15,000..... 89 35 Calibration for Chromel-Constantan Thermocouples.... 127 viii

LIST OF FIGURES (CONT.) Figure Page 36 Variation with Radius of Eddy Diffusivities for Long Tube Entrance for Re = 15,000........ 90 37 Variation with Radius of Eddy Diffusivities for Long Tube Entrance for Re = 65,000........ 91 38 Radial Distribution of Ev/v in Inlet Region for Bellmouth Entrance for the X/D's Shown (Broken line for long tube entrance). Re = 15,000.... 92 39 Radial Distribution of e /v in Inlet Region for Bellmouth Entrance for the Four X/D's Shown. Re = 65,000................. 93 40 Radial Heat Flux Distribution for Run 4...... 95 41 Variation with Radius of the Ratio C = for the Long Tube Entrance........v..... 96 ix

NOMENCLATURE a = pipe radius, ft. A' = constant in King's law equation. B' = constant in King's law equation. C = specific heat at constant pressure, Btu/lb ~F. p Cf = local skin friction coefficient. D = pipe diameter, ft. f = friction factor, (sometimes function of). -D dp f = local apparent friction factor = app 2p(ub G = mass flow rate, lb/hr sq ft. go = conversion factor, 32.2 lb - mass ft/ lb - force sec2 h = heat transfer coefficient, q/(tw - tb) Btu/hr ft ~F. i = electrical current, amperes. J = 778 ft - lb/Btu. k = thermal conductivity, Btu/hr ft ~F. K = thermal diffusivity, PCp i = mixing length, ft. L = length, ft. Nu = Nusselt number, hD/k. p = pressure, lb -force/sq. ft. Pr = Prandtl number, Cp p/k q = heat flux, Btu/hr sq ft. q = laminar heat flux, Btu/hr sq ft. qt = turbulent heat flux, Btu/hr sq ft. Q = heat generation per unit length, Btu/hr ft. r = radial distance, ft.

r = r/a. R = electrical resistance, ohms. R = wire resistance at air temperature, ohms. a R = wire resistance at ~F, ohms. 0 = Re = Reynolds number, D U%/v. Rex = length Reynolds number, ub x/v S = distance between probe tips, ft. t = temperature, OF. tb = mixed mean temperature, OF. t = inlet temperature, OF. t = stagnation temperation, ~F. tw = wall temperature, F. u = mean axial velocity at a point, ft/sec. Ub = average axial velocity, ft/sec. Um = maximum axial velocity, ft/sec. u* = friction velocity, ~To/p. u = dimensionless velocity, u/u*. u' = root mean square of instantaneous velocity fluctuations in x direction. U = ratio of mean local velocity to maximum velocity, u/u v = mean radial velocity toward wall, ft/sec. W = weight rate of flow, lb - mass/ hr. X = axial distance, ft. y = distance from wall, inches. y = dimensionless distance from wall, u* y/v. Z = dimensionless axial length, x/a, ft. a = Ec/E v ratio of eddy diffusivities. = temperature coefficient of resistance, 1/~F. xi

y = recovery factor. ec = eddy conductivity, ft2/sec. /c. Ev = eddy viscosity, ft /sec. t - t e = dimensionless temperature 0 t - t w o = viscosity, lb - force sec/ft2. v = kinematic viscosity, ft /sec. p = density, lbm/cu ft. 2 X = shear stress, lb - force / ft T = laminar shear stress, lb - force/ft Tt = turbulent shear stress, lb - force/ft2 r* r U d r. 0 xii

ABSTRACT The purpose of this study is to investigate the effect of initial velocity distribution on heat transfer to air flowing in a smooth tube. It is known that the geometric form of the inlet to a heat exchanger tube strongly influences the heat transfer coefficient in the inlet region. This effect is primarily due to the initial velocity distribution produced by the inlet. By measuring temperature and velocity profiles, and point heat transfer rates in the inlet region, it is hoped to gain a better understanding of the mechanism by which these effects occur. Measurements were made for heat transfer to air flowing in a 1.52 inch inside diameter tube with the following geometric entrances: 1) a long tube which gave essentially fully developed turbulent flow, and 2) a bellmouth entrance which gave an initially flat velocity profile. Measurements were taken at distances of.453, 1.13, 1.75, 4.12, and 9.97 tube diameters downstream from the start of heating at Reynolds numbers of 15,000 and 65,000. Pressure drop measurements were also made in this region. Longitudinal and radial temperature gradients, radial heat fluxes,' and eddy diffusivities for momentum and heat transfer were computed from the measurements. The ratio of eddy diffusivity for heat transfer to that for momentum transfer, a, was found not tio be a function of length in the thermal inlet with fully developed flow. Over most of the tube crosssection the ratio was about 1.5. The ratio a was a function of length for the bellmouth inlet. xiii

The radial heat flux was found to be essentially constant in the laminar and buffer zones and to vary linearly in the turbulent zone. Pressure drop due to acceleration effects was found to be appreciable compared to- wall friction losdes in the bellmouth inlet. It is concluded that theoretical analyses which postulate the same distribution of eddy conductivity in developing thermal boundary layers asfor fully developed ones are valid for the case of fully developed hydrodynamic boundary layers in the thermal entrance region, but may be subject to large error when the hydrodynamic and thermal boundary layers develop' simultaneously. xiv

I. INTRODUCTION Convective heat transfer to fluids flowing in circular tubes has been the subject of a large number of experimental and analytical investigations. Until recently, by far the largest part of the research on heat transfer in pipes has been concerned only with the region far downstream from the pipe entrance where all effects due to inlet disturbances have vanished. Two factors have been responsible for this neglect of the consideration of inlet effects. In the first place, in most conventional tubular heat exchangers, the tubes are long enough so that the entrance region comprises only a small part of the total heat transfer area, and therefore has little effect on the heat transfer capacity of the unit as a whole. In the second place, because of the complexity of developing flow and temperature fields, mathematical treatment of the inlet region is difficult. The analysis is particularly complicated in the case of turbulent flow. Therefore, most of the early theoretical treatments of transfer processes in the inlet length, such as that of Graetz for heat transfer (19) and Schiller for momentum transfer (53), have been limited to laminar flow. However, the case of turbulent flow is by far the most important industrially. Recent developments such as short tube nuclear reactors and aircraft heaters.in which most of the transfer area lies in the entrance region, have created a need for a more fundamental knowledge of the effect -1

-2of inlet conditions. The general impetus in the last few years in research in basic heat transfer phenomena has also heightened interest in the mechanism of heat transfer in the inlet region. Also, the advent of high speed mechanical and electronic computers has made numerical solution to several specific cases possible. Data presented by Boelter (5) and others show that the heat transfer coefficient inside tubes directly downstream from a turbulence promoting inlet may be three times that obtained far downstream of the inlet where entrance effects have died out. This effect is probably due primarily to the initial velocity distribution and level of turbulence produced. For many cases, at least, the first factor is probably the most important. This is indicated by the fact that Boelter found in his work that the effect on the heat transfer coefficient of increasing the degree of turbulence by the addition of screens was negligible. The purpose of this investigation is to study the mechanism by which the rate of heat transfer in turbulent flow in tubes is affected by the initial velocity distribution. The fact that the initial velocity distribution influences heat transfer in the inlet region can be explained by a consideration of the hydrodynamic and thermal boundary layers. In all real (non-ideal) fluids flowing past a solid boundary, a boundary layer due to viscous shearing stress is present. The hydrodynamic boundary layer in the inlet length of a circular tube is shown in figurle 1.

-3Figure 1. The Hydrodynamic Boundary Layer in the Inlet Length of a Circular Tube Here the fluid is considered to be moving with uniform velocity as it enters the tube. At the tube entrance there is a retardation of the fluid particles next to the wall because of frictional effects. A thin layer then exists in which the fluid velocity builds up from zero at the wall to the core velocity at the edge of the boundary layer. As the fluid moves down the tube, the thickness of the boundary layer gradually increases, until it merges at the center of the tube. There then exists the condition described as "fully developed flow." For a fluid with constant physical properties the shape of the velocity profile remains constant after fully developed flow has been attained. The above description is somewhat oversimplified since there is some change in the

-4shape of the velocity profile for a short distance downstream from the point where the boundary layer merges. An analogous effect occurs when a fluid of uniform temperature flowing through a tube is suddenly subjected to a step change in wall temperature, as shown in figure 2. Start of Heating t t to tw T -- --— X::- 2 I I A B C D Fi.gure 2. The Thermal Boundary Layer after a Step Change in Temperature'he fluid and wall are initially at the same temperature to As the fluid enters the heated section-the fluid particles next to the wall are heated. There is then a very thin layer in which the temperature decreases from tw at the wall to to at the edge of the unheated core. At a sufficiently great distance down the tube the temperature boundary layer merges and the fully developed thermal boundary layer is attained. The distance required for the boundary layer to merge is known as the "thermal

-5inlet length.'! It is to be noted that with the boundary condition of constant wall temperature postulated here the shape of the temperature profile continues to change even after the thermal boundary layer becomes fully developed. If the heated tube were infinitely long, the fluid would emerge, with a uniform temperature. The above picture is also an idealized model, for a minute amount of heat might penetrate to the center even at B. This difficulty can be circumvented by defining the boundary layer as that layer bounded by the pipe wall in which the temperature increase over to is less than 2 % of tw - to. The thermal and hydrodynamic boundary layers may develop simultaneously, as when heating starts at the flow inlet; or the hydrodynamic boundary layer may be partially or fully developed at the point where heating starts. As can be seen from figure 2, at a point in the fluid next to the step change in wall temperature, there is a finite temperatur.e difference tw - to over an infinitesimal distance since the thermal boundary layer has not yet had a chance to develop. This implies that there is an infinite temperature gradient at this point. Since the heat flux at the wall is defined by: at (1) q(x) = -k 1y) (y)

-6the heat flux at'a step change in wall temperature would be infinite; and the heat transfer coefficient defined by:, (2) h= q t -t w b would also be infinite. Of'course, in practice one does not obtain absolute' step changes in temperature. However, very steep temperature gradients are obtained in the thermal entrance region and account for the much higher coefficients obtained there. The temperature gradient is related to the velocity profile by the following partial differential equation which governs heat transfer in flow in a tube where both thermal and hydrodynamic boundary layers are developing. [t 3t 3 3t + t E v *,) +t V r = e ) E 1] (3) U,+ r X oC'c) F+ It~(K+ Ec) 3r Extensive experimental studies of the effect of two different initial velocity distributions upon heat transfer were made in this investigation. The first case was that where the velocity distribution is fully developed before heating begins. The second was that of uniform initial velocity, distribution with both thermal and hydrodynamic boundary layers beginning at the same point. In both of these cases the boundary condition of uniform wall temperature was imposed. The determination of temperature distribution and heat flux for these two cases has been accomplished by solving equation 3 after making certain assunptions.

-7One of these assumptions involves the functional relation for eddy conductivity ec. For the first case, this has been obtained by using the analogy between the transfer of heat and momentum, which states that the ratio of the eddy diffusivity for heat to that for momentum, a., is equal to unity:. The eddy diffusivities for momentum (eddy viscosities) were obtained using generalized velocity distributions for turbulent pipe flow. For the second case, either the analogy has been used or values of e determined for fully developed flow and temperature fields have been considered to apply also to the developing boundary layer. Both these assumptions are particularly questionable for this case. Values of a obtained in fully developed flow and temperature fields range from unity to 1.6, indicating that the analogy is not exactl correct. No data have been presented for eddy conductivities in the inlet region of a tube. Other assumptions which must be made in the solution of equation 3 for the inlet conditions considered are the variation of heat flux radar ially (or a) and the form of the velocity distribution. This investigation was made with the object of providing a better understanding of heat transfer in turbulent flow in inlet regions. By obtaining point temperature and velocity measurements the variation of such quantities as ec and cv, the radial heat flux, and temperature and velocity gradients were obtained as a function of radius and distance from the inlet.

-8This information should be of use in the prediction of the thermal transfer and temperature distribution in turbulent flow streams from a knowledge of the flow field and boundary conditions alone. For this investigation, an apparatus was constructed to measure point heat transfer rates and temperature and velocity profiles within an air stream at varying distances downstream from the hydrodynamic inlet. Such data were obtained for a long tube entrance and a bellmouth entrance at Reynolds numbers of 15,000 and 65,000.

II. SURVEY OF PREVIOUS WORK Empirical Correlations An excellent review of the literature on turbulent heat transfer in tubes is given in "Heat Transmission" by McAd.ams (40). For design purposes empirical equations derived with the aid of dimensional analysis have found extensive application because of the ease and rapidity with which they may be used. For fully developed flow in tubes dimensional analysis predicts the functional relationship: hD f(DG Cp1 k, k (4) Dittus and Boelter (13) have presented the following equations for fully developed flow: hOD 8 4 hD = 0243 (Re)' (Pr) (heating) (5) hD =.0265 (Re) (Pr)' (cooling) (6) For short tubes where entrance effects are important, the length to diameter ratio,, must be included as one of the dimensionless groups in f of equation 4. From experiments of Burbach (6) in the range L/D = 10 to 400,Nusselt (44) concluded that h is proportional to (D/L) 1/18 He found this verified by experiments of Eagle and Ferguson (14) in about the same range. -9

-10Hausen (21) proposed the following relation which takes conditions in the intake region into account: Nu =.116 [(Re) /3 -125] (Pr) [1 + ( )2/3 () o. where LB is the viscosity at bulkl liquid temperature and pW the viscosity at tube wall temperature. Experimental Investigations of Thermal Entry Length The most extensive experimental investigations of heat transfer in the inlet region for turbulent pipe flow are those of Boelter, Young, and Iversen (5) and Hartnett (20). Boelter, et al., determired point heat transfer rates in the entrance region for a wide variety of hydrodynamic entrances, including long and short calming sections, bellmouths, orifices, and elbows. A steam jacket divided into a number of compartments along its length was used for heating,and heat transfer rates were determined from measurements of the amount of condensate from each compartment. For the long tube entrance the inlet region was found to vary from L/D of 10 at a Reynolds number of 27,000 to L/D of 15 at a Reynolds number of 53,000; for the bellmouth the inlet length was 9 L/D for Reynolds numbers between 26,000 and 56,000. For values of L/D greater than about five the average heat transfer coefficient could be approximated by the equation h = h (1 + P D) where P is a constant for any avg L given inlet. Hartnett studied the flow of water and several oils in an electrically heated tube with a long calming section entrance. From heat

-11flux and wall temperature measurements he calculated the Nusselt number at various distances downstream from the start of heating. His results are particularly valuable since they cover a wide range of Prandtl numbers. His results with water covered Prandtl numbers from 7 to 9 and Reynolds numbers from 16,900 to 89,200, while the oil runs covered Prandtl numbers from 61 to 480 and Reynolds numbers from 1580 to 46,600. Al-Arabi and Davies (2) have studied several of the same entrances as Boelter, but used water as the fluid. Cholette (7) utilized a small shell and tube heat exchanger so baffled that steam could be condensed in separate compartments to obtain average local coefficients of heat transfer in the inlet region. For an initially flat velocity distribution he found that the average Nusselt number was proportional to (D/L)0l Heat transfer coefficients for the inlet region have also been reported by Aladyev (1) for water at uniform wall temperature; Johnson, Hartnett, and Clabaugh (29) for lead bismuth eutectic at uniform heat flux; and Hoffman (23) for molten sodium hydroxide at uniform heat flux. Velocity Distributions Carefitl experimental investigations of velocity distributions in fully developed turbulent pipe flow have been made by Nikuradse (4-3), Laufer (34), Deissler (10), and Sleicher (59). Measurements between parallel flat plates have been made by Laufer (35), Reichardt (48), and Corcoran et al., (9). Their results are applicable to pipe flow in the region close to the wall.

-12Various equations for correlating velocity distribution data have been proposed. These equations are described by Bakhmeteff (3), and Knudsen and Katz (30). The most commonly used correlation for turbulent velocity distributions near the wall is the Nikuradse-von Karman universal velocity distribution (30). In a review of Nikuradse's data, r + Ross (50) shows that for the region 0 <- <.85,u is not a single-valued a function of y+, but depends also on Reynolds number. For the inner 85% of the pipe radius he suggests the data be correlated by plotting (u max u)/u* against 1 - Z max r Rothfus and Monrad (51) have presented a modification of the u+, y+ relationship which does result in a unique correlation of the main stream velocity distribution in smooth tubes and extends the correlation to the case of flow between parallel flat plates. Data for velocity distributions in the inlet region for the case of uniform initial velocity distribution have been reported by Deissler (10) and Weissberg (62). Both authors reported their values as u/u as a function of r/a, without attempting a general correlation. max Ross (50) has recently published an analytical solution for the turbulent boundary-layer flow in the entrance region of a pipe. Eddy Diffusivities The relations for shearing stress and heat flux in laminar flow are: T -= y (8) 2 ~~~~~~~~~~(8)

-13-kt (9) q = -k 9 In an analogous manner, for turbulent flow one may write: T au (10) T g( V+Ev) 6y q -p C (k + ) t (11) P pCp c). where the second terms in the brackets on the right account for the contributions of turbulent action to the transfer process. Equations 10 and 11 may be considered to be the defining equations for the eddy diffusivity for momentum transfer and heat transfer respectively. Reynolds (49) suggested that momentum and heat in a fluid are transferred in the same way and that cv = e Prandtl (47) proposed a theory for turbulent heat and momentum transfer based on the concept of mixing length. He postulates a model (figure 3) in which a turbulent eddy travels from one layer of fluid at y through a distance 2 (the mixing length) to another layer (y +2 ) of different velocity and temperature. The eddy'is considered to retain the mean temperature and velocity of the original layer during its flight and to dissipate them into the second layer when it arrives there.

T <u(Y+) Figure 3. Portion'of Turbulent Velocity Profile Showing Mixing Length The difference between the eddy's old and new velocity is U (y + 2) - u (y) or approximately. The mass exchange across plane a per unit area due to eddy exchange is equal to pv. Prandtl makes v to be of the same order of magnitude as the difference in velocities u m U (y+B) - Um (Y) The shear between the layers due to eddy motion is the product of the mass exchange per second and the difference in velocities of the two layers: T Q (X2 du) du (12) t dy dy) a similar analysis for heat transfer yields: tC pP(2 ) d (13)

-15If Ev is substituted for 2 IdU in (12) and %c for 2 d in (13), we dy dy obtain the expressions for turbulent transfer in (10) and (11). Jenkins (27) modified the mixing length theory by'allowing the eddy to transfer some of its heat and momentum during its time of travel over the mixing length. His results predict that the ratio of eddy conductivity to eddy viscosity, a.? should be a function of the turbulence and physical properties of the system, rather than being equal to unity as in Prandtl's analysis. In particular, one would expect c to vary in cases where-the turbulent flow field is still developing such as in the inlet region of tubes or behind immersed bodies. Experimental values for eddy diffusivities for momentum and heat transfer have been reported for several different flow systems. Reichardt (48), using measurements of velocity and temperature profiles for pipes by Lorenz (37) and for flat plates by Elias (16), computed values of C of 1.4 and 1.5 respectively. From their experimental velocity and temperature distributions in a smooth heated tube, Seban and Shimazki (56) determined a maximum value of 1.2 for a ocurring in the region adjacent to the buffer layer. IsafQff and Drew have determined eddy diffusivities for momentum and heat in turbulent flow of mercury. They found that the ratios olds number. and ~~ )- are functions of radius but not Reynolds number. max c max For the maximum values of E and e at a given Reynolds number, they V C obtained the relations: (Va = 6.35xl10 5 (Re).85 (14) (~)max

-16-8(Re)29 (15) (EC), - 29 x 10 (Re) C max e -.46 r and present their data in a generalized plot of CS(Re) vs. a Ev Corcoran, et al., (19) computed eddy diffusivities between heated flat plates. Because of some uncertainty in their data as to the variation of a with radial position, they present average values of a for the whole channel as a function of Reynolds number. These data indicate an increase in a with Reynolds number. However, in a more recent paper (8) they report that for a slightly different level o'f turbulence the reverse trend appears to be true at Reynolds numbers above 20,000. Careful temperature measurements of Sheppard (58) made with the object of establishing the ratio between c and eev yield a value of about 1.6 for this ratio. Other authors who have reported eddy diffusivities for tube flow are Sleicher (59) for heat and momentum, and Deissler (12) for momentum. For flow behind heated cylinders it appears that the value of a is 2 (61). Prandtl (46) suggests that this difference between the value ofc in boundary layer flow and that in free turbulence may be due to a difference in the orientation of the axis of the eddies with respect to the direction of flow. Analytical Solutions for Heat Transfer in Pipes The energy equation for a fluid of constant properties in turbulent flow in the entrance region of a smooth pipe, neglecting heating

-17due to pressure changes and frictional dissipation, is (18) i [ e) H] + r 7 [r (K + Ec) ] = u + v (3) where the prime mark indicates that the diffusivities in the x and r directions are not necessarily equal. In the solution of this equation the first term on the left is generally neglected, since the amount of heat transferred longitudinally by conduction is small compared to that transferred by flow. This assumption appears to be validated by the analyses of Deissler (12) and Poppendiek (45). At a Reynolds number of 21,000 Deissler found the ratio of axial conduction to bulk transport to be.008 at x/D = 0.8 and.002 at x/D = 3.1. For fully developed turbulent pipe flow the mean radial velocity, v, is equal to zero and the second term on the right vanishes. Equation 3 then becomes:;~-[r(K+EC)~F~]r Q; [rX (K +(16) Several solutions to equation 16 have been obtained for the case of fully developed thermal and hydrodynamic boundary layers. Martinelli (39), Lyon (38), and Deissler (11) considered the case of constant heat flux at the wall, for which tr) constant. They based their analysis on the analogy between heat and momentum transfer and used 1 = 1 in their numerical calculations. Martinelli assumed that u is a constant and equal to the mean velocity. On this basis he used a linear distribution of heat flux

radially, except in the laminar and buffer layers, where he assumed the heat flux equal to that at the wall. He used the generalized von KarmanNikuradse velocity distributions to determine eddy viscosity. Lyon and Deissler retained u as a function of r and integrated the equation numerically. Lyon used the smoothed data of Nikuradse for his determination of u and Ev, while Deissler developed an empirical equation for e from his velocity dafta. In his solution the heat flux V is considered constant across the tube. Seban and Shimazaki treated the case of fully developed velocity and temperature distributions with constant wall temperature. They assumed that a generalized temperature distribution which is invariable t -t in the direction of flow exists such that (t )=. Momentum diffusivities for the turbulent core were obtained from the PrandtlNikuradse velocity distribution. Numerical solutions were obtained by use of an iterative method. Latzko (33) obtained analytical solutions for heat transfer in the entrance region for three cases: (1) hydrodynamic and thermal states fully established, (2) hydrodynamic state fully established, uniform initial temperature distribution, (3) uniform initial temperature and velocity distributions. Using Prandtl's and von Karman's equation for shearing stress and velocity distribution and the equivalence of eddy diffusivities for momentum and heat transfer, he wrote equation 16 as follows: a[ (2 - r )67 2/7 MT

-19w r 81/4 2a3/28 where M v By a method of approximation he obtained 7 1. 99 v a three term solution for case (1) which also applies to case (2) when x approaches o. For the third -case he used an integral method for computing boundary layer buildup. Boelter et al., (5) have succeeded in simplifying Latzko's equations considerably. Deissler (12) has also obtained a solution for the case of initially uniform temperature and velocity distributions using integral methods for computing velocity and temperature profiles. He assumes that expressions derived for eddy diffusivities in fully developed boundary layers apply also to developing boundary layers. Further assumptions included in his analysis are that a = 1 and that variations of shear stress and heat flux across the flow and thermal boundary layers have a negligible effect on velocity and temperature distributions. Berry (4) and Sleicher (59) have obtained solutions of equation 16 for the thermal inlet region by the method of separation of variables. Sleicher obtained numerical solutions for the case of fully developed flow with a step change in temperature by means of an electronic analog computer. Sanders (52) has obtained a general turbulent flow solution for pipe entrance regions with uniform wall temperature by transforming the turbulent core to a laminar core of equivalent thermal resistance. Levy (36) presents a method by means of which transient heat conduction solutions can be used to determine temperature distribution of fluids

-20flowing in pipes, annuli, and between flat plates. Poppendiek and Harrison (45) have reviewed several pipe solutions that are not limited to an established temperature distribution.

III. APPARATUS In this chapter is described the equipment which was constructed to obtain temperature and velocity profiles, point wall heat transfer rates, and pressure drop data in the hydrodynamic entrance region. Discussion of the hot-wire instrumentation is deferred till Chapter IV in order to make the discussion of experimental procedure more readily understandable. The hydrodynamic entrances chosen for study were (1) a long straight tube which produced essentially fully developed turbulent flow and (2) a bellmouth entrance which gave a uniform initial velocity distribution. Figures 4 and 5 show photographs of the apparatus with the long tube and bellmouth in place. A flow diagram of the apparatus is shown in figure 6. The components of the system may be classified into six divisions: air supply filtration and regulation, hydrodynamic entrance, heating section,. calorimeter, traversing mechanism, and exhaust section. The air from the supply main, after filtration,passes through an entrance section in which the initial velocity profile is established. It then passes through a heated tube where the temperature profile is developed and then through the calorimeter, where measurements of thermal flux and temperature and velocity profiles are made. In order to investigate the thermal and hydrodynamic boundary layers at different distances from the inlet, several interchangeable heating tubes of different

-22iili ~ ~ ~ ~ ~ ~ ~ jiii ~:j!~!i!ii _~!~ ii.. Z iiii i iii......! -i.::i iiiii:li~iiiiii i ~rii t 0 DED>;.ff.E.E.EN:iL ~f fiDE i............., Fig:ure 4. Experimental Apparatus wit Long Tube Entrance::::::::. b.. i......................... -. l iiiil iiiiiiiiiiiiiiii!!:i! iiiii~~~~~~~~~iii~~~~~~i~~~~ili',i~,i!!11i ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~~iiii Figure 5. Experimental Apparatus with Bellmouth Entrance

Figure 6 Flow diagram of apparatus CALORIMETER INLET T.C. PROBE ENTRANCE SECTION-itPES PRESSURE REGULATOR.-PRESSURE TAPS j HEATING SECTION FILTER ORIFICE 90 psig AIR SUPPLY I~~~~~~~~~

length were used. From the calorimeter the air flowed through an exhaust section in which the flow rate was determined by an orifice meter, after which it was vented to the outside of the building. The various components of the flow system are described below. Air Supply Air from the 90 psig laboratory supply main was passed through a cylindrical filter containing screens, glass wool, cotton wool, and activated carbon. A pressure control regulator downstream from the filter was used to maintain a constant line pressure at a point ahead of the final throttling valve. By maintaining a constant pressure at the inlet of the test section a constant flow rate was obtained, since differences in air density in the test section during a run due to changes in atmospheric pressure and temperature were negligible. After throttling,the air was conducted to the test section in a one-inch flexible hose. This arrangement permitted entrance sections of different lengths to be installed without complicated changes in piping. Hydrodynamic Entrances 1) Bellmouth To remove turbulence effects and non-symmetry in flow generated by the pressure regulating system and hose, a calming chamber was placed before the bellmouth. The hose from the throttling valve was coupled to a diverging nozzle which expanded the area for flow up to the four inch diameter of the calming section. The calming chamber consisted of an eight inch length of four inch diameter Carlon pipe.

-25A small electrical heater consisting of two layers of 30 gage enameled constantan wire criss-crossed on a plastic disk was placed at the entrance of the calming section. The purpose of this heater was to control the temperature of air entering the test section, primarily for probe temperature calibration as will be described below. Power input to the heater was regulated with a Powerstat autotransformer. The capacity of the heater was such that it was possible to raise the temperature of the incoming air by about 100F at the highest flow rate. Because of the small thermal capacity of the fine wire, temperature changes in response to changes in heater power were very rapid and fine control was possible. Two 1/16-in. mesh monel screens were placed in the calming section downstream from the heater. The purpose of these screens was to break up any large eddies that might stillbe present and to smooth the temperature distribution produced by the preheater. Available correlations for the decay af turbulence behind screens (32) indicate that most-of the fine scale turbulence produced by the-screens would be dissipated before the fluid left the calming chamber. A thermocouple to measure the temperature of air entering the test section was placed in the calming section downstream of the last screen. The couple was placed in a thermal well which consisted of a piece of 3/32-in. stainless steel tubing which extended to the center of the chamber. To prevent disturbance of the initial velocity profile, the well was withdrawn during the taking of velocity and temperature profiles.

-26The bellmouth entrance was flanged directly to the calming section. It consisted of a converging nozzle machined from aluminum such that the inside diameter was reduced from 4 to 1.520 inches in a length of about 5 inches. Because of the system of flanging used, it was necessary that the nozzle be constructed with a straight run l1 inches long at its outlet end. This is somewhat unfortunate, since the hydrodynamic boundary layer thus starts building up slightly before heating begins. However, since there is some boundary layer buildup in the converging portion of the nozzle, the complication introduced is only a matter of degree. Preliminary investigations of velocity and temperature profiles both with and without the calming section preheater in operation showed that the nozzle produced uniform temperature and velocity fields except for a thin boundary layer next to the wall. Besides its use as a distinct entrance, the bellmouth preheater combination was also installed upstream of the long tube entrances in all runs in which it was used. The purpose for this was to insure a uniform and definable velocity distribution before the long tube entrance. 2) Long Tube Entrance The long entrance consisted of a 66 inch long thick-walled copper pipe 1.520 inches inside diameter and 1.900 inches outside diameter. This length of 43.5 L/D was sufficient to give essentially fully developed turbulent flowo The required values usually recommended for attaining fully developed turbulent pipe flow vary from 50 to 100 pipe diameters. No set

-27value can be determined, however, for the critical L/D depends on the smoothness of entry as well as the Reynolds number. Velocity distributions taken at various distances downstream from the long tube entrance showed that flow was fully developed near the wall, although there was still some development 6ccuring in the center portion of the tube. The long tube entrance was also equipped with pressure taps at distances of 1, 3, 5, 15, 30, 44.5, 61, and 65 inches from the starting end. Pressure taps consisting of 1 inch lengths of thick walled 1/8 inch O. D. staihless steel hypodermic tubing were soft soldered to the copper tube. The pressure tap holes were formed by first drilling a 1/32 inch hole through the copper tube wall, and then counterboring partway through from the outside to form a hole into which the stainless steel' tubing could be driven before soldering. Burrs on the inside of the tube were removed by the honing process described below. To reduce the possible influence of one static hole upon the one downstream from it, azimuthal positions of the holes were staggered on two different generating lines of the pipe located about ten degrees apart. Heating Sections (1) Steam Jackets Four different heating sections with lengths of 1.025, 1.975, 3.540, and 14.45 inches were used to obtain different heated L/D's. Only one of these sections was used at a time. Each section was machined from the same dimension pipe as the long tube entrance.

For the longer heating sections, steam appeared to be the most satisfactory medium. This choice was based on the fact that with condensing steam the outside coefficient would be on the order of several thousand while the inside coefficient would be about one-hundredth as large. Thus the inside coefficient would be controlling,and little longitudinal temperature gradient would be expected along the tube. The two longest heating sections consisted of steam jackets constructed as shown in figure 7. Copper rings 1/8 inch thick were machined so that they would slip over the thickwalled copper pipe and fit inside the outer jack-,et, which was made from standard three inch copper pipe. The steam jackets were assembled with solder. One-eighth inch brass nipples were soldered to the jacket to provide a steam inlet, condensation outlet, and a-tap for a manometer line. Five thermocouple holes were drilled in each jacket, two in the upstream end and three in the downstream end. The holes were.020 inches in diameter and drilled at an angle so that they came within.020 inches of the inside wall at a point about 1/4 inch from the end of the jacket. Thirty-six gage chromel constantan thermocouples were inserted to the depth of the holes and secured with porcelain cement. The purpose of these thermocouples was to estimate the degree of uniformity of the wall temperature distribution both radially and longitudinally. All thermocouples used in the apparatus were made from 36 gage chromel constantan wires. The two wires were twisted together and then

LOCATION OF GASKET i 075 J ~~~~~~~~~~.075 I-0 I I I HEATING SECTION INSULATCALORIMETER ING DISK PROBE ENTRANCE SUPPORT SECTION SECTION Figure 7. Test section assembly

-30fused in an acetylene flame. The length of the bead was trimmed to about.02 inches and the tip painted with microstop electroplating lacquer. The thermocouple cold junction was immersed in purified kerosene in a thin glass tube which was placed in melting ice in a wellinsulated thermos bottle. The thermocouple and cold junction leads entered a well insulated wooden box which was lined with copper to assure its being isothermal. For thermocouples in the heating-lengths this connection was made by multi-conductor connectors so that only the heating length being used was connected. The box housed four Leeds and Northrup 2-pole, 12-position selector switches, type 31-3. Copper wires connected the switches to a Leeds and Northrup type K-2 potentiometer. The error signal from the potentiometer was fed to a Liston-Becker model 14 D. C. breaker amplifier, whose output was fed to a Brown Electronikpotentiometer used as an indicating galvanometer. It is estimated that the precision of temperature measurement was about.030~F. Two thermocouples were calibrated in a constant temperature bath against a -platinum resistance thermometer calibrated by the Bureau of Standards, A calibrated Leeds and Northrup Mueller bridge was used to measure the thermometer's resistance. The thermocouple calibration is shown in figure 35. It agrees closely with that given by General Electric (17) for their chromel-constantan couples.

-31The rest of the thermocouples in the apparatus were then calibrated against the standardized couples under isothermal conditions. Steam from the 120 psig supply main was throttled down in three stages to the pressure in the jacket. Since the desired wall temperatures were usually in the range of 100 to 1100F, corresponding to saturation pressures of 2 to 2.6 inches mercury, it was necessary to exhaust the condensate under vacuum. This was accomplished by a vacuum pump drawing through an ice trap and then a dry ice trap. An air bleed was provided on the pump as a means of fine pressure adjustment. At the low steam flow rates required, there was a tendency toward surging due to accumulation of condensate in the supply lines. This was overcome by drawing a considerable amount of vapor through the steam jacket and condensing it in the ice trap. The total amount of steam condensed during a six hour run usually amounted to about a gallon. (2) Electrically Heated Sections Because of the difficulties involved in controlling minute quantities of steam, electrical heating was used on the two shortest heating sections. The outer side of the thick walled copper pipe was painted with electroplating enamel and then wrapped with tissue paper to provide a non-conducting surface. The insulated pipe was then wound with 1/8 inch wide chromel ribbon with about 1/16 inch spacing between turns. Heating current was supplied by an adjustable autotransformer operating from a 220 volt source which was smoothed by a Sola constant voltage transformer.

-32Thermocouples were located at the same positions as in the steam jackets, except that with the electrical heaters it was possible to drill the holes perpendicular to the tube wall rather than at an angle. Calorimeter The details of construction of the calorimeter are shown in figure 8. Essentially it consisted of a one inch segment of thick-walled copper pipe, electrically heated by a closely wound 1/8 inch wide by.0126 inch thick chromel ribbon and surrounded by a heated guard to prevent external heat losses. The dead air space between calorimeter and guard was filled with loosely packed cotton to reduce convection. The calorimeter segment and guard, also of copper, were electrically insulated from their resistance windings as described above for the electrical heatingsections. The outside of the guard was wrapped with 36 gage chromel wire and heated with current from an Adjustavolt autotransformer. The calorimeter and guard heater resistances were approximately 1.35 and 140 ohms respectively. The guard heater was insulated thermally from the adjacent sections of the guard by disks of Continental-Diamond grade xx-13 paperbase laminated phenolic plastic (thermal conductivity approximately.25 BTU/hr ft~F.) The thermal expansion coefficient of this material is almost identical to that of copper, thereby reducing the possibilities of unequal expansion. The calorimeter segment, plastic disk, and guard

COPPER GUARD HE:ATER - -— 1.00.,~/.:" WELLS I 14I;iW CALORIMETER SEGMENT SECTICON DISK Figure 8 Detail of calorimeter

heater segments were held in alignment by means of.025 inch diameter chromel pins, as shown in the diagram. Thermocouples were located in the ends of the calorimeter segment and at corresponding points in the guard so that by adjustment of guard and calorimeter heater currents, it was possible to maintain caiorimeter wall temperature and guard wall temperature very close to each other. Under such isothermal conditions there was no loss from the calorimeter to the surroundings and the total heat input to the calorimeter could be considered to flow through the pipe wall into the air streaml-n. Current for the calorimeter heater was obtained from two 6-volt storage batteries connected in parallel. A battery charger was floated on the line during operation to reduce the drain on the, batteries and provide a more constant current~ Calorimeter current was controlled by a resistance network, consisting of several fixed resistors with shunting switches and a slidewire for fine adjustments. Power input to the calorimeter was obtained from measurement of the voltage across the calorimeter winding terminals with a calibrated D. C. voltmeter and measurement of current was done by determining the potential drop across a calibrated.01 ohm resistance with a Leeds and Northrup student type potentiometer. Alignment of calorimeter, heating section, and entrance section was accomplished by means of male and female joints as shown in figure 7. All sections were carefully honed to a 30 micro-inch finish to ensure smoothness of surface and avoid steps in the inside wall surface at joints

-35between sections. The maximum step found between sections was estimated to be on the order of.001 inch. The components of the test section were held together with 3/16 inch machine screws acting upon steel flanges.20 inches thick with six.20 inch holes located on a 3 1/2 inch bolt circle' The system was so designed that no flange was connected directly to the calorimeter or the thickwalled copper pipe of the heating sections. This was necessary since any flange mounted on the heat transfer surface would have disturbed the wall temperature distribution. For runs using electrically heated sections, the entire assembly was held together by one set of tie bolts running across the heating section and calorimeter from a flange on the entrance section to one on the traversing mechanism. With the steam jackets, intermediate flanges soldered on each end of the outer wall of the jackets were used. Thin gaskets of soft polyethylene sheeting were inserted between sections as shown in figure 7. The thickness of gasket used was somewhat greater then the width of the gasket space. The tie bolts were drawn up till the mating metal surfaces were in contact (as evidenced by visual inspection of the inside wall surface). This compressed the gaskets sufficiently to prevent leakage. Lock washers were used on all tie bolts. A carefully machined.20 inch thick disk of glass fibre laminated phenolic plastic (thermal conductivity.29 BTU/hr ft~F) was in. serted between the hydrodynamic entrance section and the heating section *in all cases. The purpose of this disk was to reduce end loss and more

nearly approximate the condition of a finite step in wall temperature at the start of the heated length. Exhaust Section and Gross Flow Measurement To obtain the gross flow rate a sharp edged orifice was located in the exhaust system used to vent the heated air from the test section to the outside of the building. The, orifice was located in a 2 1/2 inch pipe and had a hole diameter of 1 1/2 inches. Pressure taps were made by drilling a 1/16 inch hole in the pipe wall, counterboring the outside, and silver-soldering a short piece of 1/4 inch copper tubing in the hole. Vena contracta taps were used. Orifice temperature was measured by a mercury-in-glass thermometer located downstream from the vena contracta. The orifice installation was designed in accordance with the specifications for meter runs and orifice plates suggested in Stearns (60)~ However, since space limitations made it necessary to use a meter run somewhat shorter than that recommended by Stearns, a calibration was made of the orifice in place. A series of critical flow orifices was used as the standard. Excellent agreement was obtained between results obtained for different critical flow orifices for the ranges in which they overlapped. The calibration obtained agreed within three per cent with the theoretical predictions from Stearns. The slight deviation was probably due to the shortened meter run.

-37Pressure Measurement Two manometers were used for measurements of orifice pressure difference, static pressures, and pitot heads. Meriam red oil (sp. gr. =.817 at 850F) was used as the manometer fluid in both instruments. Pressure differences under.70 inch of meriam red oil were measured on a micromanometer which read directly in thousandths of an inch of meriam red oil. A U-tube mranometer was used for greater pressure differences. Differences in manometer fluid level were measured with a cathetometer which read to.001 cm. Tygon tubing was used for the pressure lines from the orifice and test section static taps and the total head tube. A manifold consisting of several three-way glass stopoocks connected with tygon tubing allowed pressures in different points-of the system to be read on either manometer without disconnecting pressure lines. The Temperature-Velocity Probe and Traversing Mechanism Radial temperature and velocity profiles in the flowing stream were made with a hot wire anemometer probe. A photograph of the probe is shown in figure 9. It consisted of a piece of 1/8 inch stainless steel tubing of 1/32 inch wall thickness bent to the shape shown. Before bending, two insulated copper wires were passed through the tube and soldered to steel sewing needles. The needles were then lacquered except at the tips, bound with thread to the tubing, and covered with successive layers of Saureisen cement.

-38~~~~.~~~~~ RZ.,.... 44 44.~~~~~~~~~~~~~~~~~~~~~~~~~~~~I Figure..4Velocity-Temperature Probe.'.4.4

-39During this process the needles were bent so that, when the shaft of the probe was held in a vertical position, the tips of the two needles would lie in the same horizontal plane. The Saureisen coating was sanded to a smooth streamlined shape and lacquered. This technique produced a stiff probe which could not vibrate in a rapidly flowing air stream. The actual sensing element of the probe consisted of a fine platinum wire soldered across the tips of the needles. Platinum wire.0003 inches in diameter is obtained imbedded in the center of silver wire.003 inches in diameter (Wollaston process). A short length of this wire is placed across the needle tips and one end soldered to one of the tips. Then, under a very slight tension, the wire is soldered to the other needle. The wire must be at right angles to the probe tips and horizontal with respect to the shaft axis. The surplus wire on either end is trimmed off with scissors. The silver is then etched off the center portion of the wire with a jet of dilute nitric acid solution through which a small current is passed. Completion of the etching process is indicated by a very sharp drop in the etching current. The amount of tension under which the wire is soldered is quite critical, since with too small tension the wire will not be straight, while with too much tension it will break. The etched portion of the wire was usually about.04 inches long, while the distance between needles was.14 inches.

The probe was installed in a section of plastic pipe adjacent to the downstream end of the calorimeter. A shaft bearing for the probe was constructed by filling a 1/8 inch close pipe nipple with brass and then carefully boring it out to a tight fit. The nipple was screwed into a high pressure tubing-to-pipe connector, the tip of which was filled with graphite-string packing and which served as a packing gland. This assembly is shown in figure 9. The connector was screwed into a tapped hole in the plastic pipe. The probe extended upstream so that the tip was located at the center (in the axial direction) of the calorimeter. The mechanism for traversing the tube radially is shown in figure 10. It consisted of a micrometer barrel rigidly mounted above and on the same axis as the hole into which the probe bearing assembly was screwed. The barrel bore dowwn on a 3/8 inch steel ball fixed to the top of the probe. The probe was held up against the micrometer spindle by small steel cables on each side which ran over pulleys and on which weights were hung. A pointer was attached near the top of the probe shaft so that the probe could be turned around the shaft axis. This pointer was secured to a moveable guide mounted on the rear flange of the plastic section. With this arrangement it was possible to align the probe tips parallel to the tube axis. A total head tube assembly was mounted in the side of the plastic section 90 degrees around the tube from the hot wire probe.

-41Figure 10. Traversing Mechanism

This probe extended forward into the calorimeter to a point about 1/8 inch downstream from the hot wire probe tip. The total head tube was used for calibrating the hot wire for velocity and was mounted in a packing gland so that it could be retracted against the wall when not in use. Three static pressure taps were equally spaced around the plastic tube 1/4 inch downstream from the calorimeter so that it was possible to check for possible differences in static pressure readings due to the presence of the hot wire and pitot probes in the calorimeter. However, no such difference was found and only the top tap was used during the experimental work.

IV.- EXPERIMENTAL AND CALCULATION PROCEDURES Velocity Profiles Excellent reviews of the theory and techniques of hot wire anemometry have been presented by Kovasznay (31) and Willis (63). The operation of a hot wire for determination of mean local speed depends on the relation between the rate of cooling of a small electrically heated wire placed in a gas stream, and the local velocity of the stream. For a heated wire placed normal to the stream, the relation between the rate of electrical heat production in the wire and the rate of loss to the stream for steady state can be expressed by the equation i R = (A' + B' Tu) (Tw - t) (17) where t denotes fluid temperature, T the wire temperature, R the wire w resistance and A' and B' are constants depending on the dimensions of the wire and the physical properties of the fluid. The resistance of the wire is given by R = R (1 + B T) (18) where f denotes the temperature coefficient of resistance of the wire and Ro is wire resistance at OOF. Combining (17) and (18) yields + B' - AI+BA' +BI u R - R where R is the wire resistance at the air temperature t. Thus, if i is kept constant and the quantity R/R - R determined for several a known velocities, a plot of 4u against R/R - R should give a straight line calibration.

-44The hot~ wire circuit is shown in figure 11.. Current was supplied by a 24 volt storage battery. With the double pole, double throw switch "A", it was possible to send either a large current (about 65 ma.-) for measuring velocity or a small current (about 1.5 ma.) for measuring air temperature through the 10 ohm precision resistor and the hot wire. With the large current, the equilibrium temperature of the wire was from 100OF to 2500F above the temperature of the air stream, depending upon the point velocity. The resistance determined at this temperature was used as R in equation 19. The wire resistance measured with the 1.5 ma. current passing through it was used as Ra in equation (19). Adjustment of either current within rather wide limits was possible with the variable resistors included in each branch of the parallel circuit. The voltage drop across either the hot wire or the 10 ohm precision resistor was measured with the K-2 potentiometer and amplifiergalvanometer system mentioned above in connection with determination of thermocouple EMF. The current flowing through the hot-wire was determined from the potential drop across the 10 ohm resistor; this together with the potential drop across the wire allowed the hot wire resistance to be computed. A small correction was applied for hot-wire lead resistance.

Figure II Hot wire circuit looooQ ioo2o0Q 0-1.0 MA. L A~~~~~~~~G 4762-9-C- GALVANOMEE 1iooo20Q 330QI 40QI 700Q AMPLIFI Ejl POTEN1~1METER PR~OBE 2-4 v

Because of the- presence of fluctuating velocity components due to turbulence it was necessary to include an R-C damping circuit to obtain readings of mean velocity. These fluctuations were generally small in the center of the stream, went through a maximum with increasing radius and then diminished as the wall was approached. This trend closely resembled that found for the eddy diffusivities. Wire velocity calibrations were made using the total head tube mounted at right angles to the hot-wire probe. The center velocity was determined by the total head tube; it was then retracted and the hot-wire probe moved into the center and readings taken. The procedure was repeated for several velocities over the range to be investigated and the R results plotted as Tu against R - R This plot gave a straight line a except at very low velocities, where there was a slight curvature probably due to a change in the flow regime of the air over the wire. In computing velocities from total head tube readings, the impact tube coefficient was considered equal to unity and a small correction applied for the pressure drop along the tube between the points where the total and static pressure were measured. The accuracy of velocity measurement varied from 0.5% at moderate velocities to 5% at 6 ft 1 sec. In the region very close to the wall errors are introduced due to non-linearity of the wire response to fluctuating velocity components and heat transfer from the wire to the wall. These effects are discussed in the next chapter.

-47Mean-flow rates were computed by graphical integration of the velocity profiles using the relation: b = a2 u r d r (20) 0 Mean flcw rates computed by equation (20) agreed within 3% with those determined from orifice measurements. Temperature Profiles Temperatures in the air stream were measured by using the hotwire anemometer as a resistance thermometer. This technique has been described by Schlinger (54) and Sleicher (59). The experimental procedure was the same as that described for obtaining the wire resistance at air temperature, Ra, described under Velocity Profiles. Since the resistance of the wire is a function of temperature, the wire temeprature can be calculated from its resistance after calibration. Actually, because of aerodynamic and electrical heating effects the wire is at a temperature slightly higher than the static temperature of the stream. These effects were not important in the determination of Ra for velocity measurements since they were taken in account by the calibration procedure. However, corrections for them must be applied for accurate temperature measurement. The stagnation temperature of a flowing stream of gas is given by: 2 u t - t + g JC s JC (21)

-48The wire with no current actually comes to a temperature less than ts given by: 2 T t +y w 2gc JC" (22) where Z is the "recovery factor". Hottel and Kalitinsky (24) experimentally determined an average value of Y =.66 for a range of velocities similar to that employed. They found that for small wires Y was nearly independent of diameter. The correction due to aerodynamic heating was calculated from equation 22 using 7 =.66. A correction is also necessary for heating of the wire caused by the current used to measure its resistance. This correction can be computed from generalized correlations for the heat-transfer coefficients of cylinders in cross-flow as given by McAdams, p (40). For wires with length to diameter ratios of the magnitude used here (about 130 to 1) end losses from the wire must also be considered. The fine wire is heated by the current, but the heavier supporting silver wires may be assumed to be close to Tw, the temperature assumed by an adiabatic wire. Some of the heat generated in the wire is thus conducted from the platinum wire at its ends_ The latter two corrections may be combined in a manner described by Sleicher (59). The differential equation describing the temperature of a wire with uniform heat generation per unit length, Q; uniform heattransfer coefficient h along its length axis x; and ends and surroundings at t = o is:

2 w; kWDTw+ 2 = o (23) k jtD w t (O) = O t (m) = finite The solution of the equation 23 is: T k= Q (24) V = 2 4Nu ka k w Integrating equation 24 over the wire length L gives the average wire temperature as: -k x/D X/Do (Tw)avg a [1 _ X ] -'V where the term in brackets is the correction to account for conduction cooling at the ends. This correction, which increases with decreasing velocity, amounted to 16.5% at a velocity of 10 ft/sec. Radiation corrections were found to be negligible. The temperature corrections are plotted as a function of velocity in figure 12. The turbulent velocity fluctuations mentioned in the section on Velocity Profiles caused corresponding fluctuations in temperature. The K-2 potentiometer was balanced by estimating by eye the setting at which the mean of the galvanometer settings was zero. Settings were reproducible to +.25 microvolt or better, which corresponded to a maximum error in temperature of +.08 F.

- 501.6 A - Aerodynamic Heating ~1.4 _ _ |_ |. | B - Equation (25) Correction C Total Correction 1.2.0 -I.8.6!D.2 0 20 40 60 80 100 120 u, FT/SEC Figure 12. Temperature Corrections for.3 mil Platinum Wire.0482 inches long

-51The temperature probe was calibrated against a thermocouple located in the center of the tube downstream from the probe. The installation of this thermocouple was discussed in the chapter on apparatus. The preheater in the calming section was used to heat the air stream to several different temperatures covering the range to be employed in the test run. Since the calibration couple was left unshielded in order to ensure rapid response it was subject to aerodynamic heating effects. It was assumed that the recovery factors for couple and wire were equal. Although this assumption is not absolutely true, little error was introduced on account of it because of the fact that temperature calibrations were made at a low speed (about 10 ft per sec.) where aerodynamic heating effects only amounted to.020F. The wire was calibrated for temperature and velocity before every run and several check points were taken after the run. In a few instances the calibration changed markedly during the run, probably due to a stretching of the wire by a small particle in the air stream. Location oJ The point at which the hot-wire probe tips made contact with the upper wall was determined electrically by measuring the resistance between the probe and the wall. Before each run a check was made to see that the probe needles were aligned with the axis of the tube (the meaz flow direction.) This was done in the following manner: The probe was brought to within a few thousandths of an inch of the estimated position of the

-52wallo The probe tip was then rotated about its axis so that first one side of the probe tip touched the wall, and then the other. The approximate center position was noted and the probe raised slightly. This procedure was continued until the angular position of the probe was found that would result in both sides of the probe touching the wall simultaneously as the probe was raised. This position was maintained by locking the probe pointer guide. The dimensions of each hot-wire were determined by measurement under a microscope equipped with a calibrated traveling diaphragm. Figure 13 is a view of the probe with the probe tips in contact with' the wall, as it would appear to the stream of air in the tube. Figure 13. Dimensions of Hot-Wire Probe

-53The distance y of the middle of the fine wire from the wall is given by the relation: y = a (1 -_S /4a- ) (26) This distance was considered to be the distance of the wire from the wall when the probe and wall were in electrical contact. Although not all parts of the wire were at the same distance from the wall, this was a good approximation, since the sensing element consisted only of the center third of the wire. Experimental Procedure The cold junction was filled at least an hour before the start of the run to ensure its being at OoC. Before the run the hot-wire probe was calibrated for both temperature and velocity. The flow rate was then set and the inlet temperature determined. The heaters and steam jacket (if used) were then turned on. Careful adjustment of heater inputs and steam flow rates was made until all parts of the equipment were at the proper temperature level. Special effort was made to get temperatures at adjacent points in the calorimeter and guard as nearly equal as possible. The average difference between adjacent points was less than.10F. This procedure of equalizing temperatures generally took two to three hours. The probe zero position was then checked and a temperature tra. verse started from the center of the tube and carried to the wall. A velocity traverse was then taken at the same points as the temperature

-54traverse. Although the temperatures could have been computed from the wire cold resistances obtained as part of the velocity traverse, it was considered more satisfactory to complete the temperature measurements as rapidly as possible after thermal equilibrium was established. Wall and inlet temperatures, flow rate, and probe calibrations were checked at the conclusion of the run. The maximum difference betweer initial and final inlet temperature was.3~F, or a little over 1% of the operating At, while initial and final flow rates agreed within 1%. For each entrance and L/D ratio-runs were made at Reynolds numbers of 15000 and 65000. Physical Properties of Air Values of the density, viscosity, specific heat at constant pressure, and thermal conductivity of air were required for calculations from the experimental data. The density was computed from the perfect gas law. Other physical properties were obtained from the "Handbook of Supersonic Aerodynamics" (28).

V. DISCUSSION OF RESULTS In this investigation velocity and temperature distributions and point'heat transfer rates were obtained in the entrance region for air flowing in a 1.520 inch inside-diameter heated pipe. The two hydrodynamic entrances investigated were 1) a straight tube 66 inches (43.3 pipe diameters) long which gave essentially fully developed turbulent flow and 2) a bellmouth entrance which produced an initially flat velocity distribution. Temperature and velocity profiles and point heat transfer rates were taken downstream from the long tube entrance at length-to-diameter ratios of.543, 1.13, 4.12, and 9.97 after the start of heating and after the bellmouth at X/D's of.543, 1.13, 1.75, 4.12, and 9.97 after heating began. For each entrance and X/D, runs were made at Reynolds numbers of 15,000 and 65,000. The upper limit of Re = 65,00ooo was the maximum flow rate that could be obtained with good control from the air supply system. The lower limit was chosen to give as wide a range as possible, and yet ensure turbulent flow in the fully developed hydrodynamic boundary layer. Pressure drop measurements in the entrance region were taken for these flow rates. As mentioned in the discussions of equipment and experimental procedure above, only one X/D could be investigated during eacn Thus, for a given entrance and Reynolds number, there were small differences in initial temperatures, wall temperatures, and flow rates between runs taken at different X/D's. In order to put profiles taken at different X/D's on a comparable basis and to permit the calculation of longitudinal gradients, the following dimensionless quantities were introduced: -55

-56t - t t -t w 0 x Z a r r = - a U = U Gross values for the heat transfer runs are reported in Table I of Appendix B while point values for velocity and temperature profiles are given in Table II of Appendix B. The results given in these tables and the pressure drop studies are discussed below. Pressure Drop The pressure gradient as a function of length is shown in figures 14 and 15 for the long tube with bellmouth entrance. These data were taken with the 15 inch steam jacket in place so that the total length over which data were taken was 82 inches or 54 X/D. Pressure drops were measured differentially, with all differences being taken between adjacent taps. This was done since a very small change in flow rate could cause very large, errors in pressure gradients colmputed from integral measurements, while having little effect on differential measurements. It also permitted the differenced data to be plotted directly and a smooth, equal area curve drawn through the increments. Pressure differences between the closely spacea taps in the inlet region were relatively small and difficult to determine

.2O o - Points Computed from Velocity Gradient at Wall LL. co _j.12 w 0~~.08.... (n, La... C1) ~ ~ ~ 0 ____12 16 20 24 28__ _ 04 DIAMETERS FROM ENTRANCE Figure 14. Pressure Gradient in -the Inlet Region after. Bellmouth Entrance for Re = 15.,-000 w (I) (I) 0 4 8 12 16 20 24 28 32 DIAMETERS FROM ENTRANCE Figure Pi-. Pressure Gradient in the Inlet Region after Beilmouth Entrance for Re = 15,-000

2.0__ _ _ __ _ _ _ ILL ci H 1.6..... N. C 4.j 1.2 -.. ~~~~~Fg 5 PrsF- ueGainJnteIltRgo feO3 <CV) ~ ~ ~ ~ ~ e3muh'nrnefrR 6~C z~~ C~,, a.48 U~~~ 0i.4... _ _ _ _ 0 4 8 12 16 20 24 28 32 DIAMETERS FROM ENTRANCE Figire 15. Pressure Gradient in the Inlet Region after Bellmouth'Entrance for Re = 56,000

-59accurately. For the first three taps at the lower flow rate there were periodic fluctuations in manometer readings of about.001 inch magnitude, compared to measured pressure-differences of about.0035 to.005 inches. However, these readings were reproducible within limits of less than 10 percent, while uncertainty in measurements located further downstream where taps were spaced further apart was about 3 percent. The pressure gradient became essentially constant at an L/D of 45 for Re = 15,000 and L/D of 25 for Re = 65,000. The average values of friction factors computed from several runs in the region of constant pressure gradient were very close to those reported by Moody for fully developed flow in smooth pipes. It should be noted here that the point at which the pressure gradient becomes constant is not the same as that at which the velocity profile becomes stabilized, since slight changes in the center of the profile occur without measurably influencing the pressure drop. From figure 14 it is seen that for the Reynolds number of 15,000 the pressure gradient first decreases with length, then rises, goes through a maximum, and diminishes to its asymptotic value. This can be explained by the fact that, even for high Reynolds numbers for which the fully-developed flow is turbulent, a laminar boundary layer is formed at the entry of the tube. This layer increases in thickness along the length of the tube and at some distance from the entrance undergoes transition and becomes turbulent. The point at which transition takes place depends on the Reynolds number, the entrance condition of the fluid, and the condition of the tube. Pressure gradients based on wall shear stress and computed from velocity gradients at the wall are also plotted in figure 14.

-60These points lie- considerably below the smoothed equal area curve obtained from wall static pressure measurements. This fact can be explained by a consideration of boundary layer momentum forces. The pressure drop in the tube entry is equal to the sum of two terms, the pressure loss due to skin friction plus a term representing the longitudinal rate of increase in momentum flux. The latter effect is associated with the developing velocity profile. As the boundary layer thickness increases, the frictionless core of the flow outside the boundary layer undergoes a contraction' in cross-sectional area and is therefore accelerated. The increasing core velocity produces a pressure gradient along the pipe. Shapiro, et al.,57 on the basis of their experimental results, have proposed the following relation for the local apparent friction factor in a laminar tube entry: f 1.72'Re (27) app x where f is the friction factor computed from wall pressure drop meaapp surements. For laminar flow over a flat plate with zero pressure grad18. ient the local skin friction coefficient has been found to be Cf 0.664 TRe (28) Thus the local apparent friction factor for a pipe entry is 2.59 times as great as the local skin friction coefficient for a flat plate. Theoretical analyses 57 show that, although there is a pressure gradient in a tube whereas there is none for a flat plate, the boundary layer behavior in a-tube entry is substantially identical with that on

a flat plate. Consequently, the actual skin friction coefficients (based on wall shear stress) are the same for the tube entry and the flat plate. From these considerations it is seen that in the laminar tube entry the pressure drop due to momentum changes is 1.5-9 times as large as the pressure drop due to wall friction, or 39 percent of the press sure drop in the tube entry is caused by wall friction while the remaining 61 percent is caused by momentum changes. These figures are only valid near the entrance where the boundary layer thickness is small compared with the pipe radius. The total apparent friction factor and the skin friction coefficient, based on velocity gradient at the wall, are shown in generalized form in figure 16. Points for the apparent friction factor were computed using pressure gradients read from the smoothed curve of figure 14. The skin friction coefficient near the entrance is seen to run from about 27 percent to 30 percent of the total apparent friction factor, then gradually approaches the apparent friction factor at further distances downstream. Equation 27, as proposed by Shapiro, is also plotted on figure 16. Although the slopes of the two curves for apparent friction factor are the same, Shapiro's line lies somewhat above that of the present investigation. This is apparently caused by a difference in the entrance condition of the fluid. This is indicated by the fact that Shapiro found transition occurring at a length Reynolds number of 5 x 105, while in the present study transition occurred at Re of about 1 x 105 This was probably due to the fact that in this case the entrance was not intentionally constructed so as to encourage the laminar

1000 900 A - Equation 27 800 B - From Wall Pressure Measurements 700O E \ |' C - From Velocity Gradient at Wall 600 _I 500 400 0. ~ 200,. __. I00 I 1.5 2 2.5 3 4 5 6 104 Rex ReD Figure 16. Friction Factor in Inlet Region after Bellmouth Entrance for Re = 15,000

flow regime. The net result appears to have been a shifting of the curve of figure 16 to the left. As can be seen from figure 15, for the Reynolds number of 65,000, the transition to turbulent flow appears to have taken place very close to the entrance. It was not possible to compute skin friction coefficients in this case since the velocity gradients near the wall were still increasing and the gradient at the wall could not be accurately defined. Point Heat Fluxes Heat-fluxes were computed from measurements of power input to the calorimeter, determined from-voltage and current measurements. Two corrections were applied to these values. First, a correction was applied for conduction losses through the plastic insulating disks between the calorimeter segment and the adjoining sections of the guard heater due to small non-uniformities in temperature as determined by calorimeter and guard thermocouples. These corrections were in no case over 3 percent. A second correction was necessary since even with the calorimeter segment and adjacent sections of the guard at uniform temperature, there was some temperature non-uniformity in the shell of the guard. An approximate correction was obtained for this by determining the heat input with no flow and uniform wall and guard temperatures at different levels above ambient temperature. This correction is plotted in figure 17. The corrected heat fluxes were plotted differentially as vs. x and a smooth equal area curve drawn through the increments. Point

-2o0 -I1 Of' 0 -12 16 20 24 28 -I -2 48_04-8 TEMPERATURE DIFFERENCE,~ F Figure 17. Heat Flux Correction for Calorimeter Measurements as Function of Wall to Room Temperature Differences

values of heat flux were read from the curves and Nusselt numbers computed. Figure 18 shows Nusselt numbers as a function of X/D for the long tube entrance. Also plotted on figure 18 are values obtained by Sleicher59 at three X/D's for the same entrance. The data of Boelter5 (extrapolated) for his long calming section entrance are also shown. Agreement between the three sets of data is excellent. For both Reynolds numbers the Nusselt numbers start out high and gradually decrease with distance downstream. The Nusselt number appears to have attained very close to its asymptotic value at X/D of 10. For the lower Reynolds number the Nusselt number is 2.8 percent above that computed from the Dittus-Boelter equation, while for the higher Reynolds number it is slightly below (-.35 percent) the computed value. Nusselit numbers as a function of X/D for the bellmouth entrance are shown in figure 19. Extrapolated results of Boelter for a bellmouth entrance without screens are also shown. Agreement between the two sets of data is good. For the lower Reynolds number a minimum in the Nusselt number is observed at an X/D of about 7.: The Nusselt number then starts to rise again. This effect is due to the transition from laminar to turbulent flow as mentioned under Pressure Drop above. At an x/D of 10 the Nusselt number is still rising sharply and has only reached 51 percent of the value predicted by the Dittus-Boelter equation. At a Reynolds number of 65,000 the Nusselt number diminishes uniformly, its value at X/D of 10 being 2 percent above the computed asymptotic value. The Nusselt number for the bellmouth at X/D =.453 was 32 percet below that obtained for the long tube entrance at Re = 15,000, and 17 percent lower at Re = 65,ooo.

-66220 A - Re= 65,o000 200 B - Re'15,0000- Author - Sleicher \18 A - - Boelter (5) 160 140 12 U) 100 80 60. 40 __ 20 0 I 2 3 4 5 6 7 8 9 10 II 12 DiAMETERS AFTER START OF HEATING Figure 18. Variation with Length of Point Nusselt Number for Long Tube Entrance

-67240 A Re= 65,00o 0 B - Re= 15,000 220 O- Author a Boelter (5) 200 180.. W 160 140 140 Li I..). 6 0_ _ I _ _ 60 40 20 2 4 6 8 10 12 14 DIAMETERS FROM ENTRANCE Figure 19. Variation with Length of Point Nusselt Number for Bellmouth Entrance

-68A check of wall heat fluxes was made by comparing the mixed mean temperature from integration of the temperature profile at the calorimeter with the mean temperature obtained by integration of the wall heat flux using the relation z t -t w o0 2 tw tb Cp a ub 0(29) Heat balances computed by these two methods generally agreed within better than 10 percent, except for the L/D of.453 where the combination of rapidly changing Nusselt number and small total heat addition due to short heating length caused larger percentage errors. A further rough check on point heat fluxes was made by comparing heat fluxes computed from radial temperature gradients at the wall with' fluxes computed from calorimeter measurements. This method is not very accurate since radial gradients were still changing rapidly as close to the wall as it was possible to obtain readings. However, wall slopes computed from calorimeter measurements and plotted on the temperature profiles appeared reasonable and indicated at least that no gross error in wall heat flux was present. Velocity Profiles Values of u/um vs. r/a for the long tube entrance are plotted in figure 20. These are average values of profiles taken in the range of 44 to 53.5 pipe diameters downstream from the tube entrance. At a given Reynolds number, there is a slight variation in the shape of the reduced velocity profiles obtained at X/D's of 44, 44.5, 47.5, and 53.5 pipe diameters. This is due to the fact that there is still some development of the hydrodynamic boundary layer occurring in

-691.6 - - I I A - Re= 65,000 B - Re= 15,000 1.4 1.2 o.,- 10 ___ J I o.... w..2 0..2.4.6.8 1.0 y/a, DIMENSIONLESS WALL DISTANCE Figure 20. Variation with Flow Rate of Reduced Velocity Distribution for Long Tube Entrance

-70the center of the tube, although the boundary layer has already merged. This effect is more pronounced at the higher Reynolds number, due to the fact that for higher Reynolds numbers a longer X/D is required to obtain fully developed pipe flow. The fact that the boundary layer is still developing in the center of the tube can be clearly seen from velocity deficiency curves for the Reynolds number of 65,000 at X/D's of 44.0 and 53.5 plotted in figure 21. Also plotted in figure 21 is the velocity deficiency curve given by Bakhmeteff3 for fully developed turbulent flow. This type of correlation is particularly sensitive to changes in velocity profile near the center, since it involves taking very small differences in velocities. The velocity data taken after the long tube entrance are plotted as the universal velocity distribution u+ vs. y+ in figure 22. The results of several investigations of velocity distribution in turbulent pipe flow are given in figure 23. Each of the lines is a mean through the data points of the author except the line labeled "Reichardt", which is a mean line through the points of Nikuradse, 48 Reichardt-Motzfeld, and Reichardt-Schuh as reported by Reichardt. All of the lines except Laufer's are in close agreement. However, Laufer's work was done with extreme care in a large diameter pipe. The reason for the discrepancy in his results is not apparent, but it appears that his results near the wall are not very reliable. The results of the present investigation lie slightly below the others in the region 3 < y+ < 15 This is probably due to the fact that near the wall, where the mean axial point velocity is small, the ratio of the fluctuating components to the mean point velocity, u'/iA,

-718 ____ O Total X/D = 45 A Total X/D = 54.4 Bakhmeteff (3) I I I 1 1'Cl LI 4 w~r 2 e t i cn b t f=0?3 O.I.2.3 4.5.6.7.8.9 1.0 I - r/oa Figue 21. Velocity Deficiency after Long Thbe Entrance for Re = 65,000

-7223. 2.... ~. I I1117 2 - - -Ru- i 5 _., 2 3 4 5 6 7 8 910 20 30 40 50 60 708090100 0 300 0 600 800 1000 0 O RuI 3 - -RIMV 8 3 4 5 6 7 8 9 I0 15 20 30 40 50 60 708090100 1'50 200 00 400 500 600 800 I000 _+

u+ I II I 9 / 6-4 2 l of V t P a P / 7 -- 3 4 5 6 7 -8 9 1 20 30 40 50 60 70 80 Figure 23. Comparison of Velocity Profiles near a Pipe Wall

-74becomes:large: Equation (19) is valid only for the case where u'/u is negligible compared to unity; in other words, with large velocity fluctuations near the wall the behavior of the wire becomes non-linear. 59 Sleicher derived a correction for this effect of the form u ul/[l - 1/8 (u'/u)2]2 (30) 62 while Weissberg used the correction u = u [ 1 + 1/4 (u'/u) ] (1) Here u' is the point velocity computed from the hot wire calibration. Sleicher used the measurements of velocity fluctuations reported by Laufer to compute his correction and found that the maximum correction was 4 percent. A few points calculated for the worst conditions of this investigation indicated that the largest correction would be about 3 percent. Since this is well below the accuracy expected of velocity measurements near the wall, and the profiles appeared to be extrapolating to zero velocity at the wall without the correction, it was not applied here. As seen in figure 22, for y < 3, there is an apparent increase in ve-Locity as the wall is approached. This is due to heat transfer from the heated wire to the wall when they are separated byshort distances. Attempts have been made to correct for this effect (Willis63 and Weissberg 62); however, the accuracy of the corrections is questionable and none was made here. No significant difference was found between velocity profiles taken during heating and non-heating runs.

-75Reduced velocity profiles in the inlet region after the bellmouth entrance are shown in figures 24 and 25. For the Reynolds number of 15,000 the velocity profiles are practically linear for a considerable distance from the wall. It is possible to fit a cubic parabola, characteristic of laminar boundary layers, to these curves (excluding the region outside the hydrodynamic boundary layer.) In figure 24 it is seen that the slopes at the wall progressively decrease with distance downstream until the X/D of 9.97 is reached. The gradient at -chis last position is greater than at the one preceding it, indicating that the transition to turbulent flow in the entrance boundary layer is taking place. For the higher Reynolds number velocity measurements could not be taken close enough to the wall to accurately define the gradient at the wall. Radial velocity gradients wei ~erencing and drawing smooth equal ares Temperature Profiles Dimensionless temperature profiles for the long tube entrance are shown in figures 26 and 27, and for the bellmouth in figures 28 and 29. These temperatures were then cross-plotted to obtain the longitudinal temperature profiles, such as those plotted for the long section at Re = 15,000 in figure 30. The points reported by Sleicher for the same entrance at an X/D = 3i have been included. Longitudinal temperature gradients were determined by differencing the longitudinal profiles and drawing smooth equal area curves. Slopes of the longitudinal profiles were also taken graphically and plotted on the equal area charts as an aid to drawing the

-761.00.90.80.70 u Urn.60....._ _ _ _ _ _~~~~~~.....50 40 O x/D =.453 X X/D = 1.13 A X/D =. 1.75 - l |.30 V x/D = 4.12 Co X/D = 9.97 _20.70.75.80.85.90.95 1.00 Figure 24. Dimensionless Velocity Distribution after Bellmouth Entrance for Re = 15,000

-771.00 _________ok 1 ~~~.95.90 \85 I ____ _.85 um.75.70 o X/D.-453 X /D 1. 13 A X/D - 1.75 \.65 V X/D 4.12 X/D - 9.97.60.70.75.80.85.90.95 IPO Entrance for Re = 65,000

-78-.80 0 x/ =.4*53 x/D:U1.3 X X/D 4.1.2.70 O X/D: 9.97 X/D: 31 from Sleicher (59),.60.50 40.230.10.4o0.50.60.70.80.90 1.00 r* Figure 26. Dimensionless Temperature Distribution for Long Tube Entrance for Re = 15,000

-79-.40 o x/D =.453 X x/D = 1.13 35 V x/D= 4.12 o x/D = 9.97.30.20.25.10.05 _____X_ 0 40.50.60.70.80.90 1.00 r* Figure 27. Dimensionless Temperature Distribution for Long Tube Entrance for Re = 65,000

-8o0_ _ _ _ _ _....... _ _ _ _ _ _ _ _ _ _ _.8 0 O X/D =.453 X X/D - 1.13 A X/D = 1.75-.70 V X/D 4.12 o X/D = 9.97.60.50.40 0.30.10.70.75.80.85.90.95 1.00 Figure 28. Dimensionless Temperature Distribution for Bellmouth Entrance for Re = 15,000

.44 O X/D.,453 X X/D- 1.13 - x/D =1.75.35 V X/D = 4..12 O -X/D = 9.97.30 25.20.15.10.05' L ~_ _ yX o0 40.50.60.70.80.90 1.00 Figure 29. Dimensionless Temperature Distribution for Bellmouth Entrance for Re = 65,000

000'1T = alI lo; a~ou'aeau aqrn, 2uo lo, uo'j.nq's':a axn IadmaT, -TL-pn;tTSuoT *0 a nJT'A 8, DIMENSIONLESS TEMPERATURE O..00 00 0 00 0 I OrD 0:) ~r C) 0 0)' "''_' _

-83curve. Curves drawn through these points generally gave good equal area fits. The longitudinal temperature gradients as a function of x/a with r. as a parameter for the long test section at Re = 15,000 are shcwn in figure 31. Also plotted is the longitudinal gradient of the mixed mean temperature de~ t t U = 2 Nu w b (32) dZ Pr Re tw - t where the Nusselt number is obtained from the calorimeter heat flux measurements. It is seen that far downstream the assumption that the longitudinal temperature gradient at any radius is equal to the mean gradient is quite good, except very near the wall, since for constant wall temperature the longitudinal gradient at the wall is zero. However, near the entrance the assumption is very bad. Of course, in the unheated core outside of the boundary layer in the inlet region the longitudinal temperature gradient is still zero. For a step change in wall temperature, the longitudinal temperature gradient at the wall would be infinite at x/a = O and zero for x/a > O. From figure 31 it is seen that this condition is approached'as one gets very close to the wall (large values of r*). In figure 32 the data of figure 31 have been cross-plotted to show the longitudinal temperature gradient as a function of r, with x/a as the parameter. Radial temperature gradients were computed by numerically differencing the data and drawing smoothed equal area curves. A typical curve is shown in figure 33 for run 4.

-84-.016....... N~.80'.014 t,~-.90 z o.012 01 W X.70 Ii W I::E J.008z 03.50 z.006 0 -J 0.50 W ~~~~~~~~~~~~~~~~~~~~~.70 __Ji I II I I I I I ~ -.80 Z.004 7 90 C,) a.002 0 I 0 20 30 40 50 60 X/a Figure 31. Vsariation with Length of Longitudinal Temperature Gradlenmu for Long Tube Entrance

000'gT = all lo OU'IuvX;U, aqu 2UOI Jo;J.;UGepva anm;eiaduial rutpnq.TFuo I Jo aoutmrsTsI TTPIET qtfTA UOFT JSTA'8Z a' GnBT D/J'33NVllSIG 1'latlVI 01 8' 9'' _ 0 i ~000010100 [____ _ |o800' m -0' -' r1 -— I C: ___I0 910' z AZO' L6 = a/x.~ \g -'T = (I/x ~t- =a/x — [; z. cn

RADIAL TEMPERATURE GRADIENT, d81ar o _ i)_ _ _ _ _ _ _ _ _ _: C)o 0 - N (N -.tf i 0 (-'3 0. O(D (O- H, o 1 (' 6 _ _ _ _ _ _ \_

-87Eddy Diffusivities For the long tube entrance eddy diffusivities for momentum transfer were computed from equation (35) and eddy diffusivities for heat transfer from equation (42). The derivation and use of these equations is given in Appendix A. The values for the diffusivities for the long tube entrance are listed in Table II, runs 1 through 8. For fully developed turbulent flow with constant properties, the velocity profile and the longitudinal pressure gradient are constant, therefore e should not be a function of length. As mentioned v under the discussion of velocity profile results, the flow in the thermal inlet region following the long tube entrance was still developing slightly. This caused a slight variation with length of the eddy viscosity distribution in the center of the tube. The maximum deviation (between profiles taken at total L/D's of 44.5 and 54) was about 7 percent. This occurred near the center of the stream. Calculated values of eddy diffusivities are subject to larger error in this region than near the wall because of the very low radial gradients in the tube center. Errors due to this factor may account for most of the variation. If the turbulent transfer-processes for heat and momentum transfer are similar, the eddy conductivity also should not be a function of length for fully developed flow. The values obtained here for Ec at heated X/D's of.453 and 9.97 agreed within,5 percent except for the region next to the unheated core, where radial temperature gradients were very small. The eddy diffusivities appear to drop off rapidly near the 54 tube center. The same effect was found by Schlinger, et al. and Corcoran for uniform flow between flat plates. Values of eddy

-8859 viscosities near the wall agree closely with those obtained by Sleicher for the same entrance. The variation with radius EV/v and Ec/v in the thermal inlet region following the long tube entrance is shown for Reynolds numbers of 15,000 and 65,000 in figures 36 and 37 respectively. These values are average values for the X/D's studied. The variation with radius of the ratio a = e /e is shown in c v figure 41. Values near the center are not plotted, since the temperature gradients in the tube center at the largest X/D were small and the calculated diffusivities were therefore subject to error. The ratio a increases sharply near the wall, as reported by Corc6ran.9 For the region.5 < r/a.<.9, the value of a appears to be about 1.5. The effect on a of Reynolds number in the range investigated appears to be small, except for the region close to the wall. Eddy conductivities for the bellmouth entrance were computed from equation 42. (Appendix A). They are shown as a function of radial distance with X/D as a parameter in figures 38 and 39. From figure 39 it is seen that c increases rapidly with distance downstream in the inlet region, This is because of changes in velocity distribution due to the developing hydrodynamic boundary layer and the transition from laminar to turbulent flow. Since for Re = 15,000 the bellmouth boundary layer starts out laminar, the eddy conductivity near the inlet would be expected to be equal to zero. As shown in figure 38, e is very small at the lowest c X/D and increases with distance down the tube as the transition to the turbulent boundary layer occurs.

-8920 -8 Ii U) w 0 0 4 8 0.2.4.6.8 1.0 RADIAL DISTANCE, r /a Figure 34. Longitudinal Velocity Gradient 1.5 Diameters after Bellmnouth Entrance for Re = 15,000

-9036 32 28' 24 20 12 0, 40.50.60.70.80.90 1.00 RADIAL DISTANCE, r/a Figure 36. Variation with Radius of Eddy Diffusivities for Long Thube Entrance for Re = 15,000

-91140 120 _ 100 EC ~ 80 60 ______ 40 20.72.76.80.84.88 92.96 1.00 RADIAL DISTANCE, r/o -Figure 37. Variation with Radius of Eddy Diffusivities for Long Tube Entrance for Re = 65,000

-9220 16 14 \\ 12 10 9.97 4.15.453.72.76.80.84.88.92.96 1.00 RADIAL DISTANCE, r/a Figure 38. Radial Distribution of ~c/~ in Inlet Region for Bellmnouth Entrance for the X/D's Shown (Broken Line for Long Tube Entrance). Re = 15,000

-9364 56 48 lXl o40 — 32 24 16 8 I45.90.92.94.96.98 1.0' RADIAL DISTANCE r/o Figure 39. Radial Distribution of e /v in Inlet Region for Belliouth Entrance for tfie Four X/D's Shown. Re = 65,000

-94As discussed in Appendix A, eddy viscosities in the bellmouth inlet region for laminar flow computed from equation 35 are inaccurate, since this equation neglects the core acceleration due to the development of the laminar boundary layer. That the acceleration term must be included is further substantiated by the fact that the total viscosities computed by equation 35 for the bellmouth inlet with Re = 15,000 are below the value of the molecular viscosity. This effect was also observed at the high Reynolds number. Thus, no reliable figures for the eddy viscosity in the bellmouth inlet region can be obtained from this investigation. Radial Heat Flux As shown in Appendix A, the function r* a =! U r* aC d r* 0 is proportional to the radial heat flux. The function is listed for runs 1 through 18 in Table II. The radial heat flux for run 4, computed as outlined in Appendix A, is shown in figure 40. For the region 0 < y+ < 10, the heat flux is approximately equal to that at the wall. For y greater than 10, the variation of heat flux with radius is very nearly linear. Thus the assumption made by Martinelli and others of constant radial heat flux near the wall and a linear distribution in the turbulent core appears to be a good one. Of course, if the thermal boundary layer has not merged, the heat flux diminishes to zero at the edge of the boundary layer.

-95160 140 120 C I03 I ~.2 i 60 0.2.4.6.8 1.0 Figu~re 40o. Rad~ial Heat Flux Distribution f~or Run 4t.

2.2 2.0 1.8 Re 15,000 1.6 u -L. _I 1 ~ L Re 65,000 1.4 LL 1.2 ll I.72.76.80.84.88.92.96 1.00 RADIAL DISTANCE, r/ a C Figure 41. Variation with Radius of the Ratio c: = e for the Long Tube Entrance

CONCLUSIONS 1) Significant differences in heat and momentum transfer in the inlet region are caused by the two initial velocity distributions studied in this investigation. 2) These differences are due to variations in the velocity gradient in the boundary layers developing downstream from the inlet. In addition, the bellmouth produces an initially laminar boundary layer with resulting reductions in heat transfer rate and pressure drop. 3) At a Reynolds number of 15,000, acceleration effects account for about 70 percent of the pressure drop d'irectly downstream from the bellmouth entrance. 4) For both initial velocity distributions studied, the thermal boundary layer had merged and the Nusselt number reached within 3 percent of its asymptotic value within ten diameters after the start of heating. 5) For fully developed turbulent flow, the eddy diffusivities for heat and momentum transfer in the thermal inlet region vary with radius and Reynolds number, but not length. The ratio EC/Ev varies with radius and slightly with Reynolds number. For the region.5 < r/a <.9, the range of variation is from about 1.4 to 1.6. The ratio increases sharply near the wall. 6) Eddy conductivities in the bellmouth inlet region are very low directly downstream from the inlet because of the presence of a laminar boundary layer. The conductivities gradually increase with distance downstream. -97

-987) To accurately calculate eddy viscosities in the bellmouth inlet region, one must include acceleration effects due to the developing hydrodynamic boundary layer. Neglect of these effects results in negative eddy diffusivities. 8) The assumption of constant radial heat flux in the laminar sub-layer and the buffer layer,. and a linear heat flux distribution in the turbulent core, is good, except possibly very close to the entrance. 9) Theoretical analyses which postulate the same distribution of eddy conductivity in developing thermal boundary layers as for fully developed ones are valid for the case of fully developed hydrodynamic boundary layers in the thermal entrance region, but may be subject to large error when the hydrodynamic and thermal boundary layers develop simultaneously. 10) For fully developed thermal boundary layers, the longitudinal temperature gradient at any radius is approximately equal to the longitudinal gradient of the mixed mean temperature, at points very close to the wall. This relationship is not true when thermal boundary layers are not fully developed.

APPENDIX A CALCULATION OF EDDY DIFFUSIVITIES -99

APPENDIX A CALCULATION OF EDDY DIFFUSIVITIES The equations used in computing the eddy diffusivities for heat and momentum are derived below and the method of computing the diffusivities outlined. Eddy Viscosities The momentum equation in the x direction for laminar flow 18 in a pipe inlet is au au u g ap u2 u 1 u 52u U H + v T~ =-7 + v- + H + (33) From boundary layer theory the third term in the brackets may be neglected. Assuming that eddy and molecular diffusivities may be directly added, equation (33) written for turbulent flow is au a + V - +6 a[r(v + ev) ] (34) where the diffusivities for momentum have been placed inside the derivative sign since cv is a function of radius. For fully developed flow ax and v are equal to zero and equation (34) reduces to 1 p l. (v+ p t = 1 [r Y (35) Integrating, with p considered constant, V + g= H r/ (36) -zoo

-1016p 2 Using the relation - = r Tw and the linear shear stress law for fully developed flow, it may be shown that equation (36) is the same as equation (10), the defining equation for eddy viscosity in fully developed flow. Introducing the dimensionless variables r and U, equation (36) becomes 1 g+ ap (ro) r* v + % =2-E u - (37) m 7_ Eddy viscosities for the long tube entrance were computed from equation (37). The expression for eddy viscosity in the hydrodynamic entrance region is obtained by integration of equation (34): r r au r au gc ap r" j/ ru Uxdr + r v Hr dr + - x 2 "v + E = o'u (38) r Tr The analysis under Pressure Drop in Chapter V of the relative magnitude of pressure drop due to wall skin friction and that due to momentum changes in the inlet region indicates that the sum of the two integrals in equation (38) is appreciable with respect to the dp term. The evaludx ation of both of the integrals involves a knowledge of the longitudinal velocity gradient, which appears explicitly in the first integral and implicitly in the second since v is obtained from the continuity equation 6u 1 - (vr) +,r I = 0(9)

-102The evaluation of longitudinal velocity gradients from experimental velocity profiles, especially near the edge of the hydrodynamic boundary layer, is very difficult, since the order of magnitude of the changes in velocity at corresponding radii between two adjacent traverses is of the same order of magnitude as the experimental error. This problem is further complicated by the fact that it was necessary,to make separate runs for each X/D investigated. Since increases in core velocity between adjacent profiles due to deceleration in the boundary layer were on the order of one percent, differences in flow rate of one percent between runs would be sufficient to yield a zero or even negative longitudinal velocity profile in the core. Because of these difficulties it was decided not to compute the values of the integrals for all cases. The eddy viscosities reported in Table II for the bellmouth were computed using only the dx term. This is equivalent to using a linear distribution of shear stress with radius, which is rigorously correct only for fully developed flow. The assumption is worst right at the inlet and progressively better at greater X/D's. To estimate the magnitude of the maximum error caused by this approximation, the two integrals in equation (38) were evaluated at an X/D of1.5 for Re = 15,000. Integrating the continuity equation (39), one obtains r vr - r-dr s) r v ]x dr (40) 0 The integral was evaluated graphically, using the estimated values of a shown in figure 34. The value of the integral must be zero at both

-103r = 0 and r = r, since v is zero at the wall. This condition was fulfilled by the graphical integration, indicating that the values used for.. were reasonable. ax Values of the three terms on the right side of equation (40) are tabulated as a function of r in Table III. It is seen that although the first term may be neglected except very close to the wall, the second term may be as much as 1-1/3 times as great as the dp term. Thus dx values of eddy viscosity computed by neglecting momentum transfer due to boundary layer development are not reliable in the region close to: the inlet. Table III also lists values of radial velocity at several radii for the bellmouth entrance at an X/D of 1.5 and Reynolds number of 15,000. Axial velocities at corresponding points are included for comparison. The largest ratio of radial to axial velocity found was.0037 at r. of about.85. Eddy Conductivities The equation for eddy conductivity for fully developed flow is obtained by integration of equation (16): r u r ax dr k 0 (41) Op c at As mentioned previously this equation neglects axial conduction, heating due to pressure changes, and frictional dissipation. Introducing the' dimensionless variables U, 0, and r, equation (41) becomes

-Lo4r* um a r* U d r k -+ - = O (42) pCp cr d dr This relation was used for computing eddy conductivities in the thermal inlet region following the long tube entrance. For the bellmouth entrance a term must be added to equation (41) to account for radial transfer of heat by convection due to the development of the hydrodynamic boundary layers: r r /uu dr v dr + (tJ ~~~~~x~~(43) p r Using the radial velocities from Table III the magnitude of the radial flow term in equation (43) was estimated at X/D = 1.5. It was found that the maximum error introduced by neglect of this term was 11 percent. The percentage error decreases with distance downstream. The radial convection term was therefore neglected in computing eddy conductivities for the bellmouth. This assumption introduced only small errors except possibly for the first X/D. Radial Heat Flux The radial heat flux at any radius in a tube is given by r' but p Cj r -x dr q(r) = ~, 0 (44)'r

-105For constant u (fully developed flow), the u may be taken out of the derivative. Then, introducing U. r*, and e, equation (44) becomes: r* p C (t - tt) um r. U dr p w o * q(r) = 0 p Cp (tw to) u (45) r * The radial heat flux is therefore proportional to the integral I, which appears in the expression for eddy conductivity and is tabulated in Table II. If the flow is not fully developed, a slight error is introduced by computing radial heat fluxes from equation (45), since u is not now a constant and should be left inside the differential sign.

APPENDIX B Table I. Gross Values for Heat Transfer Runs Table II. Point Values for Temperature and Velocity Traverses Table III. Momentun Terms in the Entrance Region for Bellmouth Entrance. X/D = 1.5 Re = 15,000 Figure 35. Calibration for Chromel-Constantan Thermocouples -106 -

-107TABLE I. GROSS VALUES FOR HEAT TRANSFER RUNS X ~ r Run - Re W AT q h Nu LONG TUBE ENTRANCE 1.453 15, o00 66.6 24.5 207 8.45 69.4 2 1.13 14,780 66.0 26.7 174 6.53 53.7 3 4.12 14,860 66.4 25.0 147 5.87 47.8 4 9.97 14,700 65.8 21.1 121 5.72 46.6 5.453 64,100 285.0 22.6 551 24.4 201.0 6 1.13 64,200 287.0 28.9 601 20.8 172.0 7 4.12 63,800 284.0 24.6 462 18.7 154.0 8 9.97 64,900 290.0 22.9 390 17.0 140.0 BELIMOUTH ENTRANCE 9.453 14,830 66.0 25.9 149 5.74 47.2 10 1.13 14,820 66.1 27.3 119 4.37 35.9 11 1.75 14,800 66.0 o27.4 98.3 3.59 29.5 12 4.12 14,910 66.3 29.1 78.9 2.71 22.4 13 9.97 14,820 66.2 27.5 79.1 2.88 23.7 14.453 63,900 284.0 20.1 387 20.4 167.0 15 1.13 65,5o00 291.0 27.7 535 19.3 159.0 16 1.75 64,200 286.0 26.0 456 17.9 146.0 17 4.12 65,300 290.0 5 29.8 546 18.3 150.0 18 9.97 65,350 290.0 22.1 388 17.6 144.0

TABLE II. POINT VALUES FOR TEMPERATURE AND VELOCITY TRAVERSES Run 1 u, = 20.7 ft/sec t = 104.01~F w Long Tube Entrance u* = 1.22 ft/see tb = 79.60'F Heated L/D =.453 ()b =0130 P =.0707 lb/cu ft P lb/cu Re = 15,000 to = 79.35'F k/Cp =.000251 sq ft/sec Y | r r | t | 9 a39 |2 u U C 1 c in, _ in. 6 1O - _ _ _ _ _ in, |in. _ oF a ft/sec v a I 7533.00oo67.0088 79,35 0 0 0 25.2 1.000 v.002 74.3 439 20.6.638.122.161 79.35 0 0 o 25.1.996 0.075 35.7 372 20.5.588.172.226 79-35 0 0 0 25.1.996 0o.120 31.2 343 20.5.538.222.292 79.36 0 0 0 24.8. 983 0.170 28.4 314 20.3.488.272.358 79.35 0 0 0 24.5. 972 0.224 26.3 285 20.0.438.322.424 79.35 0 0 0 24.2.961 0.275 25.4 255 19.8.388.372.489 79.35 0 0 0 23.5.933 0.330 24.4 226 -19.2.338.422.555 79.35 0 0o 0 23.0.914 0.386 23.6 197 18.8.288.472.621 79.35 0 0 0 1 22.5.892 0 1.443 23.0 1 68 18.4.238.522.687 79.35 0.002.005 21.4.851 0.505 22.3 139 17.5.188.572.753 79.37.ooo8.025.02 20.6.818-.005 1.03.578 21.3 1lo 16.9.163.597.786 79.46.o0045.052.025 20.1.800.00oo8. 367.620 20.7 9,5.jo 16.5.138.622.818 79 55. 0081.105.140 19.6.778.025 1.28.670 19.9 80..5 16.0.113.647.851 79.65.0122.197.700 18.8.755.100 4.18.772 17. 65.9 15.4.088.672.884 79.76.0166.375 2.19 18.1.717.395 9.78 1.08 13.0 51.3 14.8. o78.682.897 79.91.0227.493 2.83 17.7.702.590 11.2 1.30 10.8 1.04 45.4 14.4.0o68.692.910 80.09.0300.780 3.47 17.1.680.83: 9.66 1.55 9.03 1.07 39.6 14.0.058.702.924 80.46.0450 1.255 4.13 16.6.658 1.16 7.98 2.03 6.78 1.18 33.8 13.6.048.712 937 80.91.0633 1.92 4.72 15.8.627 1.51 6.44 2.88 4.57 1.41 28.0 12.9.0o38.,722.950 81.85.101 3.30 5.27 14.6.5i9 1.88 4.17 4.54 2.58 1.61 22.1 11.9.033.727.957 82.53.129 4.25 5.53 13.6.540 2.08 3.34 5.73 1.86 1.79 19.2 11.1.028.732.963 83.10.152 5.32 5.70 12.7.503 2,26 2.67 6.92 1.38 1.93 16.3 10.3.023.737. 970 84.15. 195 66.90 5.86 11.5.456 2.45 1,96 8.62.920 2.13 13.4 9.40.018.742.976 85.56.252 8.59 5.90 10o.1 399 2.60 1.43 0o.5.590 2.42 10.5 8.22.013.747.983 87.48.330 1.50 5.88 7.78.309 2.72. 775 13.4.256 3.03 7.58 6.36.011.749.986 88.15.357 13 40 5.83 7.01.278 2.77.490 14.7.152 3.22 6.42 5.73.009oog.751.988 89.02.392 14.70 5.79 6.10.242 2.80.327 5.7.075 4.36 5.24 4.98.008.752.989 89.30.406 15.6 5.77 5.52.219 2.81.229 L6.0.057 4.02 4.66 4.51.007.753.991 89.96.430 18.1 5.68 5.06.201 2.83.057 6.5.027 2. 11 4.08 4.13.oo6.754.992 90.41.448 0.5 5.63 4.54.180 2.84 0 6.7.015 3.50 3.71.005.755.993 90.95.470 3.o 5.52 3.96.157 2.85 16.8.01 2.92 3.24.oo004.756.9947 91.85.507 8.5 5.25 3.92 2 I.33 3.11

TABIE II. (Cont.) Run 2 Ub = 20.5 ft/sec tw =109.7'F Long Tube Entrance u* = 1.21' ft/sec tb = 83o02~F Heated L/D =1.13 ()=.0099 =.0711 lb/cu ft Re = 14,780 k/pC =.000250 sq ft/sec t0 = 82 17~F p a di 102 d 10 -(D r u in. in. F 10 dZ ft/sec V.760 0 0 82.15 0 0 O 25.91 1.000 0 0 435 21.4.734. 026. 0342 82. 15 0 0 0 25.91 1.000 0.020 26. 9 420 21.4.684.076 loo1000 82.15 0 0 0 25.81. 996 0.056 28.1 391 21.3.634.126.1658 82.15 0 0 0 25.70.992 0.0o95 -27. 5 363 21.3.584. 176. 2316 82.17 0.0001 0 25 60. 988 O.132 27.6 334 21.2.534.226.2974 82.20 o.00108.002.0020 25.20 *973 0.172 27. 2 305 20.8.484.276.3632 82.22.0oQ181.005 oo0040 25.00.965 0. 213 26.8 277 20.7 434.326.4290 82.25.00290.o007.0oo60 124,40.942,..0020 5. o6.258 26.1.193 248. 20.2.384.376.4948 82.27.00363.010. 010 24. 01.927 0035 5.35. 310 25.0.2O4 220 19.9.334.426.5606 82.30.00472. 015.025 23.43.904.010 9.94.365 24.1.412 191 19.4.284.476.6264 82.30 o00472.019 0 o48 22.70.876.020 14.8.425 23.1.640 162 18.7.234.526.6922 82.34.00617.025.o78 21.81.84).041 21.3.442 24.6. 865 134 18.0.184.576. 7580 82.40.00oo835 034.180 21.07. 813.087 31.0.580 20. 3 1. 53 105 17.4.159. 601.7909 82.43.00944.050. 430 20.50.791.146 34.1. 640 19.2 1.77 91.0 16.9.134.626.8238 82.51.0124. 095.920 19. 98.771.278 26.1.718 17.7 1.46 76.7 16.5.114.646.8501 82,79.0225.238 1.43 19.45.751.480 21.0.86 15.1 1.39 65.2 16.1.094.666.8765 83.23.0385.575 1.87 18.75.724.760 15.8 1.18 11.1 1.42 53.8 15.5.074.686.g9028 83.91.0632.948'2.36 17.75. 685 1.12 10.9 1.60 8.20 1.33 42.3 14.6.054.706.9291 84.94.101o 1.95 2.76 16.56.639 1.53 66.59 2.93 4.17 1. 58 30 9 13.7.034.726.9554 87.oo00.175 4.22 2.89 13.91.537 1.96 3.17 5.35 1.92 1.65 19. 5 11.5.024 *.736 -.9686 88.98.247 7.05 2.91 1156 446 2.15 1 53 8.65.725 211 13.7 9. 56. 019.741.9752 90.55.304 8.80 2.90 9.49.366 2. 23 1.01 11.15 325 3.11 10o.9 7.85.014.746.9817 92.17.363 1o.60 2.88 7.18.277 2.29.632 13e50.185 3.42 8.01 5.94.010.750.9870 93.94.428 12.80 2,86 5.34.206 2-32. 288 5.72 4.42.007.753 e9909 95.20.473 5. O 2. 82 4. 04.156 2.34.045 4. 00 3.34.006.754.9923 95.79 e495 J.6o05 2.60 3.61.139 2035 0 3.43 2.99.005.755.9936 96.26.512 1695 2.15 3.46 O 2.86 2.86.004.756.9949 96.64.526 18.25 1 3.41 1 0 2.29 2.74 e04{ 5.999-6 —:2

TABLE II. (Cont.) Ub = 20.5 ft/sec t = 110.80F Long Tube Entrance u* = 1.21 ft/sec tb = 85.80F Heated L/D = 4.15 b =.841 =.0714 lb/cu ft Re = 14,860 t = 83.78OF k/pC =.000251 sq ft/sec 0o p a 0 U 10 rD - y u in. in. | F a a ft/sec v| a v.7595.0005.00066 83.78 0 0 0 25.3 1.000 0 0 4 138 1 20.8.6785.0815.1073 83.78 o.oo008 0 1 25.1.992 1 0 1.o066 26.5 391 20..5785.1815.2389 83.79.00037.025.02 24.6.974 1;.149 26.1 1 333 20..4785.2815.3705 83.93.00555.052.049 24.0.951.007 1.94.232 26.0 276 19.8.3785.3815.5021 84.20.0155.105.375 1 23.0.910.033;38.315 25.9 1218 19.0.2785.4815.6337, 184.75.0359.185.740 21.8.863.250 8.4.405 25.4 160 18.0.2285.5315.6995 85.12.0496.255.956 21.0.832.540 26.7 1.470 24.1 1.11 132 11.4.1785.5815.7653 85.73.0722.416 1.22 20.3.802.970 26.9.565 21.9 1.23 103 16.7.1535.6065 *.79 2 86.16.0880.500 1.37 19.8.784 1.23 27.1.630 20.4 1.33.88.4 16.3.1285.6315.8311 86.68.107.1 582 1.48 19.2.760 1.52 27.5.730 18.2 1.52 74. 0 15..1035.6565 1.8640 -87.21.127.84o 1.52 18.6.736 1.84 22.1.870 13.6 1.63 5 9.6 15..0785.6815.8969.88.06.158 1.11 1.52 17.7.702 1 2.16 18.6 1 1.25 11.1 1.67 45.2 1 14.6.0585 1.7015 1.9232 88.98.193 1 1.69 11.51 16.4 1.649 2.41 12.8 1 2.20 1 6.10 1o 2.10 33.7 13.5 0435.7165 1.9429 190.13 1.235 2.50 1.49 1 15.1 1.596 1 2.59 8.65 3.75 3.25 2.66 1 25.1 12.4.0285.73'15.9627 91.75.295 4.37 1.39 1 12.3.485 2.73 4.50 1 7.33 1.22 3.69 16.4 10..0185.7415.9758 94. 04.380 6.80 1.24 9.24.366 2.80 3.61 11.o 0.500 10.7 7.62.0135.7465.9824 1 95.25 1.425 8.10 1.09 1 6.86 1.272 2.82 2.80 13.2.2581 1 7.78 5.6.-0oo095.7505.9877 96.47 1.470'9.27 1.02 1 5.38..213 1 2.83 1.36 15.1.1051 1 5.47 4.44.0075 1.7525 1.9903 97.16.495 10.20.850 1 4.54.180 2.83 1.1o 16.1.04 4.32 3.75.0065.7535.9916 97.52.509 10.65.810 4.oo.158 1 2.83.991 16.5.0151 3.74 3.30.0055.7545.9929 97.90 1.523 1 13.5.740 1 3.64.136 2.84.492 16.7.0051 1 3.17 3.0.0045 1.7555.9942 98.44 1.543 3.42 1 2.59 2.8.0035.7565.9956 99.20.571 3.24 1 2.02 2.6

TABLE II. (Cont.) Run 4 ub = 21.0 ft/sec tw = 108.48~F Long Tube Entrance u* = 1.24 ft/slec to = 87.35 F Heated L/D = 9.97 ( = 00757 p=.0o6g lb/cu ft Re = 14,700 to = 85.490F k/pC =.000258 sq ft/sec + 3 a 1032 1o c c Y r| d8 a- dE in. in. F a ft/ sec v a v.7076.0524.o06896 84.41o.0o364.017 -5.64 25.2 1.000.018 112.032 35.7 403 20.4.6326.1274.1677 84.49.0o400.Of56 6.03 25.1.996.080 77.7.079 35.2 360 20.3.5576.2024.2664 84.72.0492.105 6.43 24.7.980.210 68.3.130 33-9 2.01 317 20.9.4826.2774.3651 85.01.0608.154 6.86 24.2.961.410 66. 1.181 33.24 1.98 275 19.6.4076.3524.4638 85.66.0868.206 7.32 23.6.937.690 65.7.240 32.C 2.05'232 19..3326'.4274.5625 86.26.111.263 7.80 23.0.914 1.05 63.8.302 30.8 2.07 189 18.6.826.4774.6283 86.73.129.312 8.141 22.4.890 1.33 60.8.3428 29.8 2.0o41 161 18.1.2326.5274.69411 87.30.153. 392 8.49 21.9.869 1.65 54.5 1.412 27.8 1.96 132 1 17.7.1826.5774.7599 88.06.183.560 8.82 21.0.832 2.01 42.2 1.500 24.9 1.70 o104 1 17.0.1326.6274.8257 89.31.233.795 - 9.19 20.2.800 2.39 32.0.630 21.4 1.49 75.41 16.3.1076.6524.8586 90.02.261.932 9.34 19.6.778 2.60 28.3.780 17.8 1.59 61.2 16.0.0828.6774.8915 90loo0.300 1.12 9.50 18.9.748 2,79 23.5 1.14 12.4 1.0go 47.0 o 15.2.0576.7024'.9244 92.02.341 1.75 9.60 17.0.673 3.o00 15.2 2.09 6.55 2.35 32.8 13.7.0426.7174.9441 93,.23.390 2.80 9.57 15.6.619 3.12 9.25 1 3.97., 3.06 1 3.20 24. 2 12.6.0326.7274.9573 94.24.430 14.02 9.35 13.8.5491 3.19 6.06 6.65 1.45 1 4.17 18.6 11.2.0276.7324.9638 95.05.463 - 4.75 9.22 12. 6.500 3.22 4.86 8.55.92 15.7 10.2.0226.7374.97041 95.91.497 5.67 8.95 1ll.o. 435 3.241 3.85 11.05.498 12.9 8.86.0176.7424.9770 96.86.535 6.76 8.60.8.88,352 3.26 2.99 13.5.232, o10.0 7.18.0126.7474 1.9836 98.19.588 7.90 7.90 6.50.258 3. 27 2.32 15.4.089g 7.17 5.25.0096.7504.9875 99.03.622 8.80 7.00 5.29.210 3.28 e1.92 16.2.039 5.46 4.28.00oo76.7524.9902 99.59.644 9.65 6.00 oo 1 4.41.175 3.28 1.61 16.5.025 4. 32 3.57.00oo66.75341.9915 99.91.657 10.20 5.80 4.00 oo.158 3.28 1.45 16.7.012 3.76 3.22.0056.7544.9928'100.26.671 10.95 5.30Q 3.72 i428 3*28 1.25 16.9 0 3.19 3.00.oo46.7554.9941 ioo.64.686 12.10 4.80 3.65.145 0 2.62 2994.0036.7564.9954 101.33.714 3.80.151 0 2.05 3.06.0031.7569.9961 102.67.768 0o

TABLE II. (Cont.) Run 5 Ub = 88.3 ft/sec t = 104.460F Long Tube Entrance u = 4.42 ft/sec tb = 81.850F Heated L/D =.453 Zb =.0095 p =.0713 lb/cu ft Re = 64, 100 t = 81.480F k/pC =.000250 sq ft/sec o p y r I r - t o e'1a'E 2e I u U 3 E U t r 3 102at 10 c - v c + u+ in. in. t 1F1 ft/sec8 -r.638.022.0289 81.44 0 0 0 410 1.000ooo o 0o.538.122.1605 81.46 0 0 0 log109.999 0.022 373.488.272.3579 81.50.ooo87 0 0o 108.986 0.122 149 1030 24.6.438.322.4237 81.48 0 0.010 107.976.0004.177 122 925 24.3.388 372.4894 81.49.ooo44 0.019 105.961.0037.244 102 818 23.9.338.422.5552 81.49.000ooo44.005.032 103.942.0120 176. 325 86.4 2.04 713 23.4.288.472.6211 81.49.000ooo44.013.050 o101.918.0267 133.414 75.6 1.76 608 22.8.238.522.6868 81.54.00261.026.072 97.6.887.0510 116.510 67.8 1.71 502 22.1.188.572.7526 81. 59.00479.047.108 93.3.848.0870 10ol.630o 60.1 1.68 396 21.1 H.138.622.8184 81.64.oo696.079.250 88.7.806.160 97.3.765 53.7 1.81 291 20.0.113.647.8513 81.67.00827.123.510 85,8.780.240 91.2.8go90 47.9 1.91 238 19.4.088.672.8842 81.77.0126.222.930 82.2. 747.390 80.2 1.12 39.3 2. o4 186 18.6.068.692.9105 81.93.0196.435 1.60 78.5.714.620 63.0 1.43 31.6 1.99 143 17.7.048.712.9368 82.35.0379.980 2.80 74.0.673 1.00oo 43. 1 1.77 26.1 1.65 lo 16.7.038.722.9500 82.74.o548 1.55 3.60 71.5.650 1.27 33.8 1.90 24.6 1.37 80.5 16.2.-028.732.9632 83.36.0818 2.55 4.30 68.1 619 1.57 24.5 *2.85 16.3 1.50 59.1 15.4.023.737.9697 83.77.0997 3.48 4.63 65.7.597 1.75 19.7 3.80 12.1 1.63 48.6 14.9.018..742.9763 84.40.127 5.02 4.87 61.6.569 1.92 14.5 5.55 8. ol 1.81 37.9 13.9.013.747.9829 85.30.166 8.25 4.97 57.5.523 2.10 9.o4 9.0oo 4.60 1.96 27.4 13.0.011.749.9855 85.88.191 10.4 4.95 54.6.496 2.16 7.09 11.4 3.43 2.07 23.2 12. 3.oog.751.9882 86.60.223 14.7 4.50 51.0.464 2.22 4.70 17. 1.97 2.39 19. 0 11.5.o008.752.9895 87.21.249 17.7 4.20 48.3J.439 2.26 3.75 21.3 1.38 2.72 16. 10.9.007.753.9908 87.75.273 20.5 3.30 45.0.409 2.27 3.05 28.0.81 3.76 14.8 10.2.oo6.754.9921 88.35.299 22.4 2.75 39.6.360 2.28 2.67 12.7 8.96.005.755.9934 89.06.330 42.5 2.40 2.29.736.00oo4.756.9947 90.24.381 1.90.0035.7565.9954 91.79.449

TABLE II. (Cont.) Run 6 ub = 87.2 ft/sec tw = 113.65~F Long Tidbe Entrance u* = 4.36 ft/sec tb = 84.'740F Heated L/D = 1.13 00742 P =.0717 lb/cu ft Re = 64,200 to = 84.24~F k/PCp.000249 sq ft/sec y r r t e 2 U U ~ + + -l _- 8e 3 _c - aar 10 L10 C. c in. in. 0.F aZt/a ~se_ V.7385.0215.o02829 84.24 o o 0o 105 1.000 0 0o.6885.0715.og408 184.24 0o o o 10o4.990 0 o.011 431.6385.1215.1599 84.24 1 0 0 0 1041.989 0.023 352.5885.1715.2257 84.21 0.ool.0008 104.987 0.038 300.5385.2215.2914 84031.00238.002.0035 103.984.ool 66.0.058 253.4885.2715.3572 84.31.00238.0025.0075 103.980. 002 85.3.086 209 1030 23.8.4385.3215.'4230 84.28.00136.0oo45.0165 102.967.005 101.0.129 165 927 23.6.3885*.3715 1.4888 84.29.00170.006.0400 101.963.013, 172.0.190 129 1. 33 819 23.3.3385.14215.55416 841.31.00238.oog.104 loo..9947.036 280.0.270 103 2.72' 714 23.0 I.2885.4715.6204 84.31.00238.013.182 97.8.9256.086 415.0.372 83.3 608 21.5.2385. 5 15.6862 84.30.00204.018.280 94.6.896. 175 624.0.490 69.8 503 21.7.1885.5715.7520 84.42.00612.026.403 90.5.857.315 64.0 o.620 60.4 398 20.8.1635.5965.7849 84.45.00714.0 o40.480 88.3.836.415' 514.0.692 56.3 345 20.3.1385.6215.8178 84.52.00900.082.608 85.8.812.520 301.0.780 52.1 292 19.7.1185.6415.8441 84.59.0119.1035.780 83.5.791.640 218.0.847 49.3 250 19.2.0985.6615.8704 84.70.0157.195 1.14 81.0.767.810 185.0.1. 01o 42.6 208 18.6.0785.6815.9867 84.92.0231.608 1.61 77.9.738 1.05 74.0 1.23 35.9 2. o6 166 17.9.0585.7015.9230 85.47.0418.940 2.08 73.5.696 1.36 59.9 1.66 27.2 2.22 123 ~6.9.0385.7215.9493 86.58.0796 1.95 2.80 68.6.650 1.77 35.6 2.35 21.1 1.69 81.2 15.8.0285.7315.9625 87.52.112 2.88 2.89 65.1.616 2.00 26.5 3.10 14.7 1.81 60.2 14.9.0235.7365.9691 88.12.132 3.70 2.89 62.5.592 2.11 21.2 4.30 lo.14 2.04 49.7 14.14.0185.7415.9757 88.97.161 5.410 2.80 58.9.558 2.22 14.8 6.55 6.53 2. 26 39.1 13.5.0135.7465.9822 90.23.204 -8.93 2.30 53.2.504 2.31 8.65 10.3 3.82 2.26 28.5 12.2.0105.7495.9862 91.55.249 12.6 1.65 48.41.458 2.35 5.76 14.5- 2.44 2.36 22.2 11.1.00oo85.7515.9888 92.62.285 15.6 1.50 43.6.413 2.36 4.39 20.0 1.50 2.93 17. 9 10.0.0065.7535.9915 94.05.334 21.2 1.14 36.5.346 2.38 2.88 30.2.66 4.37 13.7 8.37.0055.7545.9928 94.96.365 26.o.940 32.0.303 2.38 2.07 36. o.39 5.24 11.6 7.34.0045.7555.9941 95.07.368 31.2.820 26.5.251 2.38 1.49 45-. 0.12 9.50 6.07.0035.7565.9954 96.32.411.550 21.0.199 7.38 4.8

TABLE II. (Cont.) Run 7 Ub = 84.5 ft/sec t W106.69~F Long Tube Entrance u* = 4.22 ft/sec tb = 82.05~F Heated L/D = 4.15 ( =.00638 p =.0742 lb/cu ft Re =-63,800 t = 80.400F k/pC =.000240 sq ft/sec 17595 1.0005.ooo66 180.53. o 0 102.3 I I I I.6795.0805 1059 80.40 0. i o002oai.o011 102.1;.998 0 2.029 192.5795.1805 *.2375 80.46.00228.010.0355 101.4.991 0..083152.4795.2805.3690 80.51.00418.024.104 98.2.960.030 130.149 129 1.01 1070 23.3.3795.3805.5007 80.61.00799.059.196 94.5.924.111 143.234 111 1.29 797 22.4.2795.48o5.6322 80.96.0213.158.355 90.4.884.295 112.355' 92.8 1.21 587 21.4.2295.5305.6980 81.32.0350.234!.523 87.6.856.450 104.430 84.7 1 123 482 20.8.1795.5805.7638 81.79.0529.345.820 1 84.5.826.718 103.535 74.2 1.39 377 20.0.1545.6055.7967,182.21.0689..425 1.03 82.4.806.910 101.605 68.4 1.48 325 19.5.1295.6305.8296 82. 58.-0829. 543 1.22 81.5 I 797 1.16 96.9.700 61.6 1.57 272 19.3.1045'.6555.8625 83.0o6.101.691 1.38 78.2.763 1.44 90.9. 835 53.4 1.70: 220 18.5.0795.6805.8954 83.78.129.960 1.47 74.6.729 1.74 75.5 1.025 45.0 1.68 167 17.-7.0595.7005-.9217 84.52.157 130 1.47 71.8.702 1.99 61.2 1.24 38.2 1.60 125 17. 0.0o445 7155.9415 85.37.189 1.75 1.43 69.1.675 2.18 48.6 1.52 31-7 1.53 93.5 16.4.0295.735.9612 86.41.229 2.51 1.31 65.1.636 235 35.2 2.95 16.2 2.19 62.0o 15.4..0195.7405 *9743 87.47.269 4.18 1.20 59-3.580 2.45 21.1 5.60 8.17 2.58 41.0 14.1.0145.7455.9809 88.39.304 6.07 1.11 55.4.542 2.50 14.3 9.00 4.73 3.02 30.5 13.1.0115.7485.9849 89.o09 331 8.05 1. 6 51.4.486 2.52 10.5 12.1 3.28 3.20 24.2 12.2.00o95.7505.9875 89.78.357 9.90.93 47.1.460 2.53 8.27 14.8 2.52 3.28 20.0 11.2.0075.7525.9901 90.45.382 12.7.71 42.6.416 2. 54 6.13 18.6 1.81 3.38 15.8 10.1.0065.7535.9915 190.83.397 14.8.63 39.4.385 12.54 5.08 21.4 1.44 3.53 1 3.7 1 9.33.0055.7545.9928 91.49.422 B. 3. 55 36.7 359 2.54 3.80 25.8 1.025 3.71 11.6 8.69.0045 *.7555.9941 92.18.448 21. 5.48 33.6.328 2. 55 3.04 9. 45 7.96.0035.7565.'9954 92.89.475 30.4 7.35 7.20

TABLE II.. (Cont.) Run 8 Ub = 89.35 ft/sec t = 107.49~F Long Tube Entrance u* = 4.46 ft/sec b = 84.55~F Heated L/D = 9.97 (b = 0054 p =.0718 lb/cu ft Re = 64,900 to = 81.810F k/pCp.000248 sq ft/sec aI ~~~~~r 10.63! I I VI in. in. F a _ ft/sec V.7325.0275.03618 81.88 o.00o48 0 109.8 1.000.012 158.6825.0775.1020 81.82 0.016 0 109.8 1.000. 035 153.6325.1275.1678 81.81 0.033 0 109.7.993 062 143.5825.1775.2336 81.88.00273.052.32 108.2.986.038 14.1.094 131.108.5325.2275.2993 82.00.0074.072.48 107.7.981.118 21.0..131 120.175.4825.2775.3651 82.07.0101.0975.68 105.9.965.257 28.1.175 110.255 1025 23.8..4325.3275.4309 82.37.0218.126 1.01 104.6.952.460 33. 1.222 102.325 920 23.5.3825.3775.4967 82.56.0292.162 1.44 102.8 936.800 39.2.271 96.1.408 813 23.1.3325.4275.5625 82.87 1.0413.215 1.92 100.4.915 1.33 43.4.330 89.4.487 707 22.5.2825.4775.6283 83.31.0584.287 2.44 98.0.893 2.10 46.1.395 84.2.547 601 22.0 H.2325.5275.6941 83.85.0794.385 2.90 94.8.864 3.11 45.9.473- 76.7.599 494 21.-3.1825.5775.7599 84.58 -.108. 535 3.27 90.6.826 4.40 43.0.554 71.7.599 388 20.4.1575.6025.7928 85.08.127.627 3.42 88&8.810 5.10 40.2.598 69.3.579 335 19.9.1325.6275.8257 85.66.150.752 3.54 86.9.791 5.82 36.5.648 66.4.549 282 19.5.1075.6525.8586 86.38.178.895 3.64 84.2.767 6.61 33.33.720 62.2.537 229 18.9.0825.6775.8915 87.18.209 1.08 3.74 81.4.742.7.40 29.5.860 53.8.548 176 18.3.0575.7025.9243 88.15i.247 1.40 3.80 75.9.691 8.21 24.1 1. 35 - 35.3.683 122 17.1.0425.7175.9441 88.99.280 1.70 3.84 73.4.669 8.70 20.3 1.80 26.8.757 90.4 16.5.0325.7275.9572 89.59.303 2.10 3.82 70.6.643 8.99 16.4 2.60 18.5.887 69.2 15.8.0225. 7375.9704 90-53..340 3.0o6 3.78 66.1.602 9.30 11.0 4.30 10.9 1.01,' 47.8 14.8.0175.7425.9770 91.11.362 4.75 3.72 62.3.568 9.45 6.69 6.60 6.84.978 37.2 14.0.0125.7475.9836 92.24.406 8.65 3.64 56.1.511 9.57 3.04 11.60 3.50.868 26.6 12.6.0095.7505.9875 93.27.446 12.30 3.55 50.1.456 9.62 1.73 18.60 1.81.957 20.2 11.2.0075. 7525.9901 94.21.483 16.30 3.47 44.1.402 9.68.956 26.0 1.02.937 16.0 9.89.00oo65.7535.9915 94.84.507 20.0 3.42 39.1.356 9.70.520 30.5.72.720 13.8 8.77.0055.7545.9928 95.61.537 24.9 3.37 34.6.315 9.70.139 35.4.485.287 11.7 7.77.0045.7555.9941 96.53.573 3.35 29.4.268 9.71 9.58 6.62.o0040.7560. 9947 97.15.597

TABLE II. (Cont.) Run 9 Ub = 20.4 ft/sec Bellmouth Entrance o887 = 82.25~F Heated L/D =.453 to = 81.88~F p>=.0716 lb/cu ft Re = 14,830 t = 14830 tw = 15F k/pCp.000249 sq ft/sec y r r t _ r 10 3 v e in. in. OF a ft/sec |v a.7600 0 0 81.88 0 0 0 22.1 1.00 0 0.7315.0255. 0336 81.88 0 0 0 0 22. 1 1.00 0 0.6845.0755.0993 81.88 0 0 0 22.1 1.00 0 0.58415.1755.2309 81.88 0 0 0 22.1 1.00 0 0.4845.2755.3625 81.88 0 0 Q 22.1 1.00 0 0.3845.3755.4941 81.89.00038 0 0 22.1 1.00.0 0.3345 -.4255.5599 81.89.00038 0 0 22.1 1.00 0 0.2845..4755.6257 81.91.00114 0 0 22,1 1.00 0 0.2345.5255. 6915 81.91 1.00114 005 0 22.1 1.00 0 0.1845.5755.7572 82.00.00457.022 0 22.1 1.00 0 0 0.1345..6255.8230 82.05.00647.0O7 0 22.1.996 O0.15.o845.6755.8888 82.22.0130.143.000? 21.2.958 0 1.87.0645.6955.9151 82.34.0175.520.016 19.3.876.17 1.48 4.6o 1.13 1.31.0595.7005.9217 82.51.0240.945.023 18.7.845.27 1.08 5.75 1.13. 957.0545.7055.9283 82.73.0324 1. 58.032 17.6 -.797.415.864 6.70.98.882. 0495.7105.9349 83.06.0450 2.57.041 16.4.7441.58.523 7.65.62.8414.0o445.7155.9415 83.54.0632 3.80.051 15.1.685.78.328 8.55.46.713.0395.7205.9480 184.35.09410 5.25.062 13.8.623 1.01.205 9.45.33.622.0345.7255.9546 85.47.137 6.841.076'.12.41.559 1.31.192 10.5.19 1.01.0295.7305.9612 8j.0oo.195 8.48.108 10.8. 490 1.63;18o 11.4.11 1.64.0245.7355.9678 88.68.258 10.14.126 9.21.417 1.95'.179 12.2. 03.0195.7405.9743 90. 58.331 11.85.0o99 7.29.330 2.23.126 12.5 0.0145. 7455.9809 92.66.1410 13.89.077 5.02.227 2.39 0 12.9 0.oog0095.7505.9875 94.80.492 16.39.050 3.61.163 2.47 0 13.0 0'.0075.7525.9901 95.74.528 17.60.040 2.96.134 2.49 0 13.0 0.0055.7545.9928 96.62.561 19.60.028 2.46.111 2.50 0 13.0 0.0045.7555.99411 97.18.582 20.7.023 2.37.107 2.50 0 13.0 0.0035.7565.99541 97.68.-601 21.8.018 0 0.0030.7570.9961 97.96.612 22.5.0151 0 0

TABLE II. (Cont.) Run 10 Ub = 20.52 ft/s~ec Belimouth Entrance ()=.oo6y4 t = 81.120F Zb Heated L/D = 1.13 to = 80.660F p =.0718 lb/cu ft Re = 14,820 t = 108.43OF k/PC =.000249 sq ft/sec w p y r r t a __) U u E E E a 6 %10- 10 62 E in. inl. OF a ft/sec v a v v.760.000 0 80.67 0 0 0 21.8 1.00 0 0.549.211.2776 80.66 0 0 0 21.8 1.00 0 0.349.411.5408 80.66 0 0 0 21.8 1.00 0 0.199.561.73-82 80.62 0 0 0 21.8 1.00 0.025.149.611.80o0 80.62 0 0.005 21.6.991.005.25.124.636.8368 80.67.00036.0o43.025 21.3.978.038 7.09.64 12.8.553.099.661.8697, 80.81.0054.254.109 20.6.945.210 6.26 1.55 4.92 1.27 H.084.676.-8895 81.00 -.0122.620.199 19.7.go4.435 )4.96 2.85 2.29 2.16.074.686.9026 81.38.0260 1.26.275 18.6.852.688 3.46 ) 4.13 1.30 2.66.069.691.9092 81.65.0378 1.68.325 17.9.820.839 3.00 5.00.920 3.26.064.696.9158 81.99.0479 2.23.383 17.1.786 1.00 2.52 6.oo.61o 4.13.059.701.9224 82.44.0641 2.92.452 16.3.748 1.21 2.18 7.15.360 6.06.054.706.9290 83.09.0875 3.70.534 15.5.712 1.)43 1.91 8.25.181 10.55.049.711.9355 83.84.115 4.57.645 14.4.662 1.68 1.72 9.15.067.0)4)4.716.9421 84.'87'.152 5.50.798 13.0.594 1.96 1.59 10.0 0..039.721.9487 86.18.199 6.47.950- 11.6.530 2.26 1.51 10.23 0.034.726.9553 87.81.258 7.47.965 10.0.459 2.56 1.)42 10.25 0.029.731.9618 89.o04.302 8.50.840o 8.52.391 2;81 1.'29 10.25- 0.024.736.9684 90.88.368 9.66.700 7.02..322 2.99 1.11 10.25 0.019.741.9750 92.)43.424 10.97.550 5.60 0.257 3.11.87)4 10.25 0.014.746.9816 9)4.20.488 12.6.41o 4.16.191 3.17.597 10.25 0.011.749.9855 95.6)4.54o 13.8.323 3.10.142 3.20.430 10.25 0.009.751.9882 95.76.544 1)4.8.257 2.72.125 3.21.306 10.25 0.007.753.9908 96.28.562 16.5.203 2.34..107 3.22.079 10.25 0

TABLE II. (Cont.) Run 11 Ub = 20.5 ft/sec Bellmouth Entrance )b =.00oo548 tb = 84.53~F Heatea L/D = 1.75 t = 83.78~F p =.0712 lb/cu ft Re = 14,800 tw = 111.920F k/pCp =.000250 sq ft/sec y r r t 8' is ao U e 6 u 103 c c in. in. OF at/sec.758.002.00263 83.93 0 o 0 22.1 1.000 0 0.549.211.2777 83.76 0 0 0o 22.1 1.000 0 0.349.411.5409 83.78 0 0 0 22.1 1.000 0 0.249.511.6725 83.77 0 0 0 22.1 1.000 0 o.199.561.7383 83.78 0 0\ 0 22.1 1.000 0.02.179.581.7646 83.78 0.021.11 22.1 1. 000.015 6.21.130 56. 9. 169.591.7776 83.78 0. 041. 16 22.06. 999.027 5.45.205 36.4.159.601.7909 83.8.5.00249.074.24 I22.0.996.045 4.86.300 24.9.149.611.8041 83.86.00284.114.36 21.9.991.000076 5.33.420 17.9 H.139.621.8172 83.90.00426.165.53 21.8.985.00012 5.80. 570 12.8 H.129.631.8304 83.97.00675.237.77 21.5.975.000192 6.50.765 9.70.67.119.641.8436 84.12.0121. 342 1.12 21.3. 965.00031 7.31 1. 03 7.08 2. 04.109.651.8567 84.24.0164.498 1.60 21.1.954.00oo053 8.71 1.60 4.27 2.04.09ogg9.661.8699 84. 46.0242.775 2.20 20.4.924.00075 7.66 2.40 2.57 2.99.089.671.8830 84.87. 0387 1.34 2.95 19.6.886.00104 5.72 3.33 1.51 3.55.079.581.8962 85. 51. 0615 2. 08 3.85 18.5.837.00139 4.60 4.37.920 5. 00.069.691.9094 86.48.og60 3.13 4.63 17.1.772.00180 3.70 5.47.640 5.78.059.701.9225 87.86.145 4.37 4.98 15.1.681..00221 3.00 6.65.360 8.33.049.711.9357 89.86.216 5.66 4.35 13.2.598.00258 2.49 7.95.160..039.721.9488 92.32. 303 7.02 3.47 lO.9. 493.00285 1.99 8.92.0170.029.731.9620 95.08.392 8.63 2.63 7.95.360.030303 1.48 9.35 0.024.736.9686 96.27.444 9.60 2.17 6.66 -301.00308 1.20 9.47 0o.019.741. 9752 97 47.487 10.7 1.76 5.20. 235.00311.940 9.58 0o.014.746.9817 98.68.530 12.;2 1.32 3.80.172.00312. 633 9.62 0.009.751.9883 o100. 28.586 13.3.85 9.62 0.0oo07.753.9909 100.80.605 13.9.70 9.62 0.005.755.9936 100.99.612 14.7.50 9.62 0

TABLE II. (Cont.) Run 12 Ub = 29.2 ft/sec Bellmouth Entrance = ~407 tb = 82.480F Heated L/D = 4.12 to = 81.200F P =.0713 lb/cu ft Re = 14,910 tw = 111.59F k/pC =.000250 sq ft/sec y I r I r ~I t C u U E & E Ec a; 103w 103 I c | v - l in. in. O____ F _____ a ft/sec -a.761.000oo 0 1 81.19 0 0 1 22.9 1.00 0 0.679.081.1066'81.20 0 0 0 22.9 1.00 0 0.579.181 -.2381 81.20 0 0 0 22.9 1.00 0 0.479.281.3698 81.20 0 0 0 22.9 1.00 0 0.379'.381 -. 5014 81.22..oo000o66.0025,.005 22.9 1.00 0 0.279.481.6330 81.34.00461 _,.0135 1.65 22.90.998.060 58j7.04.229.531.6988 81.35.00494.0350 2.85 22.75.992.157 53.5.20 28.9 1.85.204. 556.7317 81.40.o00658.087 3.55 22.49.980. 235 30.2.38 15.4 1.96.179.581.7646 1 81.66.0151 1.237 4.27 1 22.12.964.330 14.0.58 10.3 1.36.154.606.7975 81.89.0227.460 5.25 21.58.941.440 8.78..89 6.65 1.32.129.631.8304 82. 50. 0428.850 6.56 20.70.902.588 5.65 1.61 3.40' 1.66.104.651.8567 83.44.0737 1.45 7.80 19.21.839.725 3.49 2.22 2.30 1.52.079.681.8961 85.81.152 2057 8.60 17.09.745. 965 2.08 3.30 1.29 1.61.059.701.9225'88.23.231 3.48 8.07 14.70.641 1.10 1.43 6.00 *275 5.20.044.716.9423 91.45,.337 4.20 6.75 11.02.480 1.19 1.07 8.30 0.029.731.9620 94.31.431 4.97 3.95 7.25.316 1.20.648 8.30 0.019.741.9752 96.41.501 5.63 2.25 4.74.207 1.22.407 8.30 0.012.746.9817 97.65.541 6.15 1.47 3.51.153 1.22.242 8.30 0.011.749.9857 98.30.563 6.70 1.12 2.69.117 1.22.101 8.30 0.00oog.751.9883 98.90.582 7.50.90 2.23.0970 1.22 0O 8.30 0.00oo8.752.9896 99. 20.592 8.00.79 1.97.0859 1.22 0 8.30 0.007.753.9909 99.55.603 8.45.65 1.71.0745 1.22 0 8.30 0.005' 755.9936 100.4.632 10. 05.48 1.20.0523 1.22 0 8.30 0.00oo4.756.9949 100.75.676 10o.73.32 0 o 0 o

TABLE II. (Cont.) Run 13 Ub = 20.5 ft/sec Bellmouth Entrance ()b =.00413 = 84.20~F Heated L/D = 9.97 t = 81.62~F P.0714 lb/cu ft Re = 14,820 tw = 111.7~F k/pC =.000249 sq ft/sec y r r t a 0 u U c -3 c c a <;Lavrlv 10 10 I in. in. a ___F ft/sec' a _ a.683.077.1013 82.27.0216.0025 1.88 23.4 1.00.o014 480 0.583.177.2329 82.45.0276.0145 1.95 23.4 1.00.052 133 0.483.277.3645 82.55.0309.0240 2.12 23.4 1.00.130 128 0.383.377.4961 82.66.0346.0430 2.43 23.4.999.260 10o.030.283.477.6277 82.91.0429.09g40 2.84 23.1.988.455 65.8.188 31.6 2.06.233.527.6935 83.11.10495.175 3.12 22.6 1.969 1.583 40.3 1.347 18.6 1 2.17.183.577.7593 83.64.0672.327 3.48 22.0.940.730 24.0.620 11.0 2.18 H.133.627.8251.42.0931.630 3.86 20.7.885.910 13.7 1.31 5.16 2.65.108.652.8580 85.64.134.985 4.02 19.2.819 1.oo 8.74 1.78 3.73 2.35.0 o83.677.8909 86.84.174 1.88 4.13 17.5.748 1.12 4.29 2.54 1.44 2.98.0o3.697.9172 88.75 *.237 3. 00 4.19 15.7.670 1.17 2.19 3.76 1.35 1.62.043.717.9436 92.35 *.357 4.31 4.16 12.5.535 1.24 1.16 7. 40.22.033.727.9567 94.29.421 5.02 4.10 9.86.421 1.26.790 9.16 o.028.732 *9633 95,34 1.456 5.38 1 4.o6 8.18 349 1. 26.6291 9.41 0.023.737.9699 96.55.496 5.78 3.98 6.97.297 1.27.491 9.55 o.018.742. -9765 97.72.535 6.20 3.87 55.11.218 1.28.360 9.60 o.013.747. 9831 99.00 /.577 6.67 3.60 3.80.162 1.28.224 9.60 o.01oo.750.9870 99.76.603 7.04 3.20 2.82.120 1.29.145 9.60 o.008..752-.9896 loo.4.623 7.33 2.95 2.31:.0986.1.29.0782 9.60 o.007.753.9909 100.7.635 7.52 2.60 2.02.0862 1.29.o446 9.60 o.005".755.9936 101.3.6536 8.07 2.20 1.44.0615 1.29 9.60 o.0035.7565.9956 102.0o.6766 8.65 1.55 0o

TABLE II. (Cont.) Run 14 Ub = 86.2 ft/sec Bellmouth Entrance )b =.00731 tb = 80.27OF Heated L/D =.453 t = 80.02~F p =.0727 lb/cu ft Re = 63,900 tw = 100.40~F k/pC.000244 sq ft/sec in.. in., a F a ft/sec.7585 1 0 179.98 0 0 0 90.1 1.00 0 0.6825.0775.1020 80.01 0 0 0 90.1 1.00 0 0.5825.1775. 2336 80.00 0 0 0 90.1 1.00 0o 0.4825. 2775.3652 80.-03 0 0 0 90.1 1.00 0 0.3825 3775.4968 80.02 0 0 0 90.1 1.00 0 0.2825. 4775.6284 80.02 0 0 0 90.1 1.00 0 0.1825.5-775.7600 80.03.00049 0 0 90.1 1.00 0 0.1325.6275.8258 80.09.00343.022 O0 90.1 1.00 0.101.1075.6525.8587 80.15.00638.077 0 89.3.991 0.255.0875.6725.8850o 80.18.oo0785.01. l 88.7.986.0005.515.0775.6825.8982 80.25.0113.219.055 88.1.978.0032.775.0o675.6925.9113 80. 32.0147.305.225 86.8.963.0185.800 1.16.0575.7025.9245 80.41.0191.455.675 84.6.940.070 4.18 1.59.0475.7125.9377 80.59.0280.945 1.72 83.0.920.195 6.03 2.60.0375.7225.9508 80. 92.0442 1.52 3.45 79.0. 877.470 9.52 4.35.0275.7325 0.9640 81.42.0o687 2.68 4.92 71.4.792.945 10.9 7.35.0175.7425. 9771 82.81.137 7.60 5.13 60.3.669 1.42 4.97 12.3.0125.7475.9837 84.17.204 12.2 4.91 51.8. 575 1.61 3.10 16.8.0075.7525.9903 86.11.299 18.5 4.25 39.7.'441 1.76 1.77 24.6.0055.7545.9929 87.15.350 23.2 3.73 33.6.373 1.80 1.18 28.0.0035. 7565.9956 89.20.450 39.0 2.70 28.1.312 1.82 1.38 33.0.0025.7575.9969 90.06.493 54.0 2.10 24.1.268 1.84 0 35.4.0015 1.7585.9982 91.65.571 1 0 14~~~~~~~~~~~~

TABLE II. (Cont.) Run 15 Ub = 83.0 ft/sec Bellmouth Entrance o()b o = 80.74OF Heated L/D = 1.13 to = 80.34~F P =.0738 lb/cu ft Re = 65,500 tw = 108.450F k/Cp =.000242 sq ft/sec y r r t a __ U U aG 3 in. in. O_ a f a __ _ _.762.002 0o 80.34 0o'o o0 95.8 1.oo 0o 0.499.261.3435 80.32 0 o 0 95.8 1.00 o 0o.349.411.5409 1 80.32 0 0 0 95.8 1.00oo 0 0 o.299.461.6067 1 80.32 0 0 0 95.8 1.00 0 0 o.224.536.7054 80.31 o o 0 o 95.8.oo o 0 o.199 -.561.7383 80.32 0 0.01 1 95.6.998 0. 020.174.586.7712 1 80.32 0 0.02 1 95.1.991 0.068 1.149.611.8041 80.34 0 0.05 94.7.987 0.152.124.636.8370'1 80.34 0.050.08 94.1.981.031 124.7 1.334.099.661.8699 80.36.00071.23.35 92.5.965.085 13.8 1.635.074.686.9028 80.37.0139.57 1.15 1 90.0.939.28 18.1 1 1.25.o49.711. 9357 81.53.0423 1.51 2.20 84.6.883.73 17.0 2.80.034.726.9554 82.71.0843 3.15 3.02 77.0.803 1.16 12.3 4.70.024.736.9686 84.18.137 5.05 3.14 69.8.727 1.46 9.18 1 6.6.019.741.9752 85.16.172 1 6.35 3.12 65.2.680 1.60 7.75 7.90.014.746.9817 86.30.212 8.65 3'.06 60.0..626 1.72 5.73 9.80.011.749.9857 87.62.259 11.0 2.94 56.o.584 1.80 4.44 12.8.oog.751.9883 88.33.284 12.8 2.88 51.7.539 1.84 3.69 17.4.00oo8.752.9896 88.80.-301 13.8 2.83 50.1.523 1.86 3.36 19.8.007.753.9909 89.30.319 15.1 2.70 46.0o.479 1.87 1 2.96 22.6.00oo6.754.9923 89.95.342 18.5 2.50 43.7.456 1.89 2.18 27.0.005 1.755.9936 90.71.369 23.0 2.36 41.0.427 1.90 1 1.50 30.4.~~~~~~~~~~~~~~ 1 I s I l l l l l l I~~~~

TABLE II. (Cont.) Run 16 ub = 86.8 ft/sec Bellmouth Entrance.00620 tb = 85.40~F Heated L/D = 1.75 to = 84.89OF P =.073 lb/cu ft Re = 64,200 tw = 111.41OF k/pC =.000246 sq ft/sec y r r t a aU I U I aU I - a:r lo2F 10 i r in. - in. F a sa ft/sec av a.757 -.003.00395 84.89 0 0 0 95.3 1.00 0 0.549.211.2777 84.86 0'0o 0 95.3 1.00 0 0.349.411.5409 84.87 0 O 0 95.3 1.00 0 0.249.511.6725 84.88 o o 0451 95.3 1.00.014 0.199.561.7383 84.88 0 0.11 94.5.992.047 0.174.5836.7712 84.89 0._013. 18 94.3.990.082 287.032.149.611.8041 84.95.00226.052.335 93.5.986-. 150 125.194.129.631.8304 84.97.00302.133.60 93.1.978.242 75.8. 321.109.651. 8567 85.12.o00867.285. 95 92.2.968.410 57.4.525.o89.671.8830 85.40.0192. 565 1.33 90.2.947.665 45.3. 895. 079.681. 8962 1 85.64..0283.765 1.57 1 88.7.932. 830 41.0 1 1.18.069.691.9094 85.95 0400. 858 1.80 87.4.918 1 ol01 40.2 1.54.059.701.9225 86.32.0539 1.26 2.04 85.7.900 1.22 35.2 2.00.049.711 9357 86.85.0739 1.62 2.28 82.3.864 1.46 32.2 2.70.039. 721. 9488 87.44 0962 2.20 2.46 77.6. 815 1.70 27.0 3.70.029.731.9620 88.50.136 3.25 2.52 72.8.764 1.94 20.2 5.30.024.736.9686 89.13.160 4.35 2,51 69.0.725 2.06 15.5 6.15.019.741 9752 90.16.195 5.85 2.44 64.8.680 2.-16 11.6 8.25.014.746.9817 91.18.239;7.80 2,30 57.8.606 2.27 8.61 11.4.011.749.9857 92.16.274 09.50 2.18 53.0.557 2.32 7.0 o6 14.6.009.751.9883 92.79.298 11.2 2.08 49.0.515 2.36 5.86 18.6.007.753. 9909 93.66 331 13.7 1.84 44.0.462 2.39 4.61 23.0.00oo6.754. 9923 94.16 *.349 16.6 1.72 41.0.430 2.40 3o58 28.0.005.755.9936 95.03.382 24.7 1.64 36.6.384 2.40 1.94 39.2

TABLE II. (Cont.) Ruln 17 Ub = 87.0 ft/sec Bellmouth Entranceb = 00619 b.87 F Heated L/D = 4.12 t = 81.28 ~F P =.0739 lb/cu ft Re = 65,3QO. tw = 112.65 OF k/PCp =.000241 sq ft/see y I' I r r t e 6e u U 6 - r ar 10 10- t in.'in. O__ Fak t /s fta/sec.7595.0005.ooo66 81.22 0 0.0 92.9 1.00 0 0 0.6775.0825.01086 81.22' 0 0 0 92.9 1.00 0 0 0.5775.1825.2402 81.22 0 0 0 92.9 1.'00 0 0 0.4775.2825.3718 81.28 0.003.024 92.9 1.00 0 0 o 0.4275..3325.4376 81.31.0009og6.oc5.o0 60 92.9 1.00.00oo8 139.00oo5.3775.3825.5034 81.32.00128.017.12 92.9 1.00..039 157.035.3275.4325.5692 81.34.00191.036.21 92.9 1.00.095 160.082.2775.4825.6350 81.51.00734.074.34 92.9 1.00.202 148.149 l.2525.5075.6679 81.60 1.0102.107.43 91.1.9811.285 137.181 l l.2275.5325.7008 81.73.0143.156.55 90.5. 974.390 122.225.2025.5575.7337 81.92.0204. 239.74 89.7.965.550 107.275.1775.5825.7666 82.23.0303. 350 1.01 88.8.956.745 94.7.336.1525.6095.8021 82.72.0459.490 1.40I 87.6.943 1.06 91.6.445.1275;.6325.8324 83.35 o.0660.640 1.68 86.1.927 1.40 89.6.625.1025.65575..8653 84.01.0871.860 1.86 83.0.893 1.87 85.4.970.0775.6825.8982 85.02.119 1.25 1.90 79.6.856 2.34 70.5 1.40.0575.7025.9245 86.32.161 1.69 1.85'75.7.814 2.69 57.2 1.75.0275.7325.9640 88.85.241 2.99 1.65 -66.9.720 3.24 36.9 4.30.0225.7375.9706 -89.54.263 3.62 1.59 63.7.685 3.31 30.4 6.10.0175.7425.9771 90.36.290 4.85 1.52 60.7.653 3.38 22.6 9.35.0125.7475.9837- 91.68.332 7.70 1.43 52.7.567 3.42 13.7 14.6.0075.7525.9903 93.76.398 14.1 1.30 41.6.448 3.47 6.84 25.4.0065.7535.9916 94.42.419 16.1 1.28 38.2.411 3.47 5.88 31.2.0055.7545.9929 95.13.442 18.0 1.24 34.0.366 3.48. /5.07 35.8.0045.7555 1.9942 95.89.466 18.8 11.21 30.8.331 3.48 4.83.0035.7565.9956 96.20.476 1.14 26.9.290 3.49

TABLE II. (Cont.) Run 18 Ub = 87.7 ft/sec Bell-mouth Entrance ) = 9 tb = 84.90bF Heated L/D = 9.97 t = 81.320F p =.0738 lb/cu ft Re = 65,350 ktw = 106.99~F k/pC.000242 sq ft/sec r I I r t _8 u E 6..03TZr iU 10,D c -.. a | Ua in. in. OFa ft/sec a.732;.028.0368 81.45.00506.0075 1.8 99.8 -1.00.0024 341.001.632.128.1684 81.65.0129.043 2.39 100. 0 1. 00.0325 62.5.018.532.228.3000 81.89.0222.101 3.28 99.6.998.12 146.042.432.328.4316 82.30.0382.178 4.45 98.2.984.31 149.0o95.382.378.4974 82.66.0522.227 5.12 97.6.978.45 147..15.332.428.5632 83.10.0o693.285 5.71 96.6.968.63 144. -.235.282.478.6290 83.63.0900.368 6.24 94.3.945.85 135.330.232.528.6948 84.36.118.477 6.71 92.0. 922 1.12 124,.445.182.578.7606 85.26.154.615 7.15 88.7.889 1.42 11 1.600.157.603.7935 85.86.177.703 7.30 86.8.869 1.60 104.690.132.628.8264 86.46.200.810.7.51 84.8.850 1.76 94.9.805.107.653.8593 87.25.231.940 7.68 81.9.821 1.94 86.8.945, 082.678.8922 88.05.262 1.14 7.81 79.0.792 2.11 74.4 1.15.062.698.9186 88.90.295 1.34 7.92 75.5.757 2.26 65.6 1.38.047.713.9383 89.62.323 1.60 7.97 72.9.730 2.37 55.8 1.85.032.728.9580 90.64. 363 2.08 7.95 68.2.683 2.47 43.4 3.03,.027.733.9646 91.05. 379 2.49 7. 90 66.3.664 2.50 36.2 3.80.022.738.9712 91.46. 395 3.19 7.80 63.4.635 2.54 28.1 5.00.017.743.9778 92.16.422 4.45 7-55 60.7.608 2.56 19.9 7.30.012.748.9844 93.05.457 7.30~ 7.24 54.5.546 2.59 11.6 13.8.010. 750.9870 93.68.482 9.80 7.00 49.4.495 2.60 8. 33 18.6.008.752.9896 94.45.512 13.05 6. 80 43.7.438 2.61 5.80 24.2.007.753.9909 95.01.533 14.7 6.55 40.8.409 2.61 5. o6 26..00oo6. 754.9923 95.47 *551 16.6 6.35 37.2.373 2.62 4.33.31.4.005.755 * 9936 96.04.573 18.5 6.20 32.9.330 2.62 3.74 35.5.004.756.9949 96.45.589 0035.7565.9956 196.65.597

-126TABLE III. MOMENTUM TERMS IN THE ENTRANCE REGION r r 4 4u 4 u 4 g0 6 r -10 rv v a 0o1 r u x dr 10 p 2 o a rr -v u in. ft2/sec ft2/sec ft /sec ft/sec ft/sec.76 1.66 5.26 0 0.74 1.65 2.68 5.12.0081 5.72.72 1.52 3.06 5.17.019 11.5.69 1.59 8.48 9.27.057 17.7.66 1.61 30.5 23.5.074 20,.6.64 1.72 65.3 49.7.079 21.3.62 1.53 128 93.7.079 21.7.60 i.18 241 174.078, 21.9.58.98 179 408.075 22.0.40.049 22.0.20.017 22.0 Bellmo,uth Entrance X/D = 1.5 Re = 15,000

-127112 108' I 1 1 104 I00 LL 996 1.5 1.7 1.9 2.1 2.3 2.5 27 EMF, MILLIVOLTS 92 e 8, 1.5 1.7 1.9 2.! 2.3 2.5 2.7 EMF, MILLIVOLTS Figure 35. Calibration for Chromel-Constantan Thermocouples

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