ENGINEERING RESEARCH INSTITUTE THE UNIVERSITY OF MICHIGAN ANN ARBOR INVESTIGATION OF THE PERFORMANCE OF VANE-TYPE ANEMOMETERS IN A FOUR-INCH DUCT Report No. 57 Edwin H. Young Assistant Professor of Chemical Engineering Dennis J. Ward Marvin L. Katz Clifford T. Terry Research Assistants Project 1592 WOLVERINE TUBE DIVISION CALUMET AND HECLA, INC. DETROIT, MICHIGAN November 1955

ENGINEERING RESEARCH INSTITUTE * UNIVERSITY OF MICHIGAN - TABLE OF CONTENTS Page ABSTRACT iii INTRODUCTION1 DESCRIPTION OF ANEMOMETER1 APPARATUS AND PROCEDURE1 DISCUSSION OF TEST PRINCIPLES 6 A. CRITICAL-FLOW ORIFICE THEORY 6 B. ROTAMETER THEORY 8 EXAMPLE CALCULATIONS 9 A. COMPUTATION OF AIR FLOW FROM FLOW PROVER 10 B. AIR VELOCITY AS MEASURED BY THE ANEMOMETER 10 C. CHECK BY ROTAMETER 11 DISCUSSION OF RESULTS 11 RECOMMENDATIONS 13 ii

ENGINEERING RESEARCH INSTITUTE * UNIVERSITY OF MICHIGAN INTRODUCTION The Biram's type vane anemometer has been widely used for measuring air velocities in finned-tube heat transfer investigations. As a result of inconsistencies in the heat transfer data obtained by the use of this instrument, an investigation of the influence of the duct diameter on the performance of the instrument was undertaken. The instrument is sensitive to fluctuations in air velocity and appears to give excellent reproducibility. It averages out the variations in flow during a test run and is very simple to operate. The instrument is ideally suited for accurate velocity measurements, provided the influence of the duct diameter is known. DESCRIPTION OF ANEMOMETER The Biram's type anemometers under consideration were manufactured by the Taylor Instrument Co., Rochester, N. Y. Figure 1 shows one of the anemometers tested and the orifices used in the critical-flow prover, The unit is identified by the manufacturer as the "No. 3132 Taylor Anemometer," It has a four-inch-diameter frame with three dials reading to 10,000 feet. The movement has jeweled bearings, a disconnector, and an automatic zerosetting attachment. The instrument is delivered with calibration corrections obtained in wind-tunnel testing by the Taylor Instrument Co. The calibrations are obtained by comparative tests with standard instruments certified by the National Physical Laboratory (England) and the Bureau of Standards. The instrument is designed for use with air speeds from 200 to 3000 ft/min. APPARATUS AND PROCEDURE A Pierce critical-flow orifice prover, manufactured by the American Meter Co., Inc., was used to measure the actual quantity of air flow J I 1

ENGINEERING RESEARCH INSTITUTE * UNIVERSITY OF MICHIGAN INTRODUCTION The Biram's type vane anemometer has been widely used for measuring air velocities in finned-tube heat transfer investigations. As a result of inconsistencies in the heat transfer data obtained by the use of this instrument, an investigation of the influence of the duct diameter on the performance of the instrument was undertaken. The instrument is sensitive to fluctuations in air velocity and appears to give excellent reproducibility. It averages out the variations in flow during a test run and is very simple to operate. The instrument is ideally suited for accurate velocity measurements, provided the influence of the duct diameter is known, DESCRIPTION OF ANEMOMETER The Biram's type anemometers under consideration were manufactured by the Taylor Instrument Co., Rochester, N. Y. Figure 1 shows one of the anemometers tested and the orifices used in the critical-flow prover. The unit is identified by the manufacturer as the "No. 3132 Taylor Anemometer." It has a four-inch-diameter frame with three dials reading to 10,000 feet. The movement has jeweled bearings, a disconnector, and an automatic zerosetting attachment. The instrument is delivered with calibration corrections obtained in wind-tunnel testing by the Taylor Instrument Co. The calibrations are obtained by comparative tests with standard instruments certified by the National Physical Laboratory (England) and the Bureau of Standards. The instrument is designed for use with air speeds from 200 to 3000 ft/min. APPARATUS AND PROCEDURE A Pierce critical-flow orifice prover, manufactured by the American Meter Co., Inc., was used to measure the actual quantity of air flow - 1

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ENGINEERING RESEARCH INSTITUTE * UNIVERSITY OF MICHIGAN ing through a rotameter, a four-inch-diameter duct and then through the four-inch anemometer, discharging to the atmosphere. Figure 2 presents a schematic diagram of the test arrangement. A gas rotameter was placed between the critical-flow prover and the anemometer for a second check on the volumetric throughput. The rotameter had previously been calibrated with water. This calibration is given in Table IV and graphically in Fig. 4. Air pressures and temperatures were measured upstream from the orifice by means of a mercury-in-glass thermometer and a calibrated pressure gage. The Sargent ID6489 thermometer was previously calibrated against Bureau of Standards certified thermometers and the pressure gage was calibrated against a Meriam one-hundred-inch mercury column. These calibrations are given in Tables V and VI, respectively. A typical experimental run was made in the following manner, referring to Fig. 2: 1. The air-line control valve was opened until the pressure gauge read higher than 15 psig (see page 8). The barometric pressure was recorded. 2. The system was allowed to reach a steady-state operating condition as indicated by constant inlet air temperature and pressure. 3. The air anemometer and stop watch were started simultaneously. 4. During the run, several readings of the rotameter, air temperature, and air pressure were taken and recorded. 5. The anemometer and stop watch were stopped simultaneously, completing the test run, and the data were recorded. Table I presents a typical laboratory test run. 3

- ENGINEERING RESEARCH INSTITUTE * UNIVERSITY OF MICHIGAN FIGURE 2 _ ir oRITIAI L-FLOW PROVER - TEST APPARATUS (SCHEMATIC) _VWI I. I #- %.,. _v. __. _ a W - DUCT AIR LINE - CONTROL VALVE - ROTAMETER ORIFICE PLAT'E MERCURY- INGLASS THERMOMETER PRESSURE > GAUGE 4

- ENGINEERING RESEARCH INSTITUTE UNIVERSITY OF MICHIGAN - TABLE I TYPICAL EXPERIMENTAL DATA RUN NO. 10 Taylor Anemometer No. A413. Barometric Pressure = 739 mm Hg. Duct Size = Four Inches, ID. Rotameter No. D8-1638. Critical-Flow Prover Orifice = 3/8 in. Nominal. Orifice Constant = 2.115 sec/ft3. Pre s sure -Gage Reading psig Air Temperature ~C Rotameter Reading 22.4 32.9 34.4 22.5 32.9 34.4 22.5 32.85 34.4 22.5 32.80 34.4 22.5 32.80 34.4 Avg 22.48 32.85 34.4 ~~~~~3.8 3.4. Elapsed time of run Anemometer reading = 1 min, 31.5 sec. = 2000 ft. Table VII contains a summary of the experimental data. 5

ENGINEERING RESEARCH INSTITUTE * UNIVERSITY OF MICHIGAN DISCUSSION OF TEST PRINCIPLES A. CRITICAL-FLOW ORIFICE THEORY The throughput of a critical-flow orifice is based on the theory of "sonic flow." When the pressure drop across the orifice exceeds a certain critical value, sonic velocity is reached in the orifice throat. Under this condition, any further increase in upstream pressure does not increase the velocity of flow through the orifice. Therefore, the volumetric throughput through the orifice is constant. The mass throughput, (lb/hr), however, does increase with increase in air density. The air-time constants for the orifices used are tabulated in Table II. TABLE II AIR-TIME CONSTANTS FOR CRITICAL FLOW ORIFICES Nominal Orifice Diameter Air Time for One Cu Ft at 60~F in. sec 1/16 80.7 1/8 18.82 1/4 4.555 3/8 2.115 1/2 1.197 5/8 0.757 The "gas time" for a test with an orifice depends on the size of the orifice, the ratio of specific heats, the temperature, and the specific gravity of the gas. The correction factors as provided by the manufacturer, for air at temperatures other than 600F, are tabulated in Table III. To determine the air throughput from such an orifice, fundamental relationships are required. Gas-flow relationships for flow of gas at high velocities through orifices have been developed and are available in the literature.1 2'314 The derivations of the applicable theoretical re1 Brown, G. G., et al., Unit Operations. New York: John Wiley and Sons, Inc., 1950, pp. 198-205. 2Dodge, B. F., Chemical Engineering Thermodynamics. New York: McGraw-Hill Book Co., 1944, pp. 324-36. I 6

- ENGINEERING RESEARCH INSTITUTE * UNIVERSITY OF MICHIGAN TABLE III TEMPERATURE-COREECTION FACTORS Temperature ~F Correction Factor 80 82 84 86 88 90 92 94 96 98 100 o.981 0.979 0.978 0.976 0.974 0.972 0.971 0.969 0.967 0.965 0.964 lationships therefore will not be presented here. A summary of the applicable relationships with restrictions will be given. The following discussion follows the development of Brown (see footnote 1). For maximum mass velocity, the critical pressure ratio is determined by Pc k 2 kll where: PC = the upstream pressure, psi Po = the downstream pressure, psi k = the ratio of Cp to Cv Cp = specific heat at constant pressure Cv = specific heat at constant volume. 3 Perry, J. H., Chemical Engineers' Handbook, 3rd ed. New York: Book Co., 1950, pp. 402-3. McGraw-Hill 4 Marks, L. S., Mechanical Engineers' Handbook, 4th ed. New York: McGrawHill Book Co., 1941, pp. 354-5. 7

ENGINEERING RESEARCH INSTITUTE * UNIVERSITY OF MICHIGAN For air k = 1.403 at 17~C. Therefore, 1.403 PO 2 0.)403 (0.832)3481 Po " = 0,527. PC Therefore, if the discharge pressure is one atmosphere (14.7 psia). then the upstream pressure necessary to establish critical flow is: pc= P. 7 14.7 = 279 psia c=.527 =0.527 If the atmospheric pressure is 14.7, then Pc = 27.9 - 14.7 = 13.2 psig. The velocity of the gas through the orifice under critical-flow conditions is given by the well-known equation for the velocity of sound in an ideal gas (see footnote;2): V(max) = g k P2 2 where V(max) = orifice velocity, ft/sec g = gravitational constant$ ft/sec2 k = ratio of specific heats P2 = upstream pressure, psfa v2 = specific volume of upstream gas, cu ft/lb. The acoustical velocity given by the above equation when critical flow is reached represents the maximum velocity at which the gas can flow through an orifice under the influence of pressure effects. This velocity is independent of the upstream pressure as long as the upstream-downstream pressure ratio exceeds the critical value. B. ROTAMETER THEORY The theory of gas and liquid flow measurement by means of rotameters is available in the literature.5 The relationship derived from the 5 Brown, G, G., et al o op. cit., pp. 161-2. - t 8

I - ENGINEERING RESEARCH INSTITUTE * UNIVERSITY OF MICHIGAN forces involved is: W = CrAo, 2g p(pf-p)Vf where W = mass rate of flow, lb/sec Cr = coefficient of discharge of the float Ao = area of flow, sq ft g = gravitational constant, ft/sec2 p = density of flowing fluid, lb/ft3 pf = density of float, lb/ft3 Vf = volume of float, ft3 Af = area of float, ft2. In the case of calibration of a rotameter for air by means of water throughput, the amount of air flowing at a given rotameter reading may be obtained from the corresponding water flow rate as follows: WU _ |Pw(Pf-Pw) Wa - Pa(Pf'Pa) where Ww = mass flow rate of water, lb/sec Wa = mass flow rate of air, lb/sec = density of water Pa = density of air pf = density of float. Since the density of air is infinitesimal in comparison with that of the float metal, the value of (Pf-Pa) is set equal to pf.. _Ww _ Pw(pf-Pw) Wa \ PaPf The above relationship permits conversion of a water calibration to an air calibration. EXAMPLE CALCULATIONS Example calculations of test run No. 10 are presented for the critical-flow orifices and for the rotameter. The data are presented in Table I, page 5. L 9

ENGINEERING RESEARCH INSTITUTE * UNIVERSITY OF MICHIGAN A. COMPUTATION OF AIR FLOW FROM FLOW PROVER Atmospheric pressure = 739 mm Hg = 14.29 psia Upstream absolute pressure = 14.29 + 22.49 = 36.78 psia Correction for pressure-gage calibration = -0.25 Air pressure = 36.53 psia Air temperature = 32.85~C = 94.17~F Temperature-correction factor (Table V) = 0.969 Orifice constant = 2.115 sec/ft3 Corrected orifice constant = (0.969)(2.115)= 2.050 Air density = ( 5 4927 64.7) = 0.1782 lb/cu ft w = (' 1 /(60) = 5.21 lb/min F16oFour-inch duct cross-sectional area = Mass flow rate in duct = 021 = 59,75 Air density in duct = 0.074 530 l14.7 Air velocity in duct = 5975 = 807 std 0.074 = 0,0872 ft2 lba/ft2/min = 0.0688 lb/ft3 ft/min B. AIR VELOCITY AS MEASURED BY TEE ANEMOMETER 2000 ft(60) -91.5 se = 1311 ft/min 91.5 sec Correction for density of air:6 Standard air density =. V = 1311. 0.07 0.074 V0 = VOPo 1p0 0. 074 lb/ft3 1265 std ft/min 6 Ower, E., Measurement of Airflow. London: Chapman and Hall, Ltd., 1927, pp. 118-9. 10

ENGINEERING RESEARCH INSTITUTE * UNIVERSITY OF MICHIGAN Taylor anemometer calibration correction = -17.. Corrected anemometer reading = 1248 ft/min Ratio of velocities = 84 = 54 807 Therefore. the anemometer is reading 54% high. C. CHECK BY ROTAMETER Rotameter reading = 34.4 Corresponding water flow = 8,700 lb/hr at 11~C PaPf Wair = Wwater /Pw(Pf' w) Pwater = 0.99963 x 62.4 - 62.4 lb/ft3 Pfloat = 7.8 x 62.4 = 486 lb/ft3 Pair = 0.0698 lb/ft3 Substituting: War = 8700'(o.o698)(486) 62.4(486-62.4) = 312 Ib/hr = 5.20 lb/min. air velocity = 0872(007 = 806 std ft/min as compared to 80'7 ft/min by the flow prover. Therefore, the anemometer is reading 54% high. DISCUSSION OF RESULTS A summary of the calculated results is given in Table VITI. These results are presented graphically in Fig. 3. Figure 5 indicates a linear relationship between the actual air velocity in the four-inch duct and the computed air velocity obtained from the anemometer reading. The slope of this line is: J L 11

VELOCITY FROM ROTAMETER AND CRITICAL-FLOW PROVER -It;. SFM ro IU 0.0 0 0 P O 0) a 0 0 0O 0 0 0 0 0 0 o o 0 O 0 0 I 0 1 o o o o o o 0) o o o o,.0 0 0, 0) 0 C)I C: C 1 C) I C) C) c: rm > C) D D:::o (l C)1 C:I C) ro o o o IN ro m 0 0 o o r 0 N 7) 0 0 ro O 0 o 0 (0 0 0 0 X 0 r I7 3~ 0 c 0 mCO C g1 -i 2 n > r — i 1 I r 1 3 m. m

ENGINEERING RESEARCH INSTITUTE * UNIVERSITY OF MICHIGAN True Air Velocity (SFM) Anemometer Air Velocity (SFM) This indicates that the actual air velocity is 66% of the anemometer indicated velocity. The anemometer is therefore indicating velocities which are 52% high. As indicated above, the true air velocity can be obtained by multiplying the anemometer air velocity by 0.66, RECOMMENDATIONS It is recommended that in all future air tests in which this model of anemometer is used with a four-inch duct the air velocities so indicated be reduced by 345% -I 13

----—,ooo —--- I- 12,000 -1 10,000 C17-. -',, J 8,000 HF-J ~ 6,000 ooo 0 Crl 400ooo0 FIGURE 4 I ____ ____CALIBRATION OF ROTAMETER NO. C17-94 WITH WATER 2,000 0 /~ 1 ~~WATER TEMPERATUREa IIC 0 4 8 12 16 20 24 28 32 36 40 44 4 82 ROTAMETER READING m z z m m z I1 C, Im 3, m z -- m I c:.< z

l - ENGINEERING RESEARCH INSTITUTE UNIVERSITY OF MICHIGAN - TABLE IV WATER CALIBRATION OF ROTAMETER NO. C17-94 Rotameter Water Lb of Elapsed Time Lb/Hr Reading Temp Water Time Lb/Hr oC min sec 10.0 11 100 2 33.3 2350 20.2 11 200 2 24.2 4990 30.0 11 300 2 25.6 7420 39.7 11 300 1 49. 9910 39.8 11 300 1 46.9 10,110 49.0 11 300 1 25.8 12,590 49.9 11 300 1 25.2 12,690 J 15

- ENGINEERING RESEARCH INSTITUTE * UNIVERSITY OF MICHIGAN - TABLE: V CALIBRATION OF SARGENT 1D6489 MERCURY-IN-GLASS THERMOMETER FOR USE IN CRITICAL-FLOW ORIFICE PROVER I Thermometer Reading Correction to be Added oC ~C 0.5 -.10 5 -.15 10 -.10 15.10 20 -.10 25 -.10 50 0 35 o 40 -.05 45 -.10 50 -.20 55 -.25 60 -.20 65-.15 70 -.20 75 -.20 80.55 85 -.40 90o -.45 95 -.55 l 16

I - ENGINEERING RESEARCH INSTITUTE * UNIVERSITY OF MICHIGAN TABLE VI CALIBRATION OF PRESSURE GAUGE C2-347 WITH MERIAM ONE-HUNDRED-INCH MERCURY COLUMN AS A STANDARD L C2-347 Meriam Column Correction to Observed Pressure Inches of Hg be Added psig psig 3.5 6.60 -.27 6.3 12.20 -.33 10.3 20.34 -.35 15.0 29.62 -.52 20.0 39.90 -.49 24.0 48.56 -.25 30.0 60.61 -.56 35.0 70.90 -.23 40.0 80.98 -.40 45.0o90.51 -.74 49.55 100.52 -.40 J

- ENGINEERING RESEARCH INSTITUTE * UNIVER TABLE VII SUMMARY OF EXPERIMENTAL DATA SITY OF MICHIGAN L Observed Observed Run Upstream Air Tem- Barometric Orifice No. Pressure perature Pressure Constant psig ~C mm Hg sec/ft3 Reading Reading ft 1 29.66 2 61.00 3 82.00 4 82.00 5 21.54 6 19.15 7 39.63 8 60.40 9 21.97 10 22.48 11 29.26 12 38.37 13 24.50 14 23.82 15 22.52 16 20.93 17 36.52 18 21.00 19 19.81 20 22.56 21 38.21 22 49.22 23 70.94 24 20.88 25 21.99 26 38.33 27 38.90 28 21-73 29 24.26 30 42.86 33.70 34.02 34.19 34.11 33.49 33.00 33.30 33.49 33.00 32.85 33.56 32.57 33.20 33.33 34.15 31.22 31.33 32.08 32.93 33.55 33.21 33.22 33.27 33.24 33.56 32.90 32.94 32.96 33.13 33.58 737 737 737 737 737 739 739 739 739 739 739 739 739 739 739 740 740 740 740 740 740 740 740 741 5 741.5 741.5 741.5 741.5 741.5 741.5 18.82 18.82 18.82 18.82 4.535 4.535 4.535 4.535 2.115 2.115 2.115 2.115 1.198 1.198 2.115 2.115 2.115 1.197 1.197 1.197 4.535 4.535 4.539 2.115 2.115 2.115 2.115 4.535 4.535 4.535 14.40 22.64 31.38 33.95 34.40 40.12 48.70 61.94 60.96 34.17 32.38 46.38 56.85 54.58 58.7 22.8 26.39 35.29 300 500 600 60o 1000 800 1200 2000 2100 2000 2200 3000 5000 4000 2200 2000 3000 3400 5000 5500 1500 2400 3000 103.8 97.4 91.8 92.8 103.2 89.6 85.7 100.6 97.1 91.5 85.3 95.9 123.8 101.4 103 99.6 100 91.4 139.2 140.8 106.6 142.2 131.8 100.8 98.4 101.4 100.4 105.6 100.6 133.6 A413 A413 A413 A413 A413 A413 A413 A413 A413 6759 6759 6759 6759 6759 6759 6759 6759 6759 A413 A413 A413 A413 A413 A413 A413 A413 A413 A413 A413 A413 J 2000 2000 3000 3000 1000 1000 2000 18

\ 7- ENGINEERING RESEARCH INSTITUTE * UNIVERSITY OF MICHIGAN - I TABLE VIII SUMMARY OF CALCULATED RESULTS Velocity from Velocity from Velocity from Run Anemometer Critical-Flow Prover Rotameter No. SFM SFM 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 184 315 315 392 578 534 819 1143 1240 1250 1465 1759 2202 2186 1190 1128 1660 2061 1988 2144 803 944 1269 1140 1166 1667 1682 567 593 874 111 191 191 244 361 336 536 762 791 807 949 1140 1497 1471 800 767 114o 1327 1341 1400 536 669 873 764 787 1147 1159 365 392 578 339 533 739 801 806 947 1150 1458 1433 8o5 768 1100 1378 1323 1388 539 623 834 J1 19