The flow of air through circular orifices with rounded

HIL L I N 0 I SUNIVERSITY OF ILLINOIS AT URBANA-CHAMPAIGN

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THE FLOWORIFICES

OF AIR THROUGH CIRCULARWITH ROUNDED APPROACH

BY

JOSEPH A. POLSONJOSEPH G. LOWTHER

AND

BENJAMIN J. WILSON

BULLETIN No. 207

ENGINEERING EXPERIMENT STATION

PoUsLSHED sT TH UmvOasrITY 0F ILLINOIS, URaBAa

Pas: THIsTY CENTs

p-', --'.': } * ' T , *';' ' . , - / , ' , \ ^ ̂ * . ''7 '

SHE Engineering Experiment Station was established by act

of the Board of Trustees of the University of Illinois on De-cember 8, 1903. It is the purpose of the Station to conduct

investigations and make studies of importance to the engineering,

manufacturing, railway, mining, and other industrial interests of the

State.

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in an Executive Staff composed of the Director and his Assistant, the

Heads of the several Departments in the College of Engineering, and

the Professor of Industrial Chemistry. This Staff is responsible for

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including the approval of material for publication. All members of

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research, either directly or in cooperation with the Research Corps

composed of full-time research assistants, research graduate assistants,

and special investigators.

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the public, the Engineering Experiment Station publishes and dis-

tributes a series of bulletins. Occasionally it publishes circulars of

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The volume and number at the top of the front cover page are

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For copies of bulletins or circulars or for other information address

THE ENGINEERING EXPERIMENT STATION,

UNIVERSITY OF ILLINOIS,

UB3ANA, ILLINOIS

UNIVERSITY OF ILLINOISENGINEERING EXPERIMENT STATION

BULLETIN No. 207 MAY, 1930

THE FLOW OF AIR THROUGH CIRCULARORIFICES WITH ROUNDED APPROACH

BY

JOSEPH A. POLSONPROFESSOR OF STEAM ENGINEERING

JOSEPH G. LOWTHERRESEARCH ASSISTANT IN MECHANICAL ENGINEERING

BENJAMIN J. WILSONRESEARCH GRADUATE ASSISTANT IN MECHANICAL ENGINEERING

ENGINEERING EXPERIMENT STATIONPUBLISHED BY THE UNIVERSITY OF ILLINOIS, URBANA

UNIVE RSIT

6000 2 $0 7764 : & 0ss

TABLE OF CONTENTS

I. INTRODUCTION. .

1. Purpose . . . . . .2. Scope . . . . . . .3. Acknowledgments .

II. RELATIONS BETWEEN PRESSURE,

WEIGHT OF AIR DISCHARGED

4. Adiabatic Flow5. Fliegner's Formula .

PAGE

5555

TEMPERATURE, AND

III. TEST APPARATUS . . . . . . . . . . .

6. General Description. . . . . . . . .7. Air Weighing Tank and Scale . . . . . .8. Orifice Tank, Manometer, and Thermometers .9. Orifices

IV. METHOD OF CONDUCTING TESTS . . . . . . .

10. Leakage . . . . . . . . . . .11. Method of Weighing; Use of Substitute Weights

V. CALCULATIONS.

12. Corrections . .13. Standard Conditions14. Coefficients . .15. Sample Calculations

VI. DISCUSSION OF RESULTS .

16. Accuracy of Results.

VII. CONCLUSIONS . . . . .17. Summary of Conclusions

APPENDIX . . . . . .

Bibliography .

LIST OF FIGURESNO. PAGE

1. Weighing Tank and Compressor. . . . .. . . . . . . . 92. Copper Tubing Connectors ... . . . . . . . . . . 103. Diagram of Air Weighing Tank and Connections to Orifice Tank. . . 114. Orifice Tank, Control Valves, and Manometer . . . . . . . . 125. Dimensions of Orifices . . . . . .. . . . . . . . . 146. Leakage Curves for Weighing Tank. . . . . . . . . . . . 157. Leakage Curves for Orifice Tank .... . . . . . . . 168. Correction Curve for Pressure Drop in Discharge Line . . . . . . 189. Air Discharge Curves for Various Orifices Using Water Manometer . . 20

10. Air Discharge Curves for Various Orifices Using Mercury Manometer. . 2111. Coefficient Curves for Various Orifices Using Water Manometer . . . 2212. Coefficient Curves for Various Orifices Using Mercury Manometer. . . 23

LIST OF TABLES

1. Test Results of a M-in. Orifice, Using Water Manometer . . . . . 272. Test Results of a Y%-in. Orifice, Using Water Manometer . . . . . 283. Test Results of a Y-in. Orifice, Using Water Manometer . . . . . 294. Test Results of a %-in. Orifice, Using Water Manometer . . . . . 305. Test Results of a Y4 -in. Orifice, Using Water Manometer . . . . . 316. Test Results of a Y7 -in. Orifice, Using Water Manometer . . . . . 327. Test Results of a 1-in. Orifice, Using Water Manometer. . . ... . 338. Test Results of a M-in. Orifice, Using Mercury Manometer . . .. . 349. Test Results of a %-in. Orifice, Using Mercury Manometer . . .. . 35

10. Test Results of a 1 -in. Orifice, Using Mercury Manometer . . .. 3611. Test Results of a %s-in. Orifice, Using Mercury Manometer . . .. 3712. Test Results of a 4-in. Orifice, Using Mercury Manometer. . . . . 3813. Test Results of a i/-in. Orifice, Using Mercury Manometer. . . .. . 3914. Test Results of a 1-in. Orifice, Using Mercury Manometer . . . . . 4015. Mean Discharge of Air in Pounds per Minute per Square Inch of Orifice . 4116. Mean Discharge of Air in Pounds per Minute per Square Inch of Orifice . 4117. Coefficients of Discharge for Various Inlet Pressures and Diameters of

Orifices . . . . .. . . . . . . . . . . .. . 4218. Coefficients of Discharge for Various Inlet Pressures and Diameters of

Orifices .......... . . . . . . . 42

THE FLOW OF AIR THROUGH CIRCULAR ORIFICES WITHROUNDED APPROACH DISCHARGING INTO

THE ATMOSPHERE

I. INTRODUCTION

1. Purpose.-The purpose of this investigation was to make astudy of the flow of air through orifices by a precision method, and todetermine coefficients to be applied to Fliegner's formula for the flowof air. Briefly, the method consisted of weighing the air dischargedper unit of time while maintaining control of pressure on the inlet sideof the orifice. This method will be referred to as the "weighing tankmethod," and has been previously described in Bulletin No. 120.*

2. Scope.-In this investigation(1) Ordinary atmospheric air was compressed and stored in the

weighing tank with no particular attempt to remove the moisture orcontrol the humidity.

(2) The pressures on the inlet side of the orifices were varied from1 in. of water to 35 in. of mercury.

(3) No attempt was made to hold the temperature constant; itvaried slightly from room temperature.

(4) Only one type of orifice was used, namely, a circular orificewith rounded approach; the diameters of the smallest sections variedfrom Y4 in. to 1 in.

(5) Duplicate orifices were tested to determine the accuracy ofduplication.

3. Acknowledgments.-This investigation was made under the aus-pices of the Engineering Experiment Station of the University of Illi-nois, of which DEAN M. S. KETCHUM is the Director. The work wascarried out as one of the investigations of the Department of Mechan-ical Engineering, of which PROF. A. C. WILLARD is the head. G. A.GOODENOUGH, Professor of Thermodynamics, and A. P. KRATZ, Re-search Professor in Mechanical Engineering, gave valuable advice andsuggestions. Valuable assistance and helpful suggestions were alsogiven by C. G. BRADLEY, laboratory mechanician.

*"Investigation of Warm Air Furnaces and Heating Systems," Univ. of Ill. Eng. Exp. Sta. Bul.120, 1921.

ILLINOIS ENGINEERING EXPERIMENT STATION

II. RELATIONS BETWEEN PRESSURE, TEMPERATURE, AND WEIGHTOF AIR DISCHARGED

4. Adiabatic Flow.-On the assumption that air is essentially aperfect gas under the conditions of entrance to the orifice and that theflow is adiabatic, the weight M, in lb. per min. discharged, is*

[ 2 k+1-I

M= 60a 2gk P[ P (P k(1)k -_1 V, IP,] P,

in which

a = area of smallest section of throat of orifice, sq. in.g = acceleration of gravity, 32.2 ft. per sec. per sec.k = ratio of specific heat at constant pressure to specific heat at

constant volume, 1.4.Pi = absolute pressure of air on entrance side of orifice, lb. per

sq. in.Vi = specific volume of air on entrance side of orifice, cu. ft. per lb.Ti = absolute temperature of air on entrance side of orifice,

deg. F.P = absolute pressure of air in throat of orifice, lb. per sq. in.

This expression may be reduced to simpler terms by substitutingthe constant values of g = 32.2; k = 1.4.

Pi _ P 12

V, BT,

where B has the value 53.34.

F 10 121

M = 123.36 ( n -T( 1) j (2)(Tl )t P \pj.

The weight of air flowing through an orifice depends on the pres-sure P in the throat of the orifice; if the orifice ends at the throat sec-tion, the pressure in the throat and the pressure on the exit side of theorifice P2 are identical. For any given type of orifice the ratio of thepressure P in the throat to the pressure on the inlet side Pi, remainsconstant as long as the pressure on the exit side P 2 is equal to or less

*G. A. Goodenough, "Principles of Thermodynamics."

FLOW OF AIR THROUGH CIRCULAR ORIFICES

Pthan P, the pressure in the throat. The value of this ratio -Pis 0.53;

PIthat is, P = 0.53Pi as long as P 2 is equal to or less than 0.53P 1 .

For all cases where P 2 is greater than 0.53Pi, the pressure in thethroat P becomes equal to the pressure on the exit side P 2. The valueof P that is equal to 0.53P, is called the critical pressure.

Since all orifices discharged into the atmosphere where the pres-sure remained practically constant at 14.5 to 14.7 lb. per sq. in. abs.,it follows that for all pressures Pi less than 27 lb. per sq. in. abs., thethroat pressure P becomes equal to the atmospheric pressure P2 . By

Psubstituting the value 0.53 for the ratio - , Equation (2) will be re-

duced to

PiaM = 31.8 (Ti) (3)

which applies in all cases where P, is higher than 27 lb. abs. while dis-charging into the atmosphere.

5. Fliegner's Formula.*--Equation (3) is the same as Fliegner'sformula for the weight of air in pounds per minute when P 2 is belowthe critical pressure, or when P1 is more than 27 lb. per sq. in. abs.while discharging into the atmosphere.

Fliegner's formula for conditions such that P2 is above the criticalpressure, or where P1 is less than 27 lb. per sq. in. abs. when discharg-ing into the atmosphere, is

M = 63.6 (T 1) P2 (P 1 - P 2)]' (4)

where the symbols have the same meaning as before.

Srd'By substituting - for (a), where d is the throat diameter in

inches, Equation (3) becomes

24.98 d2 P1

M = (TI) (5)

where P1 is greater than 2P 2, and Equation (4) becomes

*See References 4 and 10 in Bibliography.


49.95d 2

M =- (T1)t 2 (P 1 - P2) (6)

where P1 is less than 2P 2 .It is conceivable that the critical ratio may not be 0.53 for various

shapes of orifices, and the question may arise as to what discrepancywill be introduced in such cases. As a basis for comparison* Equation(2) may be made to equal (4) by replacing the constant 63.6 by b,a coefficient, and determining its value for various pressure ratios.

S 10 12 baPia p2 \ 7 P_ -2 P ba 2(P1 P

123.36 TL P [P, (P - P)][(P,) (TI)^[P

P2P- = 0.5 0.6 0.7 0.8 0.9P\

b = 63.66 64.38 64.86 65.28 65.58

This would indicate that Fliegner's formula (Equation 4) gives adischarge of from 1 to 3 per cent less than Equation (2). As will beseen by Tables 17 and 18, the results of the tests show that the co-efficients are smallest for small inlet pressures and increase as thepressure is increased. The coefficients also increase as the orifice di-ameter is increased. This is contrary to the deduction given above.

III. TEST APPARATUS

6. General Description.-The method of weighing the air dis-charged through orifices used in this series of tests was first developedand used for calibrating the air measuring instruments employed inthe Investigation of Warm Air Furnaces and Heating Systems,t asconducted by the Engineering Experiment Station of the Universityof Illinois. The weighing tank is charged with air by means of a two-stage compressor (Fig. 1). When the tank is charged to the requiredpressure, the valve B (Fig. 3) is closed and the pipe union A is discon-nected so that the tank is entirely free at this end. The air is dis-charged from the opposite end through a number of copper tubes, 2in. in diameter, as shown in Fig. 2. The tubes are approximately 16feet in length and have four right-angle bends to insure flexibility.

*G. A. Goodenough, "Principles of Thermodynamics."fSee Univ. of Ill. Eng. Exp. Sta. Bul. 120, Chap. VIII, p. 81.


FIG. 1 WEIGHING TANK AND COMPRESSOR

7. Air Weighing Tank and Scale.-The weighing tank (Fig. 3) is42 in. in diameter and 13 ft. long, and was designed for a workingpressure of 300 lb. per sq. in. At this pressure the tank will holdabout 200 lb. of air, by weight. The tank is supported on the scaleplatform so that the scale beams are perfectly free and unrestrained.It is slightly inclined toward one end so as to facilitate the removal ofmoisture through a drain valve. The pressure in the tank is indicatedon a pressure gage.

The scale is a four-ton, heavy-duty, built-in suspended platformtype. The lever ratio is 500 to 1, and, since the weighing beam movesless than 1 inch, the load platform moves less than 1/500 of an inch.Therefore, the change in resistance of the tubing at the discharge endof the tank is so small that it has no perceptible effect on the sensi-tivity of the scale.

The movement of the weighing beam was multiplied 91 times by abeam of light reflected by a mirror mounted on the weighing beamand focused on a graduated scale directly in front of the operatorwhen standing at the controlling valves.

The sensitivity of the scale was determined by the vibrationmethod:* (a) with the tank fully charged at 300 lb. per sq. in., and(b) with the tank empty. The procedure was as follows:

*"Method of Precision Test of Large Capacity Scales," Bureau of Standards Bulletin No. 199.


FIG. 2. COPPER TUBING CONNECTORS

An arbitrary reference line was placed on the blank scale near themid-point of the travel of the beam of light as the weighing beamwas moved from the bottom to the top of the trig loop or stop. Thescale with its load was then balanced so that the weighing beam wouldvibrate without striking the top or the bottom of the trig loop. Thedistance that the beam of light traveled from the arbitrary referenceline on two successive upward swings was measured and the two read-ings were averaged. The distance traveled by the beam of lightbelow the arbitrary reference line on the downward swing, which oc-curred between the two successive upward swings, was measured.This distance, a negative quantity, was added to the average of thetwo successive upward swings and the result divided by two. This


_

~

Nk ~.~ .~ ~

cz~


FIG. 4. ORIFICE TANK, CONTROL VALVES, AND MANOMETER

distance measured from the arbitrary reference line would be theposition of the beam of light when the weighing beam was at rest.The point of rest was determined several times and the mean posi-tion was used. Then, without in any way disturbing or changingthe counterpoises, a half-pound weight was placed on the scaleplatform and a new point of rest determined.

By dividing the difference in weights on the scale (one-half pound)by the distance between the first and second rest points, the "sensi-tivity reciprocal," or the weight in pounds that will cause the restpoint to change one inch, was determined.


It was thus found that 0.063 lb. added to the scale platform wouldchange the rest point one inch when the tank was empty, and 0.064lb. when the tank was fully charged. As a further test of the sensi-tivity, a weight of 0.2 lb. placed on the scale platform caused a de-flection of the beam of light of 3.15 in. This method of checking wasused at intervals to determine if the sensitivity had changed.

8. Orifice Tank, Manometer, and Thermometers.-The orifice tank(Fig. 4) is 6 ft. in length and 24 in. in diameter, and was designed for aworking pressure of 75 lb. per sq. in. It contains two baffles, one atthe entrance to break up the stream of the incoming air, and theother, a screen baffle at mid-section, to quiet eddy movements. Thegeneral arrangement of the orifice tank and controls is shown sche-matically in Fig. 3. The air was throttled through the manifold andinto the orifice tank at the desired pressure. This pressure was indi-cated on the manometer M and the temperature by the thermometerT. The manometer is of the single leg reservoir type, and is connect-ed at a point 7 inches from the end of the orifice tank in which theorifices are placed. The area of the reservoir basin is 4.91 sq. in. andthe area of the glass manometer tube about 0.078 sq. in., so that whenthe liquid in the manometer read one inch on the steel scale the actualdistance between liquid surfaces was 1.0159 in. This difference is ap-preciable, and the correction was made. The liquid level in the man-ometer was illumined by a small shaded electric light and the en-tire manometer was adjustable so that the liquid level could alwaysbe placed on a level with the eye of the operator.

All thermometers used were calibrated by comparison with astandard thermometer. A bare thermometer was used in the orificetank so that the bare mercury bulb was in direct contact with the air.It was placed 16 in. from the end of the tank. Leakage around thestem was prevented by the use of a packing gland. The effect of thepressure on the mercury bulb would tend to increase the temperaturereading. However, the effect is slight for low pressures. The cor-rection usually applied is 0.01 deg. F. per lb. per sq. in. of pressure.*Since the maximum pressure used was 35 in. of mercury, the correc-tion may be omitted.

9. Orifices.-All orifices used were geometrically similar and alldimensions are given in terms of the orifice diameter (see Fig. 5).The orifices were carefully machined to templets, and the throat di-ameter was measured to 0.0001 in. The insides of the orifices were

*"Mechanical Engineering," May, 1926, p. 520. 4

14 ILLINOIS ENGINEERING EXPERIMENT STATION

Approwlx/i',e Actual/ e,-/',1'/ ?/S ofD/'a/e7en-, , D/arete, 0, .4gOiraac,, 0,

/,,c/7es /7ches Alu/her /nIc/2es

O.Z498 .2498-Az f O0d .2500-A0.2504 .2504-A

0.3759 .3759-A0.3764 .3764-4 j03766 .3766-A

S05008 .5008-A 2

S e.6z34 .6384-A1 _

S0.7S07 .7507-A

S087763 .8763-A

/ /.023 /.023-A /

FIG. 5. DIMENSIONS OF ORIFICES

made smooth and even by filing, scraping, and the use of fine emerycloth. Precautions were taken to make the curvature as nearlycorrect as possible.

IV. METHOD OF CONDUCTING TESTS

10. Leakage.-It was necessary to know the rate of leakagethroughout the entire apparatus. This was determined in two steps:first, the leakage of the weighing tank and piping up to the controlvalves; and second, the leakage of the orifice tank and piping fromthe control valves.

Since leakage is proportional to pressure, it was necessary to deter-mine the leakage at a number of different pressures from 300 lb. to40 or 50 lb. per sq. in. The amount of air lost was determined di-rectly by weighing, as described later. Curves were plotted givingloss by leakage in pounds per minute against weighing tank pressures(see Fig. 6).

In a similar manner the leakage in the orifice tank was determined,but at pressures from 35 in. of mercury to 1 in. of water. The loss inweight on the scale was the loss from the high pressure part as well as


PIres1AKre UR/V? O. 5E 7 s /7? •A eFIG. 6. LEAKAGE CURVES FOR WEIGHING TANK

the low pressure part of the apparatus. By subtraction, the loss inthe orifice tank was determined separately. These results wereplotted as described for the high pressure leakage (see Fig. 7).

11. Method of Weighing;* Use of Substitute Weights.-The follow-ing procedure was used in determining the weight of air dischargedthrough an orifice during a test.

The weighing tank (see Fig. 3) was charged to a pressure of about300 lb. per sq. in. gage. Valve B was then closed and union A dis-connected so that the tank was entirely free at that end. The weigh-ing tank then rested freely on the scale except for the copper tubing atthe opposite end, which was connected to the orifice tank. A drainvalve at the bottom of the weighing tank was then opened for a shorttime to remove any moisture that might have collected. The weigh-ing beam on the scale was underbalanced so that it remained at thetop of the trig loop. The amount of underbalance (1 to 10 lb.) de-pended on the rate of flow and, consequently, the time required forsecuring the proper pressure in the orifice tank. As the scale beamapproached equilibrium the beam of light moved toward its mid-position giving a warning to the observers, who started their stopwatches as the beam of light passed its mid-position. The operator atthe control valves continued to regulate the pressure in the orifice

*"Weighing by Substitution," Bureau of Standards, Bulletin 430, Univ. of Ill. Eng. Exp. Sta.Bul. 120.


e. 7. L-e /GE /eCURVES oFR ORIFICE TANKec'FIG. 7. LEAKAGE CURVES FOR ORIFICE TANK

tank to keep the pressure at the required amount, thereby maintain-ing a steady rate of flow. Another operator then placed standardweights (2 to 100 lb.) on the scale platform without disturbing or inany way changing the counterpoise weights on the scale beam. Thisagain made the scale beam underbalanced by the amount of theweights put on the scale platform minus the weight of air discharged.When finally a weight of air had been discharged equal to the sub-stituted weights, the scale beam again approached equilibrium andthe beam of light started to move. As it crossed its mid-position theobservers stopped the stop watches and recorded the elapsed time.

By the use of this method errors or variations due to the "break"of the scale beam were avoided, since the scale beam was floatingfreely at its mid-position at the beginning and end of the observationperiod.

The total weight on the scale was the same at the beginning andthe end when the scale beam was falling or approaching mid-position.The beam of light had a full travel of more than 24 in. and hencemoved 12 in. before crossing its mid-position, thus giving amplewarning to the observers. The mid-position of the travel of the beamof light corresponded closely to the position of equilibrium of the scalebeam as determined by the tests for sensitivity, hence the scale beamwas very close to equilibrium at the beginning and the end with thesame total load on the scale. Since the rate of discharge was keptconstant during the observation period, the rate of movement of thebeam of light was the same at the beginning and end of the period.

Before starting these tests it was decided that no readings wouldbe used that showed a variation of more than 0.5 per cent from the


mean. All tests were duplicated and all elapsed time was checkedindependently by two observers with stop watches. The standardweights were checked and found to be correct within 50 grains in50 lb. It was found that the scales were affected by vibration causedby certain machines in the laboratory and by heavy trucks passing onthe street 75 feet away. It was necessary, therefore, to avoid testingduring the time these machines were running in the laboratory. Ifthe results were affected by a truck passing, it became necessary tore-run that particular test. For tests made on the 4 -in. and 8-in.orifices, at low pressures particularly, the discharge rate was so slowthat friction in the scales did not permit a clean "break" of the lightbeam nor a continuous movement of the beam. To avoid this diffi-culty, three orifices placed in parallel 8Y2 in. from center to centerwere used. A considerable number of runs were made at night whenless disturbance was encountered. No difficulty was experienced inmaintaining the required pressure in the orifice tank.

The cross hair on the manometer slide was set at the requiredpoint on the steel scale, and the adjustable light and the vertical heightof the manometer liquid were brought to the level of the eye of theobserver. For the higher pressures in the orifice tank mercury wasused as the manometer liquid. For lower pressures water was used,and for pressures less than 3 in. an inclined Ellison draft gage wasemployed. The total range of pressures was from 1 in. of water to35 in. of mercury. A thermometer was fastened to the manometercolumn to indicate the temperature of the manometer liquid. Theheight of the manometer liquid was indicated on a steel scale grad-uated to 0.01 in. The scale was adjustable, and could be set to zero atthe top of the liquid when the pressure tube was disconnected.

The manometer reading was not corrected to standard conditions.Since the highest room temperature observed during the tests was90 deg. F., the difference between this and standard conditions is only30 deg. F. Using this difference with the highest manometer readingand the smallest orifice, a maximum error of 0.15 per cent is obtained.The error for smaller manometer readings or for larger orifices will becorrespondingly less. Since the average room temperature was be-tween 80 and 85 deg. F., a still further reduction in the error occurredfor the majority of the tests. Loss due to leakage was corrected, sothat no error was introduced thereby. The accuracy of these resultsmay be affected by (1) variations in pressure of air in the orifice tank;(2) variations in temperature of air in the orifice tank; (3) variationsin observation of the time of flow. Since these variations were keptwithin one-half per cent it is considered that the results are correct to


0.70 - --- ---F - - ---- ----

0.60 - - - - - - - - - - -

I if - I I - t I - - I - I - t - I - [ - I ~I"i f - I - I -

I .: /-_ _ / _ _ _ _'\ 7--------^--------------

0460---- -

0jo

0.0 ----

00-- -

20 40 60 g80 /00 /120 /40 /60/Press&'re Dror i/7 lb ,ver sq. /?.

FIG. 8. CORRECTION CURVE FOR PRESSURE DROP IN DISCHARGE LINE

that extent, because tests were duplicated purposely many times,with the results agreeing within one-half per cent of the original re-sults. Duplicate 1

4-in., Ys-in., and Y4 -in. orifices were made, andtests show that results from these duplicate orifices check closely.

V. CALCULATIONS

12. Corrections.-In calculating the weight of air discharged twocorrections were made, for the leakage of air from the apparatus, andfor the error introduced by the pressure drop in the pipe line from theweighing tank to the control valves.

In all cases the loss by leakage was a small part of the air dis-charged. However, the loss for the mean pressure existing in theweighing tank and the orifice tank was subtracted from the totalweight discharged.

In correcting for the pressure drop a constant temperature of 75deg. F. was assumed for the air in the pipe line between the weighingtank and the control valves in the regulating manifold. The error inthis assumption is negligible, since the total pressure drop correction


is comparatively small. This correction was calculated by the perfectgas law and was added to the total weight discharged. Thus

VM - BT(PI - P 2) (see curve, Fig. 8)

where M = correction, pounds.V = volume of pipe line, 0.817 cu. ft.

Pi = initial pressure in weighing tank and pipe lines, lb. persq. in.

P 2 = final pressure in weighing tank and pipe lines, lb. persq. in.

T = temperature of air, assumed 535 deg. F. abs.B = gas constant for air, 53.34.

The velocity of approach was assumed negligible, since the great-est velocity through the orifice tank was 1.1 ft. per sec. This wouldgive no appreciable velocity head.

13. Standard Conditions.-The standard conditions adopted inthis work are: barometric pressure of 29.921 in. of mercury and tem-perature of 60 deg. F. The results were reduced to standard con-ditions as follows:

Writing Equation (4) for standard conditions

aM'= 63.6 T) [P2 ' (PI'- P2-)

in which M' = weight of air discharged into atmosphere under stand-ard conditions, lb. per min.

a = area of orifice, sq. in.Ti' = standard temperature of air entering orifice, that is,

60 deg. F. = 520 deg. F. abs.Pi' = pressure of air on inlet side of orifice, lb. per sq. in.

abs., referred to 29.921 in. of mercury.P2' = pressure of air on exit side of orifice, that is, standard

barometric pressure, lb. per sq. in. abs. (29.921in. of mercury).

For the actual test conditions, Equation (4) is

M= 63.6 T [P2 (PI - P 2)]'


I(J-

Q1

P-ressuire /,'c/,es of 4/a/'er

Fio. 9. AIR DISCHARGE CURVES FOR VARIOUS ORIFICES USING WATER MANOMETER

where T1 = observed temperature of air entering orifice, deg. F. abs.P1 = pressure of air on inlet side of orifice, lb. per sq. in. abs.

referred to barometric reading.P 2 = pressure of air on exit side of orifice, barometric reading

in lb. per sq. in.The ratio of the weight M' discharged under standard conditions

to the weight M discharged under test conditions is

M' (T)4 [P 2 ' (P' -P')

I.I (Tj1') Lr 2 ýr1 - t'2)j


Fla. 10. AIR DISCHARGE CURVES FOR VARIOUS ORIFICES USINGMERCURY MANOMETER

The pressure difference Pi - P2 = Pi' - P 2' is actually the same forboth conditions, since it is the manometer pressure, and Equation (9)will reduce to

LM ~ TP 2 jP (10)

M = TIPsI

M' = M T (11)

This correction applies to conditions where the pressure on the exitside of the orifice is more than the critical, or where the inlet pressure

Pr-es-s Z-e //2 /r-c1?es of"/07'c'-/-u-


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FIG. 11. COEFFICIENT CURVES FOR VARIOUS ORIFICES USING WATER MANOMETER

Pi is below 27 lb. per sq. in. abs. when discharging into the atmos-phere.

In a similar manner the correction may be made to apply toEquation (3) and becomes

1P' T1 2M' = M PLTJ

P, TI'(12)

This correction applies to conditions where the pressure on the exitside of the orifice is less than the critical, or where the inlet pressure Piis more than 27 lb. per sq. in. abs. while discharging into the atmos-phere.

The weight of air discharged has been converted into cubic feet onthe assumption that the air was dry.

14. Coefficients.-In this work the results of the tests have beencompared with Fliegner's formula, and coefficients determined asgiven in Tables 17 and 18 and curves in Figs. 11 and 12, for inletpressures from 1 in. of water to 35 in. of mercury. The relation is

M" = CM'

where M" = the weight of air in lb. per min. discharged through theorifice from the weighing tank, under standardconditions.

M' = the lb. of air per min. as computed by Fliegner's for-mula, under standard conditions.

C = the coefficient as determined by these tests.

ni

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0 4 s32 36

mr=X

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/ Orif/ce * ~' ~6½f~e.... 2 j

FLOW OF AIR THROUGH CIRCULAR ORIFICES 23

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y x 7 lflce A '/f O-//'e_I +d "° r̂/9 i î <PI

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FIG. 12. COEFFICIENT CURVES FOR VARIOUS ORIFICES USING MERCURY MANOMETER

For conditions where the pressure P 2 on the exit side of the orifice ismore than the critical (or the inlet pressure P1 is less than 27 lb. persq. in. abs. when discharging into the atmosphere) the weight of airdischarged is (from Equation 4)

M" = CM' = C X 63.6 --- [P 2 ' (Pi' - P 2')]i (13)

For conditions where the pressure P 2 on the exit side of the orifice isless than the critical (or where the inlet pressure P1 is more than 27lb. per sq. in. abs. when discharging into the atmosphere) the weightof air discharged is (from Equation 3)

P1 'aM" = CM' = C X 31.8 (T 1i') (14)

15. Sample Calculations.*-(a) Fliegner's formulas for standardconditions are:

aPl'M' = 31.8 (T)t (15)

and

M' = 63.6 - [[P 2' (Pi' - P 2 ')]i (16)

*All sample calculations are made for the M-in. orifice, area = 0.19697 sq. in.

. 0/06'

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a = area of orifice, sq. in.Ti' = absolute temperature of air entering orifice under stand-

ard conditions, that is, 520 deg. F. abs.Pi' = pressure of air on inlet side of orifice, lb. per sq. in. abs.

referred to standard barometric pressure of 29.921in. mercury = 14.696 lb. per sq. in.

P2' = pressure of air on exit side of orifice, that is, standardbarometric pressure, lb. per sq. in. abs. (14.696 lb.per sq. in.)

Constants used are:

0.489789 = constant transferring inches mercury at 60 deg. F. to lb.per sq. in. (Smithsonian Tables)

0.0361934 = constant transferring inches water at 60 deg. F. to lb.per sq. in. (Smithsonian Tables)

At 30 in. mercury, by Equation (15)

(29.921 + 30) X 0.489789M' = 31.8 X 0.19697 X - /52o

= 8.0618 lb. per min.

At 15 in. mercury, by Equation (16)63.6 X 0.19697

M' = .- 520 [14.696 (15) X 0.4897891]

= 5.7083 lb. per min.

At 15 in. water, by Equation (16)

63.6 X 0.19697M' = [V520 [14.696 (15) X 0.0361934I1

= 1.5520 lb. per min.

(b) The experimental results are as follows:

mM" - Xc (17)

where m = air discharged, lb. *t = duration of test, minutes.c = correction factor to standard conditions.


When the pressure on the exit side of the orifice is less than thecritical

Pi' Tic = T 2 ( 1 8 )

and when the pressure on the exit side of the orifice is more than thecritical

Ti1 X P2' 2c = - _ (19)

where Pi' = pressure on inlet side of orifice, referred to barometricpressure of 29.921 in. mercury, lb. per sq. in. abs.

Pi = observed pressure on inlet side of orifice, lb. per sq. in.abs.

P 2' = standard barometric pressure, 29.921 in. mercury.P 2 = observed barometric pressure, in. mercury.Ti' = standard temperature, 520 deg. F. abs.Ti = observed temperature on inlet side of orifice, deg. F. abs.

For observation No. 15, Table 10 (inlet pressure more than two timesexit or atmospheric pressure)

m = 50 - leakage + pressure drop correctionLeakage = sum of orifice tank leakage at 30 in. mercury and weigh-

ing tank leakage at the average pressure for the testmultiplied by duration of test. (Leakage fromcurves in Figs. 6 and 7 = 0.02865 lb.)

Pressure drop correction = 0.335 lb. (from Fig. 8).m = 50 - 0.02865 + 0.335 = 50.30634 lb.t = 6.4466 min.

From Equation (18)

(29.921 + 30) X 0.489789 .1546.81c - --' - 1.03329

(29.47 + 30) X 0.489789 520

From Equation (17)50.30634

M" - X 1.03329 = 8.0632 lb. per min.6.4466

For observation No. 9, Table 10 (inlet pressure less than two timesexit or atmospheric pressure)

m = 29.995 - 0.020009 + 0.205 = 30.18999 lb.t = 5.44166 min.


From Equation (19)

,1548.25 X 29.921

c 520 X 29.56 1.03306

30.18999M" -= 3.1 X 1.03306 = 5.7313 lb. per min.

5.4416

(c) The coefficient for Fliegner's formula isM" (Experimental Results)M' (From Fliegner's Equation)

For observations Nos. 15 and 16, Table 10,8.0539

C = 618 0.999028.0618

VI. DIscussION OF RESULTS

16. Accuracy of Results.-The results have been tabulated inTables 1 to 14, as well as plotted for comparison in Figs. 9 to 12, in-clusive. Since in the tests on the Y4 -in. and Y8-in. orifices three ori-fices were used in parallel, the total discharge was divided by three todetermine the discharge curves, Figs. 9 and 10, for those particularorifices.

Referring to Tables 1 to 14, inclusive, it may be noted that in nocase does the deviation in "time in seconds" for duplicate tests varymore than one-half of one per cent and that the average variation isapproximately two-tenths of one per cent. This average was slightlylower for tests made with the mercury manometer than for thosemade with the water manometer.

In Tables 1 to 7, inclusive, the pressures on the inlet side of theorifice are given in inches of water, from 1 in. to 35 in. In Tables 8 to14, inclusive, the pressures on the inlet side of the orifice are given ininches of mercury, from 1 in. to 35 in.

Referring to the curves in Figs. 11 and 12, and to Tables 17 and 18giving the coefficients as applied to Fliegner's formula, it is observedthat the coefficients are smaller for the lower inlet pressures than forthe higher inlet pressures. This indicates that Fliegner's formula

P2gives values too high where the ratio P approaches unity. This may

be due to the fact that, with reduced velocity, friction is more effectivenear the wall of the orifice.*

*Experiments by Bean, Buckingham, and Murphy, in Research Paper No. 49 of the Bureau ofStandards, show the same effect at low velocities. This is attributed by the authors to skin effect ordrag at the wall of the orifice.


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Referring to Fig. 11, it is seen that the coefficient increases as thediameter of the orifice increases. This is also true for the lower pres-sures shown in Fig. 12. It may also be observed from Fig. 12 that,for all orifices 12 in. and larger, the coefficients agree so closely thatone curve suffices for these orifices. It should be noted that, due tothe rather low range of pressures (35 in. of mercury) used in thesetests, Fliegner's formula

M' = C X 63.6 (T) [p 2' (Pl' - P')]

applies to all cases where the inlet pressure P1 is less than 26 in. ofmercury in the manometer. Considering that this formula is em-pirical it gives rather remarkable agreement. For the lowest coeffic-ient determined by these tests, one inch of water for the 4 -in. orifice,Fliegner's formula gives results 6.2 per cent high. For the largestcoefficient, at 5 and 10 inches of mercury, Fliegner's formula givesresults about 0.5 per cent low.

The apparent contradiction as to the change in the coefficientdetermined by tests compared with the change discussed on page 9,where Fliegner's formula is compared with the theoretical adiabatic

P 2flow for various values of P , has been observed by others, particularly

in the flow of steam through nozzles.* No explanation of this dis-crepancy can be given at this time.

Tables 15 and 16 give the mean discharge in pounds per minute ofweighed air per sq. in. of orifice; inlet pressures are given in inches ofwater and mercury, respectively.

VII. CONCLUSIONS

17. Summary of Conclusions.-The general conclusions that maybe drawn from this investigation are as follows:

(1) The weight of air discharged through orifices withrounded approach agrees very closely with that calculated by theuse of Fliegner's formulas for the range of inlet pressures used inthis investigation, namely, 1 in. of water to 35 in. of mercury.

(2) The coefficients as applied to Fliegner's formulas show amore rapid change for low pressures on the inlet side of the orificeand for small orifices. As the inlet pressure is increased and asthe orifice diameter is increased, the value of the coefficients

*"Northeast Coast Institution of Engineers and Shipbuilders," February 18, 1921.


tends to become more uniform. Due to the rapid change in thevalue of the coefficient at low heads, interpolation cannot bemade as definite as at the higher heads, where the value of thecoefficient is more constant. It is, therefore, not advisable to usethis type of orifice for pressures on the inlet side of the orifice lessthan 10 in. of water, unless the orifice is carefully calibrated forthe required condition. The change in the value of the coeffi-cients is slight for inlet pressures above 10 in. of water for pres-sures up to 35 in. of mercury, the limit of this investigation.

(3) It is advisable to use water or oil as the manometer liquidfor all pressures within the limit of the manometer. For thehigher pressures mercury should be used. However, mercuryshould not be used in glass tubes less than Y8-in. in inside di-ameter. Capillary tubes of 2 to 3 millimeters inside diameter arelikely to introduce considerable lag in movement both up anddown.

(4) The use of Fliegner's formulas with a coefficient of unityfor inlet pressures between 1 in. of water and 35 in. of mercurymay introduce errors ranging from 6.2 per cent too high to 0.5per cent too low.

(5) The type of orifice used is not difficult to produce, and theresults of tests on duplicate orifices agree closely.

It should be noted that the effect of humidity has not been takeninto consideration in this investigation.


APPENDIX

BIBLIOGRAPHY

NO. YEAR I AUTHOR TITTE ANt iEtmrErNwI -

W. Froude

1859

1871

1874

1874

1874-7

1886

1889

1896

1898

1899

Weisbach

G. Zeuner

A. Fliegner

G. Zeuner

A. Fliegner

(Abstracts)

0. Reynolds

I. P. Church

H. DeParenty

A. Fliegner

Weyrauch

I

"On the Law which Governs the Discharge ofElastic Fluids under Pressure through ShortTube Orifices," Inst. of C.E., vol. 6, 1847.

"Der Civilingenieur," vol. 5, p. 546, 1859,vol. 12, p. 177, 1866.

"Technical Thermodynamics," vol. 1, p. 225,vol. 2, p. 153.

"On the Flow of Atmospheric Air," Inst. ofC.E., vol. 39, pt. 1, p. 370, 1874.

"Results of Experimental Researches on theDischarge of Air under Great Pressures,"Inst. of C.E., vol. 39, pt. 1, p. 375, 1874.

"Der Civilingenieur," vol. 20, p. 13, 1874,vol. 23, p. 443, 1877, vol. 24, p. 39.

"Experiments on the Flow of Air throughOrifices in a Thin Plate," Van Nostrand'sMag., vol. 25, p. 217, 1881.

"Experiments on the Flow of Air throughWell-rounded Orifices," Inst. of C.E., vol. 53,p. 295.

"On the Flow of Gases," pt. 1, PhilosophicalMagazine, p. 185, 1886.

"Flow of Fluids," Mechanics of Engineering,J. Wiley & Sons, New York. Chap. VIII,Dynamics of Gaseous Fluids, 1889.

"On the Discharge of Perfect Gases and ofSteam under Pressure through Orifices" (Surla debit des gaz parfaits et de la vapeur d'eausous pression a travers les orifices), Annalesde Chimie et de Physique, ser. 7, vol. 8, p. 5,1896.

"Investigations in the Discharge of Air fromConical Diverging Nozzles" (Versuche fiberdas Ausstr6men von Luft durch DivergenteRohre) (3 articles), Schweizerische Bauzei-tung, March 12, 19, 5, 1898.

"The Efflux of Gases and Steam under Di-minishing Pressure and Volume" (tUber denAusfluss von Gasen und Dimpfen bei Abneh-menden Druck und bei Abnehmenden Vol-umen), Zeitschrift des Vereines deutscherIngenieur, September 23, 30.


No.

R. Bachmann

YEAR

1901

1903'

1905

1905

1905

1906

1906

1906

1907

1908

1909

1911

1912

1912

AUTHOR

M. A. Rateau

(Abstracted)

A. E. Zahn

A. Borsody,R. C. Cairncross

S. A. Moss

R. J. Durley

S. A. Moss

F. Foster

H. Judd,R. S. King

C. Monteil

A. 0. Muller

J. Orr

J. Weisbach

W. Watson,H. Schofield

T. R. Weymouth

TITLE AND REFERENCE

"Experiments on the Escape of Steamthrough Orifices," Inst. of M.E.

"The Flow of Steam through Orifices," Eng.Record, October 26, 1901.

"Air Flow. Measurement of Air Velocityand Pressure," Physical Review, Ithaca,N. Y., vol. 17, p. 410.

"Pressures and Temperatures of Free Expan-sion," A.S.M.E. Tran., vol. 26, p. 114.

"An Experimental Determination of the Co-efficient of Discharge of Air," Amer. Mach.,vol. 28, p. 193.

"On the Measurement of Air Flowing into theAtmosphere through Circular Orifices in aThin Plate and under Small Differences inPressure," A.S.M.E. Tran., vol. 27, p. 193.

"Flow of Air and Other Gases with SpecialReference to Small Differences in Pressure,"Amer. Mach., vol. 29, p. 368, vol. 29, p. 407.

"Flow of Air in Nozzles," Mech. Eng., vol. 18,p. 574.

"Some Experiments on the Frictionless Ori-fice," Eng. News, vol. 56, p. 326.

"Output of a Circular Orifice" (Debit d'unorifice circulaire), 8th serie Annales des pontset Chaussees, pt. 3, p. 139, 1907.

"Measurement of Gas Flow with Plate Ori-fice." (Messung von Gasmengen mit derDrosselscheibe) Mitteilung Forsarbeit Ingen-ieurwerkes, Berlin. Zeitschrift des Vereinesdeutscher Ingenieur, vol. 52, p. 285.

"The Measurement of Compressed Air,"Mech. Eng., vol. 24, p. 70.

"Air Flow" (Versuche fiber den Ausfluss vonLuft), Zeitschrift fur die Sauerstoff-undStickstoff-Industrie, Leipzig, vol. 3, p. 7.

"On the Measurement of the Air Supply toInternal Combustion Engines by Means of aThrottle Plate," Inst. of M.E., pt. 1, 2, p. 517.

"Measurement of Natural Gas," A.S.M.E.Tran., vol. 34, p. 1091.

"Air Measurement" (Messung von Luft-mengen), C. Pfeffer, Darmstadt.


No.

27 1913

1913

1913

1913

1913

1914

1914

1914

1915

1915

1915

1916

1916

1916

1916

1916

1916

YEAR AUTHOR

1010 f~1 ' T .C E. s. iuucKe

J. Brandis

W. Rosenbain

J. B. Henderson

H. Gaskell

H. E. A. Raabe

J. G. Stewart

W. E. Fisher

T. Trupel

A. L. Westcott

E. 0. Hickstein

T. B. Morley

H. Judd

E. G. Bailey

T. G. Estep

S. A. Moss

H. B. Reynolds

TITLE AND REFERENCE

"Flow of Gases and Vapors in Pipes, Flues,Ducts, and Chimneys," Engineering Thermo-dynamics, McGraw-Hill Book Co., N. Y.p. 1111.

"Measurement of Air Flow by Plate Orifice"(Genaue Messung der durch eine LeitungStromende Gas (Luft) Menge Mittels Dros-selmes scheibe Staurand), M. Krayn, Berlin.

"Experiments on a Steam Jet," Inst. of C.E.,p. 199.

"Theory and Experiment on the FlowTofSteam through Nozzles," Inst. of M.E., vol.193, p. 253.

"The Diaphragm Method of Measuring theVelocity of Fluid Flow in Pipes," Inst. ofM.E., vol. 197, p. 243.

"The Flow of Air through an Aperture," Int.Marine Eng., September.

"The Theory of the Flow of Gases throughNozzles," Inst. of M.E., vol. 1914, p. 949.

"The Discharge of Steam through Nozzles,"Inst. of M.E., vol. 1914, pt. 3-4, p. 927.

"Action of an Air Jet on the SurroundingAir" (Uber die Einwirkung eines Luftstrahlesauf die Umgebende Luft), Zeitschrift fir desgesamte Turbinenwesen, vol. 12, p. 53.

"The Flow of Air and Steam through Ori-fices," Power, vol. 42, p. 515.

"The Flow of Air through Thin Plate Ori-fices," A.S.M.E. Tran., vol. 37, p. 765.

"The Flow of Air through Nozzles," Eng.,vol. 101, p. 91.

"Experiments on Water Flow through PipeOrifices," A.S.M.E. Tran., vol. 38, p. 331.

"Steam Flow Measurement," A.S.M.E. Tran.,vol. 38, p. 775.

"Measuring the Flow of Compressed Air,"Jour. Iron Age, vol. 98, p. 1049.

"The Impact Tube," A.S.M.E. Tran., vol. 38,p. 761.

'The Flow of Air and Steam through Ori-fices," A.S.M.E. Tran., vol. 38, p. 799.



AUTHOR

B. S. Nelson

J. L. Hodgson

L. Hartshorn

1917

1917

1917

1917

1917

1919

1919

1919

1920

1920

1920

1920

1920

1920

1920

1921

1921

1921

No. YEAR TITLE AND REFERENCE

"Flow of Air through Orifices against BackPressure," Eng. News, vol. 77, p. 19.

"The Commercial Metering of Air, Gas, andSteam," Inst. of C.E., vol. 204, p. 108.

"The Discharge of Gases under High Pres-sure," Proc. of the Roy. Soc., London, vol. 94,p. 155.

"A Study of the Thin Plate Orifice," SibleyJour., 1917, p. 144.

"Study of Air Measurement and Air Flow,"A.S.H. & V.E. Jour., vol. 23, p. 577.

"Flow and Measurement of Air and Gases,"C. Griffin & Co., London.

"Gas Measurements with Plain Orifices,"Power, p. 801.

"Differential Pressure Meters for MeasuringAir, Gas, and Steam Flow," Journal, Societyof Chemical Industry, vol. 38, p. 222t.

"High Efficiency Air Flow," A.S.H. & V.E.Jour., vol. 26, p. 403.

"Calibration of Nozzles for the Measurementof Air Flowing into a Vacuum," A.S.H. &V.E. Tran., vol. 42, p. 621.

"Small Meters for Air, Especially OrificeMeters," U. S. Dept. of Com. Tech. Papers,Bur. of Stds., Dec. 20.

"The Flow of Air through Small BrassTubes," A.S.M.E. Tran., vol. 42, p. 334.

"The Flow of Air through Small BrassTubes," Power, p. 1022.

"Measuring Flow of Fluids," Power, vol. 51,p. 503.

"Principles of Thermodynamics," Chap. 9,"The Flow of Fluids," p. 137, Henry Holt &Co., New York, N. Y.

"The Metering of Compressed Air," Tran.Inst. of Mining Engineers, vol. 60, p. 271.

"The Orifice Meter and Gas Measurement,"Foxboro Co., Foxboro, Mass., Jan.

"Viscosity in Orifice Flow," Proc. PhysicalSociety, vol. 33, p. 225.

U. R. Gage

0. K. Ohmes

A. B. Eason

A. H. Blaisdell

J. L. Hodgson

E. N. Fales,F. W. Caldwell

W. DeBaufre

E. Buchington

T. S. Taylor

T. S. Taylor

J. M. Spitzglass

G. A. Goodenough

J. L. Hodgson

W. C. Brown,M. B. Hale

W. N. Bond


No.

A. B. Cox

YEAR

1922

1922

1922

1922

1922

1923

1923

1923

1923

1923

1924

1924

1925

AUTHOR

J. L. Hodgson

G. Stoney,E. Norman

M. Ware

H. W. Diebart

Stratton

R. Glazebrook

J. L. Hodgson

J. G. S. Thomas

J. M. Spitzglass

R. 0. King

J. Taylor

G. B. Shawn

H. P. Westcott

R. 0. King

J. L. Hodgson

TITLE AND REFERENCE

"Kent Hodgson Steam Meter," South AfricanEngineering, vol. 32, p. 243.

"Notes on Flow of Air and Steam in Nozzles,"Engineering, vol. 112, p. 750.

"Effect of Reversal of Air Flow upon the Dis-charge Coefficient of Durley Orifice," Nation-al Advisory Committee for Aeronautics,Technical Note No. 40.

"Discharge through Orifices in Series," Mech.Eng., vol. 44, p. 764.

"Stratton Air Flow Meter," Power, vol. 55,p. 387.

"Dictionary of Applied Physics," London,Macmillan, vol. 3, 1922-23.

"The Metering of Steam," Tran. Inst. ofNaval Architects, vol. 64, p. 184.

"Discharge of Air through Small Orifices andthe Entrainment of Air by the Issuing Jet,"Phil. Mag., vol. 44, p. 919.

"Orifice Coefficients-Data and Results ofTests," A.S.M.E. Trans., vol. 44, p. 919.

"The Measurement of Air Flow by means ofa Throttle Plate with Special Reference to theMeasurement of the Air Supply to InternalCombustion Engines," Eng., vol. 115, p. 456.

"Experiments Develop New Constants in AirFlow," Auto. Ind., vol. 48, p. 1126.

"Flow of Gases through Orifices," Amer. GasJournal, vol. 118, p. 23.

"Measurements of Gas and Liquids by Ori-fice Meters," Metric Metal Works, Erie,Pennsylvania.

"Fluid Meters," Pt. 1, Report of A.S.M.E.Special Research Committee on Fluid Meters,2nd Ed., New York, N. Y.

"Measurement of Air Flow, Callendar HotWire Anemometer," Eng., vol. 117, p. 136,vol. 249, p. 51.

"The Orifice as a Basis of Flow Measure-ment," Inst. of C.E. Selected paper No. 31,1925.

"New Theory of Fluid Flow," Jour. FranklinInst., vol. 198, p. 769.


AUTHORNo.

79

80

81

TITLE AND REFERENCE

"The Practical Measurement of Air Flow,"Domestic Eng. (London), vol. 45, p. 229,vol. 46, p. 3, Jan.

"Die Ausflussformel von Saint-Venant undWantzel," Zeitschrift des Vereines deutscherIngenieur, vol. 70, July 17.

"Die Messungstr6mender Luft und Gaseunter besonderer Beriicksichtigung desdynamischen Messprinzips," Chemiker-Zei-tung, vol. 50, p. 533; vol. 50, p. 574, Aug. 4.

E. Ower

F. Kretzschmer

0. Mattner

YEAR

1925

1926

1926

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tCopies of the complete list of publications can be obtained without charge by addressing theEngineering Experiment station, Urbana, Ill.

*A limited number of copies of the bulletins starred are available for free distribution.


*Bulletin No. 184. The Measurement of Air Quantities and Energy Losses inMine Entries. Part III, by Alfred C. Callen and Cloyde M. Smith. 1928. Thirty-five cents.

*Bulletin No. 185. A Study of the Failure of Concrete Under Combined Com-pressive Stresses, by Frank E. Richart, Anton Brandtzaeg, and Rex L. Brown. 1928.Fifty-five cents.

*Bulletin No. 186. Heat Transfer in Ammonia Condensers. Part II, by AlonzoP. Kratz, Horace J. Macintire, and Richard E. Gould. 1928. Twenty cents.

*Bulletin No. 187. The Surface Tension of Molten Metals. Part II, by Earl E.Libman. 1928. Fifteen cents.

*Bulletin No. 188. Investigation of Warm-air Furnaces and Heating Systems.Part III, by Arthur C. Willard, Alonzo P. Kratz, and Vincent S. Day. 1928. Forty-five cents.

*Bulletin No. 189. Investigation of Warm-air Furnaces and Heating Systems.Part IV, by Arthur C. Willard, Alonzo P. Kratz, and Vincent S. Day. 1929. Sixtycents.

*Bulletin No. 190. The Failure of Plain and Spirally Reinforced Concrete inCompression, by Frank E. Richart, Anton Brandtzaeg, and Rex L. Brown. 1929.Forty cents.

Bulletin No. 191. Rolling Tests of Plates, by Wilbur M. Wilson. 1929. Thirtycents.

Bulletin No. 192. Investigation of Heating Rooms with Direct Steam RadiatorsEquipped with Enclosures and Shields, by Arthur C. Willard, Alonzo P. Kratz,Maurice K. Fahnestock, and Seichi Konzo. 1929. Forty cents.

Bulletin No. 193. An X-Ray Study of Firebrick, by Albert E. R. Westman.1929. Fifteen cents.

*Bulletin No. 194. Tuning of Oscillating Circuits by Plate Current Variations,by J. Tykocinski-Tykociner and Ralph W. Armstrong. 1929. Twenty-five cents.

Bulletin No. 195. The Plaster-Model Method of Determining Stresses Appliedto Curved Beams, by Fred B. Seely and Richard V. James. 1929. Twenty cents.

*Bulletin No. 196. An Investigation of the Friability of Different Coals, by CloydeM. Smith. 1929. Thirty cents.

*Circular No. 18. The Construction, Rehabilitation, and Maintenance of GravelRoads Suitable for Moderate Traffic, by Carroll C. Wiley. 1929. Thirty cents.

*Bulletin No. 197. A Study of Fatigue Cracks in Car Axles. Part II, by HerbertF. Moore, Stuart W. Lyon, and Norville J. Alleman. 1929. Twenty cents.

*Bulletin No. 198. Results of Tests on Sewage Treatment, by Harold E. Babbittand Harry E. Schlenz. 1929. Fifty-five cents.

*Bulletin No. 199. The Measurement of Air Quantities and Energy Losses inMine Entries. Part IV, by Cloyde M. Smith. 1929. Thirty cents.

*Bulletin No. 200. Investigation of Endurance of Bond Strength of VariousClays in Molding Sand, by Carl H. Casberg and William H. Spencer. 1929. Thirtycents.

*Circular No. 19. Equipment for Gas-Liquid Reactions, by Donald B. Keyes.1929. Ten cents.

*Bulletin No. 201. Acid Resisting Cover Enamels for Sheet Iron, by Andrew I.Andrews. 1929. Twenty-five cents.

*Bulletin No. 202. Laboratory Tests of Reinforced Concrete Arch Ribs, byWilbur M. Wilson. 1929. Fifty-five cents.

*Bulletin No. 203. Dependability of the Theory of Concrete Arches, by HardyCross. 1929.

*Bulletin No. 204. The Hydroxylation of Double Bonds, by Sherlock Swann, Jr.1930. Ten cents.

*Bulletin No. 205. A Study of the Ikeda (Electrical Resistance) Short-Time Testfor Fatigue Strength of Metals, by Herbert F. Moore and Seichi Konzo. 1930.Twenty cents.

*Bulletin No. 206. Studies in Electrodeposition of Metals, by Donald B. Keyesand Sherlock Swann, Jr. 1930. Ten cents.

*Bulletin No. 207. The Flow of Air Through Circular Orifices with RoundedApproach, by Joseph A. Polson, Joseph G. Lowther and Benjamin J. Wilson. 1930.Thirty cents.

*A limited number of copies of the bulletins starred are available for free distribution.

UNIVERSITY OF ILLINOISTHE STATE UNIVERSITY-

URBANADAVID KIINLEY, Ph.D., LL.D., President

THE UNIVERSITY INCLUDES THE FOLLOWING DEPARTMENTS:

The Graduate School

The College of Liberal Art; and Sciences (Curricula: General with majors, inthe Humanities and the Sciences; Chemistry and Chemical Engineering;Pre-legal, Pre-medical, and Pre-dental; Pre-journalism, Home Economics,Economic Entomology, and Applied Optics)-• , -

The College of Commerce and Business Administration (Curricula: GeneralBusiness, Banking and Finance, Insurance, Accountancy, Railway Adminis-tration, Railway Transportation, Industrial Administration, Foreign Com-merce, Commercial Teachers, Trade and Civic Secretarial Service, PublicUtilities, Commerce and Law)

The College 6o Engineering (Curricula: Archttecture, Ceramics; Architectural,Ceramic, Civil, Electrical, Gas, General, Mechanical, Mining, and RailwayEngineering; Engineering Physics)

The College of Agriculture (Curricula: General Agriculture; Floriculture-; HomeEconomics; Landscape Architecture; Smith-Hughes-in conjunction withthe College of Education). ,

The College of Education (Curricula: Two year, prescribing junior ~tanding~ oradmission -General Education, Smith-Hughes Agriculture, Smith-HughesHome Economics, Public School Music; Four year, admitting from the high-school-Industrial Education, Athletic Coaching, Physical Education. TheUniversity High School is the practice school of the College of Education)

The School of Music (four-year curriculum)The College of Law (three-year curriculum based on a college degree, or three

years ,of college work at the University of Illinois)The- Library School (two-year curriculum for college-graduates)The School ofJournalism (two-year curriculum based on two- years of college

work)The College of Medicine (in Chicago)

The College of Dentistry (in Chicago)K ---The School of Pharmacy (in Chicago)

The Sun•tner Sessiotn (eight weeks)Experiment Stations and Scientific Bureaus: U. S. Agricultural ExperimentStation; -Engineering Experiment Station; State Natural History Survey;

State Water Survey; State Geological Survey; Bureau of EducationalResearch.

The Library Collections contain (June 1, 1929) 762,166 volumes and 73000

For catalogs and information address

THE REGISTRARUrbana, Illinois

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