The eccentric orifice as a flow measuring device in small

Scholars' Mine Scholars' Mine

Masters Theses Student Theses and Dissertations

1965

The eccentric orifice as a flow measuring device in small diameter The eccentric orifice as a flow measuring device in small diameter

pipes pipes

James E. Casale

Follow this and additional works at: https://scholarsmine.mst.edu/masters_theses

Part of the Mechanical Engineering Commons

Department: Department:

Recommended Citation Recommended Citation Casale, James E., "The eccentric orifice as a flow measuring device in small diameter pipes" (1965). Masters Theses. 6684. https://scholarsmine.mst.edu/masters_theses/6684

This thesis is brought to you by Scholars' Mine, a service of the Missouri S&T Library and Learning Resources. This work is protected by U. S. Copyright Law. Unauthorized use including reproduction for redistribution requires the permission of the copyright holder. For more information, please contact [email protected].

https://library.mst.edu/

https://library.mst.edu/

https://scholarsmine.mst.edu/

https://scholarsmine.mst.edu/masters_theses

https://scholarsmine.mst.edu/student-tds

https://scholarsmine.mst.edu/masters_theses?utm_source=scholarsmine.mst.edu%2Fmasters_theses%2F6684&utm_medium=PDF&utm_campaign=PDFCoverPages

http://network.bepress.com/hgg/discipline/293?utm_source=scholarsmine.mst.edu%2Fmasters_theses%2F6684&utm_medium=PDF&utm_campaign=PDFCoverPages

https://scholarsmine.mst.edu/masters_theses/6684?utm_source=scholarsmine.mst.edu%2Fmasters_theses%2F6684&utm_medium=PDF&utm_campaign=PDFCoverPages

mailto:[email protected]

THE ECCENTRIC ORIFICE

AS A

FLOW 1-1EASURING DEVICE

IN

SMALL DIAMETER PIPES

BY

JAMES E. CASALE

A

THESIS

submitted to the faculty of the

UNIVERSITY OF MISSOURI AT ROLLA

in partial fulfillment of the work required for the

Degree of

MASTER OF SCIENCE IN MECHANICAL ENGINEERING

Rolla, Missouri

fi_/ /' / Approved by\.).1 1'. +- ·~~< '··--*

~~/- (Adv:Lsor) --1._....;_,~-~~....;._ __ , ,_._·_..... __

-< fi' {!_' t:!pL ~ --6/.u.f x/~_u.-

ii.

ABSTRACT

This thesis reports and evaluates the use of an eccentrically

placed orifice as a flow measuring device in s.mall pipe sizes. The

orifice is placed in a concentric location and moved to

increasingly eccentric locations until full eccentricity is

reached. At fUll eccentricity the circumference of the orifice

is tangent to the circumference of the pipe.

The effects of increasing eccentricity are evaluated for four

orifices of o.3002", o.400011 , o.5013" and o.6005" diameter placed

in a 1.0043" diameter pipe. Flow coefficients for the orifices

in different locations are plotted against Reynolds numbers.

The eccentric orifice is a reliable, accurate now measuring

device for metering or controlling the now of fluids. Design

criteria can be established which will allow its use for situations

where complete drainage of piping systems is required.

iii.

ACKNO\VLEOOEMENT

The author wishes to thank Professor G. L. Scofield for his

advice and encouragement during the conducting of this investigation

and through out the author's past year of study at the

University of Missouri at Rolla. Without his help the past year's

achievements would not have been possible.

A word of thanks is due to all the staff of the Mechanical

Engineering Department, in particular to Mr. L. Anderson and

Mr. R. D. Smith who were especially helpful in the fabrication

and assembly of the apparatus.

A special thanks to the author's wife and children who have

had to put up with many inconveniences for the past two years. They

are due appreciation beyond words.

TABLE OF CONTENTS

ABSTRACT. • • • • • • • • • • • • • • • • • • • • • • •

ACKNOVJLEDGEMENT • • • • • • • • • • • • • • • • • • • •

LIST OF TABLES •• • • • • • • • • • • • • • • • • • • •

LIST OF FIGURES • • • • • • • • • • • • • • • • • • • •

I.

II.

III.

IV.

v.

VI.

VII.

INTRODUCTION. • • • • • • • • • • • • • • • • • •

DISCUSSION. • • • • • • • • • • • • • • • • • • •

DESCRIPTION OF APPARATUS. • • • • • • • • • • •

Orifice Flanges • • • • • • • • • • • • • • • Orifice Plates ••••••••••••••• Resistance Flow Straightener. • • • • • • • • Pressure Gages and Manifolds ••••••••• \'later Deli very System • • • • • • • • • • • • Temperature and Weight Measurement. • • • • •

ORIFICE THEORY. • • • • • • •

EXPERIMENTAL RESULTS. • • • •

First Test Set-Up • • • • • Second Test Set-Up. • • • • Third Test Set-Up • • • • • Test Procedure ••••••• Discussion of Test Results

CONCLUSIONS • • • • • • • • • •

RECOMMENDATIONS • • • • • • • •

BIBLIOGRAPHY. • • • • • • • • •

VITA •• • • • • • • • • • • • •

APPENDIX. • • • • • • • • • • •

• • • • • • • • •

• • • • • • • • •

• • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • •

and Figures. • • •

• • • • • • • • •

• • • • • • • • •

• • • • • • • • •

• • • • • • • • •

• • • • • • • • •

•

•

•

•

•

•

•

• • • • • •

•

•

• • • • •

•

•

•

•

•

iv.

Page

ii

iii

v

vii

1

5

6

6 8

10 10 13 15

15

19

19 20 20 21 23

27

29

31

32

33

v.

LIST OF TABLES

Table Page

(Note: these tables are in the Appendix)

I DATA FOR DETERMINING FI.D\v COEFFICIENTS FOR ORIFICE PLATES IN A ltt LINE, DIAMETER - o .3002", ECCENTRICITY - O. • • • • • 34

II DATA FOR DETEill1INING FLOW COEFFICIENTS FOR ORIFICE PLATES IN A 1" LINE, DIAMETER - o .300211 , ECCENTRICITY - 1/3 • • • • • 35

III DATA FOR DETERMINING FLOW COEFFICIENTS FOR ORIFICE PLATES IN A 1 11 LINE, DIAMETER - o.3002", ECCENTRICITY - 2/3 • • • • • 36

IV DATA FOR DETERMINING FLOW COEFFICIENTS FOR ORIFICE PlATES IN A 1" LINE, DIAHETER - o .3002n, ECCENTRICITY - 1. • • • • • 37

v DATA FOR DETERMINING FLOVf COEFFICIENTS FOR ORIFICE PlATES IN A 1" LINE, DIANETER- o.4000", ECCENTRICITY - O. • • • • • 38

VI DATA FOR DETERMINING FLOW COEFFICIENTS FOR ORIFICE PLATES IN A 1" LINE, DIAMETER - o. 400011 , ECCENTRICITY - 1/3 • • • • • 39

VII DATA FOR DETE:Rl-IDUNG FLO\v COEFFICIENTS FOR ORIFICE PlATES IN A 1" LINE, DIAMETER - o .4000", ECCENTRICITY - 2/3 • • • • • 40

VIII DATA FOR DETEill1INING FLOW COEFFICIENTS FOR ORIFICE PlATES IN A 1n LINE, DIAllliTER - o.4000", ECCENTRICITY - 1. • • • • • 41

IX DATA FOR DETEill·ITNING FIDW COEFFICIENTS FOR ORIFICE PlATES IN A 1n LINE, DIAMETER - o. 5013", ECCENTRICITY - O. • • • • • 42

X DATA FOR DETERMINING FLOl.V COEFFICIENTS FOR ORIFICE PlATES llJ A 1" LINE, DIAMETER - o. 5013", ECCENTRICITY - 1/3 • • • • • 43

XI DATA FOR DETERNINING FLOvl COEFFICIENTS FOR ORIFICE PLATES IN A 1" LINE, DJ:Alvffi:TER - o. 5013", ECCENTRICITY - 2/3 • • • • . 44

vi.

Table Page

XII DATA FOR DETERMINING FLOW COEFFICIENTS FOR ORIFICE PlATES IN A 1" LINE, DIAMETER - o. 5013 11 , ECCENTRICITY - 1. • • • • • 45

XIII DATA FOR DETERMINING FLO\'l COEFFICIENTS FOR ORIFICE PlATES IN A 1" LINE, DIAMETER - o. 600511 , ECCENTRICITY - O. • • • • • 46

XIV DATA FOR DETERMINING FLO~v COEFFICIENTS FOR ORIFICE PIATES IN A 1 11 LINE, DIAHETER - o .6005", ECCENTRICITY - 1/3 • • • • • 47

XV DATA FOR DETERMINING FLO~i COEFFICIENTS FOR ORIFICE PlATES IN A 1n LINE, DIAMETER - o. 600 5", ECCENTRICITY - 2/3 • • • • • 48

XVI DATA FOR DETERMINING FLOW COEFFICIENTS FOR ORIFICE PlATES IN A 1" LINE, DIAMETER - o.6005", ECCENTRICITY - 1 • • • • • • 49

Figure

I

II

III

IV

v

VI

VII

VIII

IX

X

1

2

3

LIST OF FIGURES

ORIFICE TEST SECTION • • • • • • • • • • • • • • • •

ORIFICE FLANGES. • • • • • • • • • • • • • • • • • •

PRESSURE TAP LOCATIONS • • • • • • • • • • • • • • •

ORIFICE PlATE MOUNTED ON FLANGES • • • • • • • • • •

PRESSURE GAGES AND MANIFOLDS • •

OVERALL VIEW OF TEST SET-UP.

• • • • • • • • • •

• • • • • • • • • •

WATER DELIVERY SYSTEM ••••• • • • •

ORIFICE NOMENCLATURE FOR DERIVATION. •

ECCENTRICITY LOCATIONS OF ORIFICE. • •

ORIFICE COEFFICIENTS BY URQUHART • • •

• • • • •

• • • • •

• • • • •

• • • • •

(Note: The remaining figures are in Appendix)

GAGE CALIBRATION CURVE, 10 psi DIFFERENTIAL GAGE

GAGE CALIBRATION CURVE, 30 psi DIFFERENTIAL GAGE

FLOW COEFFICIENTS FOR SHARP EOO:ED ORIFICE PlATES IN A 1" LINE, ECCENTRICITY - O, (AT REDUCED VERTICAL SCALE) •••••••••••••••••

• •

• •

• •

• •

• •

• •

• •

• •

vii.

Page

5

6

8

9

11

13

14

16

23

25

51

51

52

4 FLOW COEFFICIENTS FOR SHARP EOO:ED ORIFICE PlATES IN A 1" LINE, DIAMETER - o.J002". • • • • • • • • • 53

5 FLOW COEFFICIENTS FOR SHARP EDGED ORIFICE PlATES IN A 1 11 LINE, DIAMETER -- o.4000". • • • • • • • • • 54

6 FLOW COEFFICIENTS FOR SHARP EDGED ORIFICE PlATES IN A 1" LINE, DIAM&TER -- o.5013"• • • • • • • • • • 55

7 FLOW COEFFICIENTS FOR SHARP EDGED ORIFICE PlATES IN A 1 11 LINE, DIAMETER - o.6005"• • • • • • • • • • 56

8 FLOW COEFFICIENTS FOR SHARP EDGED ORIFICE PlATES IN A 1 11 LINE, ECCENTRICITY - O. • • • • • • • • • • 57

9 FLOW COEFFICIENTS FOR SHARP EDGED ORIFICE PlATES IN A 1" LINE, ECCENTRICITY - 1/3 ••••••••• • 58

Figure

10

11

FLOW COEFFICIENTS FOR SHARP EOOED ORIFICE PIA TES IN A l" LINE, ECCENTRICITY -- 2/3. • • • • • • •

FlOW COEFFICIENTS FOR SHARP EDGED ORIFICE PLA.TES IN A l" LINE, ECCENTRICITY - l. • • • • • • • •

viii.

Page

• • 59

• • 60

1.

I. INTRODUCTION

The orifice meter is one of the oldest flow devices known to man,

having first been used by the Romans to regulate domestic water

supplies (1}*. The use of the orifice as a modern flow meter began

in earnest at the start of the Twentieth Century. Since that time

many investigations have been conducted on the use of the thin plate

orifice as a metering device. These investigations have produced

very accurate measurements of flow characteristics of such orifices.

The majority of this work has, however, been directed towards

concentrically placed orifices in large diameter pipes.

As the reliability and accuracy of the orifice was established,

its use became more widespread and varied. The pressure drop across

an orifice is a function of the flow rate through the orifice. A

control system sensitive to the differential pressure across the

orifice plate can be used to regulate the flow through the orifice

and its associated flow system.

Many flow systems, particularly those associated with highly

reactive or explosive fluids, such as rocket propellants, must be

purged of all fluid when not is use. Valves, low spots in system

piping and other flow restrictions, such as orifice plates, can

act as traps to hold these dangerous liquids. Such areas of

collected liquid make purging the system very difficult and time

consuming. \·Jhile good design practice can relieve or eliminate a

number of the problems cited, the orifice plate for flow metering

often remains as a primary source of propellant or oxidizer entrapnent.

*Numbers in parentheses are references listed in the Bibliography.

2.

A solution which has been offered involves the use of an eccentric

orifice so that the bottom of the orifice is tangent to the bottom

of the pipe in which it is installed. Such an installation would

reduce the collection of fluid at this location and thus make

internal cleaning, or purging, of the system much more ef.ficient

and certain. It is not unusual for heated nitrogen, or some other

inert gas, to be pumped through the system to act as a cleaning

agent. The cleaning is brought about by vaporizing the toxic and

reactive fluids and then carrying them, in mixture with the

purging gas, to a satisfactory exhaust point. The toxicity of some

.fuels and oxidizers is such as to make disposal of these toxic

fumes require an exhaust point a mile or more from occupied spaces

and in a favorable location with regard to wind and terrain.

In a liquid fueled rocket or in a test complex for rocket testing,

ori.fice plate flow control systems can be used to regulate fuel and

oxidizer flow rates. Such flow rates may represent either

propellant trc:msfer or hot .firing of the reaction chamber and rocket

motor.

It was in the developnent of static test complex requirements for

secondary rocket testing that the author's advisor,

Professor Gordon L. Scofield, found a need for an investigation of

eccentrically placed orifices (2). While the eccentric location

was an asset to eliminate trapped pools of propellant it represented

an unknown quantity when designs involving its .flow coefficient

were required.

Another feature of the eccentric orifice of potential impor

tance in flow through small line sizes is the apparent displacement

3·

of the vena contracta downstream from the location of the

concentric orifice vena contracta. This locates the vena contracta

beyond flanges and nor.mal appurtenances and makes installation of

a vena contracta pressure tap easier.

In 19311 a Joint American Gas Association-American Society of

Mechanical Engineers Orifice Coefficient Committee was formed to

report on the use of the orifice as a reliable fluid meter. In 1935,

a report was presented to the parent organizations and the use of

the orifice as a metering device seemed to be established and

sanctioned officially.

One of the earlier reports 1 by Judd (3) 1 included character

istics of an eccentric orifice in a 5" line. It is significant to

note that the experimenter in his conclusions states that the

"eccentric ••• diaphragms are advantageous in that they increase the

drop readings." Even at that time the possible advantages of the

eccentric orif'ice were recognized but most o:f the later investigations

were directed at :finding the characteristics o:f concentric orifices

in large diameter pipes.

In most of the reports on orifice tests and discharge

coefficients, the use of an eccentric location is mentioned but

no characteristics are given to establish reliable design criteria.

In most of the tests particular care was taken to insure that the

eccentricity did not exceed certain limits. The ASME Power Test

Codes, in fact, state that the orifice "shall be centered within

o.Ol5 DJ. (~/n2 -1) with respect to the inlet and/or outlet conduits"(4).

Because of the apparent lack of information on the flow characteristics

of eccentric orifices in small diameter pipes this investigation

was undertaken.

The primary objective of this investigation was to study the

effects of eccentricity on the flow coefficient for a sharp edged

orifice. A coordinate objective was to establish reliable design

criteria in a specific range of Reynolds numbers. The location

of the vena contracta was sought at various ratios of

eccentricity whenever reliable data could be obtained.

II. DISCUSSION

This discussion will be concerned with the work required to

buil.d the apparatus and to conduct various experiments on an

eccentric orifice. It will include a description of the

construction of equipment, the procedure for conducting the tests

for flow characteristics, the theory associated with the use of

orifices as flow meters and a discussion of the test results.

The fluid used in the test was water. The thermo-physical

properties of many of the liquid fuels and oxidizers, pa.rticularily

the hydrocarbons, are not dissimilar to the thermo-physical

properties of water (5). M:>reover, the use of water reduces many

problems in the conducting of the tests. It is non-toxic, non

explosive, easily handled by pumping equipnent and is economical

and available. If Reynolds number is used as the argument :for

plotting now coe:f:ficient curves, then now of any Newtonian fiu:i.d

IJPSTREAM FLANGE -----~r---....1

---------DOWNSTREAM FLANGE

RESISTANCE FLO\'/ STRAIGHTENER

Figure I

ORIFICE TEST SECTION

6.

may be calculated from these curves.

Figure I is a sketch of the orifice test section showing the

major components that will be referred to in the succeeding sections.

DESCRIPTION OF APPARATUS

Orifice Flanges - The major pieces of equipnent which had to

be fabricated were the flanges for holding the orifice plates.

These pieces are shown in Figure II. The material used for the

flanges was scrap steel from a heavy duty drive shaft. The upstream

and downstream flanges were roughed out, then clamped together with

Figure II

ORIFICE FLANGES

the four blank orifice plates between them. The orifice plates and

flanges were drilled in this clamped condition to insure perfect

mating of the components. Six bolt holes and two guide pin holes

were drilled. The upstream test section flow tube was designed to

be long enough to incorporate a resistance flow straightener at

least 8 clear diameters upstream of the orifice plate.

The upstream flow tube and flange were pressed together into

an integral unit. The two flanges were then bolted together and

centered as a unit in a lathe. The bore was carefully machined

throughout its entire length, insuring concentricity and

continuity of the bore on both sides of the orifice plate location.

In this way there were no surface irregularities upstream of the

orifice plate to the .flow straightener. While the unit was in the

lathe the orifice holes were bored in the plates. This operation

will be described later.

After boring the .flanges and upstream flow tube, the integral

unit was set up in an end milling machine for drilling the pressure

taps. It was desirable to have the taps as close together as

possible and in an axial line along the bottom and top of the bore

downstream from the orifice plate. These taps were spaced 1/4"

apart. A series of intercepting holes were staggered on the

outside of the flange as shown in Figure II and III. The unrequired

portions of the holes were sealed and the pressure line fittings

mounted on the flange. The inside of the bore was carefully

inspected for defects and burrs on the pressure tap inlets. All

pressure tap inlets were vecy s1ight1y ro\Ulded and blown out with

compressed air to remove any trapped foreign material left from

the machining.

Orifice Pl.ates - Four orifice plates • 1/1611 thick• of Type 304

8.

stainless steel.• were fabricated for the tests. The orifice diameters

were o.J002"• o.4000", o.5013" and o.6005"· The pl.ates were

designed to be moveable verticall.y along slots as shown in Figure IV.

These guide s1ots were cut so that the orifice could move in a

vertical plane from a fully concentric to a f~ eccentric

position.

BROKEN OUT 0 TAP 2T

BLANK TAP

7TAPS END VIEW @ 1/4" ---+----.!

,f2~g}

~ER~~

Figure III

PRESSURE TAP WCATIONS

Figure IV

ORIFICE PLATE MOUNTED ON FLANGES

This movement was colinear with a line drawn between the bottom

row o:f pressure taps and the top row located 180 o away.

In boring the orifice holes in the individual plates, each

plate was placed between two 5/16" altnn.inum plates and bolted to

the :face of the downstream flange while the flange was still centered

in the lathe :following the machining o:f the bore. This procedure

insured that all ori:fices were per:fectly centered in the bore when

they were in the concentric position on the guide slots. Also, the

rigid bolting between the aluminum plates eliminated plate flexing

during the boring operation and helped to insure that each orifice

was true and free of burrs.

10.

After each orifice plate was fabricated it was carefully

inspected under an intense light and fo1.md to be free of flat spots,

dents, and burrs. Then the orifice was measured on four diameters

with a small hole gage or telescoping gage and stamped with the

average diameter.

Resistance Flow Straightener - A resistance type flow straighten

er was fabricated for installation in the upstream flow tube.

Twenty-five 1/St' holes were drilled in a 5/St' long threaded plug. The

plug was then screwed into the upstream flow tube and a standard

1n pipe nipple was brazed into the upstream flow tube ahead of the

plug as can be seen in Figure II. The main advantage of this method

of installing the flow straightener was that at least eight diameters

of smooth, continuous pipe remained between the orifice and the

straightener with no fittings or area changes to cause flow

disturbances just ahead of the orifice.

Pressure Gages and Manifolds - The extensive manifolding as

shown in Figure V was necessary to attempt to locate the vena

contracta downstream of the orifice and to provide flexibility in

operation. The upstream pressure was sensed through two taps

one diameter upstream from the orifice plate and 180 o apart in the

bore. These taps were connected to a common, vented manifold.

The upstream static pressure gage and the high side of the

differential pressure gage were connected to the manifold through

Figure V

PRESSURE GAGES AND MANIFOLDS

a common~ vented line. The vents allowed the system to be

completely purged of trapped air. This was necessary to eliminate

the compressible air. This air entrapment would cause inaccuracies

in the readings.

Each of the downstream taps was connected to a common~ vented

manifold through copper tubing with individual shut off valves in

each line. The low side of the differential pressure gage was

ll.

12.

connected to this manifold. Through this system of taps, valves

and manifolds the experimenter was able to read the differential

pressure between the upstream station and any downstream station

desired.

In addition to the differential gage across the orifice plate,

a differential pressure gage was placed to read the differential

pressure between any station connected to the dow.nstrerun manifold

and at a station 13 diameters downstream. This gage was used to

try to find the vena contracta. This installation can be seen to

the left of center in Figure VI.

The upstream static pressure gage was used to monitor the

pressure in the system so that reasonable pressures could be

maintained w:i thout damaging the gages or exceeding allowable

working pressures in the piping system. The differential gage used

across the orifice plate was an Ashcroft double bourdon tube gage

with a range of zero to !: 30 psi differential pressure in increments

of 1 psi. With this gage the differential could be estimated to

1/4 psi. The vena contracta differential gage was an Ashcroft M:>del 110,

single bourdon tube in a sealed pressurized case with a range of zero

to ~ 10 psi differential pressure in increments of 1/4 psi. With

this gage the differential could be estimated to 1/20 psi.

The differential gages were calibrated with a dead weight tester

on one pressure tap and atmospheric pressure on the other. Figures

1 and 2 in the Appendix show the gage calibration curves. No

calibration curve is supplied for the upstream static pressure gage

since the line pressure is monitored only for safety and comparative

Figure VI

OVERAIJ.. VIEW OF TEST SET-UP

purposes.

Water Delivery System - In rurming a test o:f this nature it

is very important to have :flexibility in the pumping system which

supplies :fluid to the test section. The system as shown in

Figure VII was used in the :final test a:fter several :false starts

with other equipnent. The pump used was an Aurora, double impeller

centri:fugal pump which is usually used as a boiler :feed pump

13.

Figure VII

\vATER DELIVERY SYSTEM

l4.

in the Mechanical Engineering Laboratory. A bypass valve was installed

across the pump suction and discharge so that the total flow could be

split as desired. The pump was supplied with water from a combination

of storage tanks with a total capacity of approximately 550 gallons.

The tanks were kept full from a continuously flowing external water

source. This continuous filling of the storage tanks kept the

suction head on the pump constant and steady flow was easily obtained.

The test section, composed of the flanges, orifice, upstream

flow tube and resistance flow straightener, was completed using

1" steel. pipe incorporating val.ves for .fl.ow control. There were

gl.obe val.ves in both upstream and downstream locations and a

lubricated plug valve upstream of the entire section as seen in

Figure VI. This system of throttling valves, used in conjunction

with the pump bypass val.ve, gave excellent control. of the water

flow and pressure.

Temperature and Weight N:easurement - The temperature o~ the

water was read on a mercury-in-gl.ass thermometer using a tee as a

thermometer well. This themometer coul.d be estimated to o. 5F:

No emergent stem correction was applied since in the range of

temperatures encountered a reading of ! 3Fo woul.d be adequate to

give ± o.l% accuracy in the fluid density.

The water flow through the orifice for each test was collected

in 100 pound increments. The water flowed into a 55 gal.l.on barrel

on a beam scal.e. The time to accumulate 100 pounds was measured

with a l.O seconds/revolution stop watch. The watch was calibrated

to o.l. seconds and coul.d be estimated to o.Ol seconds. Al.though

the readings were read to o.Ol. second it is real.ized that this is

~alse accuracy and the readings were averaged and rounded off.

ORIFICE THEORY

15.

The equation for fl.ow through an orifice as shown in Figure VIII

is given by the ASME Power Test Code for an "incompressibl.e"

liquid as:

where

-Q- = weight flow in J.b mass per second.

A2 = orifice area in square inches.

K = now coefficient (coefficient of discharge with approach

factor included) dimensionless.

;o = fluid density in J.b mass per cubic foot.

16.

Ap • differential pressure across orifice in J.b force per square inch.

ORIFICE PLATE

I DL I

-----@1-! r----em-VARIES-SEE FIGURE III

Figure VIII

ORIFICE NOMENClATURE FOR DERIVATION

17.

This equation can be derived in several ways, the simplest being by

the use of the continuity equation for steady flow and the general

energy equation.

In the folloli.Lng derivation the assumptions are:

1. The fluid is an incompressible, ideal fluid, that is, one

with no viscous action.

2. Steady state has been achieved. This is a good assumption

since the orifice is only good for relatively stable flo~r measurememts.

The general energy equation for steady flow is: v2 v2

P]_ vl + 1 + zl + ul -t- Qin = p2 V2+ _g_ .... z2 + ~ + 'vfout ~ 2g

but for the orifice we can say,

w = 0 out

qin = 0

ul ... ~

Zl= z2

(temperature is constant)

(horizontal line)

therefore, V2 v2

p1 vl"" 1 ::. p2v2 -\'-~ :: constant for any point in the streamtube, 2g 2g

which is recognized as Bernoulli's equation. Rearranging, this becomes:

~- ~ = (Plvl- P2v2) 2g~ 2g (pl- P2) /-'

since from assumption 1,

1 vl = v2=- •

p The equation of continuity of mass for steady state is:

Rearranging,

v1=- p~2 v2 -=- (::_D12)2 v2,

flAl

where f> 1 ::. /' 2 from assumption 1.

where

D2 = diameter at A2 in inches

~ = diameter at ~ in inches.

or solving for v2 , in the energy equation:

The expression 1 is called the approach factor.

Jl- (~) 4

18.

Since the actual flow is not as high as the theoretical as given

above it is common practice to correct the theoretical value by

defining a coefficient of discharge:

_ *actual cd = * . theoretical

Now,

If the coefficient of discharge is combined with the approach factor,

;. = A2 K .j 2g,PAP

If Ap is in psi and the ..J2i is evaluated this expression becomes,

w-= o.668 A2 KJft.P

which is the equation as given previously.

The Reynolds number as used on the graphs in the Appendix is

defined as:

Re = pV2D2 • p

By substituting for v2 from the continuity equation and applying

appropriate conversions to make the group dimensionless,

Re = 15.28 -*D2fl

where n2 is the orifice diameter.

EXPERIMENTAL RESULTS

This section will describe the test procedure used to evaluate

the orifice coefficients. Several test set-ups were tried before

satisfactor.y results were obtained.

First Test Set-Up - Initially the orifice test was to be run

at pressures in the 250 to 300 psi range. A John Bean triplex piston

ptmlp, capable of pressures up to 1000 psi, was connected to the system.

It was immediately apparent that this pump would not be satisfactory

since it did not give enough flow to generate appreciable pressure

drops across even the smallest orifice. In addition, this positive

displacement pump gave pulsating flow that made it virtually

impossible to read the pressure gages satisfactorily. At this point

20.

pulsation dampeners were installed on the main differential gage

in an attempt to steady out the pulsating. Although this aided in

the reading of the gages the low volume of flow from the pump

required that this set-up be abandoned.

Second Test Set-Up - The next set-up used a small nylon roller

pump. This pump was also a positive displacement pmnp but because

of its eight roller impeller and high rotative speed it was felt

that this pump would be satisfactory. To help smooth out the

pulsations a surge tank 6" in diameter and 3' long was placed be

tween the pump and test section. The surge tank working in

conjunction with the pulsation dampeners seemed to give steady

readings, so the tests were started. A system of throttling valves

and a pump bypass gave good flexibility of operation and flow rates

from better than 1 lb mass per second to shut off were obtained.

Even though all the equipment seemed to be performing satisfactor

ily for this set-up the data was completely unsatisfactory. At this

point it was determined that the pulsations generated by the positive

displacement pump were contributing to the inaccuracies in the

results and that some elaborate pulsation dampening system would have

to be devised or a centrifugal type pump used.

Third Test Set-Up - The centrifugal type pump previously

described was used in the final set-up. The surge tank and

pulsation dampeners were taken out of the system so that any

pulsations and fluctuations could be immediately sensed on the gages.

With this pump, very smooth delivery was experienced throughout the

testing.

21.

In the third set-up the method o£ throttling the £low was

changed £rom the method used previously. In the £irst two set-ups

the amount of water a.J.:lowed to now through the test section was

regulated by closing down the globe valve downstream from the ori£ice

as the pump bypass was opened. This procedure caused erroneous

differential pressure readings and in the third set-up the £low was

regulated by the plug valve upstream o£ the ori£ice and the pump

bypass, as previously described. The error was dete:nnined to be

one o£ overcontrol by this valve, which thus took over the metering

fUnction from the ori£ice.

Test Procedure - The procedure established £or running the tests

was simple and al.lowed aJ.:l data to be taken by one man. Initially

each plate woUld be placed in the concentric position to establish

a 11nomal" £low characteristic curve with which to compare the curves

obtained £rom the eccentric positions. Then the orifice was moved to

two intermediate positions and £inally to a fully eccentric position.

The plate eccentricity is de£ined as shown on Figure IX.

At each plate position the maximum now that could be run

through the test section was £ound be£ore taking any data. The

differential pressure £or this maximum. £low was read and then the

flow was regulated so as to give six now rates corresponding to

six dif£erential pressures in equal increments £rom zero to the

maximum possible.

In each run the £low was a.J.:lowed to stabilize after the valves

had been adjusted and then, three 100 pound weighings were timed into

a collecting tank. As the weighings were being taken, the temperature,

22.

upstream static pressure and the orifice differential pressure were

read. The average of the three sets of readings was used to

deter.mine the physical properties of density and viscosity. These

averages were also used in the calculations.

Each time the plate was moved or changed the entire test section

was vented of any trapped air. irlhenever the apparatus was shut down

for a length of time it was again vented. The venting system and

vent locations worked very satisfactorily as no erratic readings

due to air pockets were observed on the pressure gages during the

testing.

During the initial stage of testing the use of the 10 psi

differential pressure gage was abandoned. For the first few runs

the differential pressures were read between all the downstream

stations in the flange and the pipe tap 13 diameters downstream.

Due to fluctuations in pressure it was very unstable and accurate

readings were very difficult to obtain. The gage was very

sensitive to disturbances in the test section due to valve adjustment

and several times the needle was driven off scale. In order to

preclude damaging the instrument it was removed from the system for

the remainder of the testing. The objective of finding the vena

contracta was abandoned along with this gage. Knowledge gained

would indicate that further testing for vena contracta location

will require better instrumentation. The downstream tap should be

moved further downstream so the fluctuations will not be as

pronounced. Shut-offs should be installed in the gage pressure

lines to allow flow valve adjustments without affecting or

23.

damaging the sensitive gage required in this portion of the test.

As the orifice was moved towards an eccentric position, the

pressure was read at the tap 180° from the eccentric position. This

was in accordance with the recommended procedure by Stearns (6), but

was not the same method as used by Judd (3) in his investigation.

FUU.Y CONCENTRIC POSITION

ECCENTRICITY : e : +

Figure IX

ECCENTRICITY LOCATIONS OF ORIFICE

Discussion of Test Results and Figures - The following discussion

will pertain to Figures 3 to ll found in the Appendix. In all the

data collected during this investigation the differential pressure

across the tap 1.0D1 upstream and the tap o.5D1 downstream was used

24.

for the determination of values for the flow coefficient~ K.

The curves were fitted in the same manner as by Beitler (7).

The flow coefficient was plotted against the reciprocal of the square

root of Reynolds number. These plots gave a good correlation and

smooth curves were fitted to the data points. These curves were

then redrawn on regular coordinates of flow coefficient and

Reynolds number. These curves are presented in the Appendix.

Figure 3 was drawn with the vertical scale in the same relative

proportion as is nonn.ally found for orifice coefficient curves. The

family of curves were very close together and in order to emphasize

the variation in the curves from the concentric to eccentric positions

the vertical scale was expanded in Figures 4 to ll.

The nnonn.alized" curves in Figure 8 are the ones for the orifices

in a concentric location. These curves show the expected trend of

increasing then decreasing flow coefficient with increasing Reynolds

numbers. This tendency is very vividly brought out in a curve

presented by Urquhart (8) which is reproduced as Figure X.

The small orifice was only slightly affected by eccentricity

as it was initially moved to a 1/3 eccentric location. As the

orifice approached and then was placed fully eccentric, a

significant change took place as can be seen in Figure 4. For zero

eccentricity at Reynolds numbers above 70,000 the flow coefficient

stays constant at about o.600. At the 2/3 eccentricity location

the flow coefficient is constant at about o.608 for all values of

Reynolds numbers and then at full eccentricity the flow coefficient

is again approximately constant at o.6oo. This can be attributed

25 •

•••

~

b ~ ~ .. .,

r ~.::.""- ... ;=====~ ·.--.r-f---- -·-...

I . .

••• I 10 ·- - ...... a-o ,ooo \ooo.oo. r•,o .. 1ooo

Re

Figure X

ORIFICE COEFFICIENTS BY URQUHART

in great measure to the effects of the boundary layer at the pipe

wall. In the small orifice the boundary layer at full eccentricity

occupies a considerable portion of the overall orifice area and

influences the flow through the orifice. In addition6 the eddy

currents on the upstream side of the orifice plate are not present

on the total circurn.ference of the orifice. Flov-r then is much

smoother through the lower portion of the orifice against the

pipe wall and no contraction takes place. This effect could explain

the increasing flow coefficient with increasing eccentricity, that is,

less energy is lost in now eddys and disturbances.

26.

As might be expected the largest orifice was least effected by

eccentricity in the range of Reynolds numbers tested. As shown in

Figure 7 the r.low coefficient curve flattened out rather smoothly.

At eccentricity ratios of 0 and 1/3 practically the same flow

coefficient values are observed. The flow coefficient is decreasing

with increasing Reynolds number from about o.7000 at Re o:f 50,000

and is still decreasing at o.635 for the maximum Re on the curve of

130,000. At the 2/3 eccentricity location, the :flow coefficient is

leveling off through the entire range of Reynolds numbers from about

o.692 at Re of 30,000 to again about o.635 at Re of 130,000. At the

:fully eccentric position the :flow coefficient is decreasing from

o.675 at Re of 30,000 to o.647 at Re of 130,000. Since the orifice

diameter is approximately 6~ of the pipe diameter 1 the boundary

layer at the pipe wall did not occupy a very large percentage of

orifice area and did not cause the disturbance that is observed for

the smaller orifices.

In the intermediate orifice sizes the effects, emphasized by

the large and small sized orifices, are not as striking, but as

Figure 5 and 6 show, the same effects are present.

III. CONCLUSIONS

The purpose of the test was to study the use of an eccentric

orifice as a flow meter and to determine its flow characteristics.

The results show that it is practical and reliable to use an orifice

in an eccentric position as congruous flow coefficients are obtained.

Further study will be required to provide accurate data over a large

range o:f Reynolds numbers, but no problems should be encountered

in the collection of this data. This data, When collected, will be

satisfactor,y for use in design criteria over a wider range of flows

than were possible in this investigation.

Certainly the intended use of the orifice will have to be

considered in selection of an orifice size. For large pressure

drops a small orifice is selected, but care must be taken in its

placement since it seems to be most effected by position as a fully

eccentric position is approached. The larger orifice is probably

better for use in eccentric positions unless rnnall flows or large

pressUre drops are required. It is least effected by eccentricity

and gives much smoother data over the range of Reynolds numbers

experienced in the test.

One factor which is certainly subject to question is the

roughness of the upstream flow tube as compared to a commercial

grade pipe. In small sizes roughness can be a significant factor

in affecting flow. In most cases it is considered constant over a

wide range of sizes. In the machining of the flow tube, the bore

was deliberately left with the tool marks not smoothed. This was

to simulate a commercial pipe and it is believed that the assumption

is valid.

28.

Because of the difficulty in controlling the flow rate with the

downstream globe valve in the first and second set-up, the author

has doubts about the ASME code requirement for downstream apparatus.

The code requires only 5 pipe diameters downstream and in this test

30 diameters were allowed and still the globe valve had a profound

influence on the orifice.

IV. RECONMENDATIONS

The results from this investigation indicate that further

study of eccentric orifices is worthwhile. The scope of any

further investigation should be broadened to include a wider range

of Reynolds numbers. A multiple pumping system should be employed

along with a better water supply and storage system.

The instrumentation should be improved for obtaining differential

pressures across the orifice plate. The tests were, of necessity,

restricted to :flows which could be kept within the range of

differential. pressures readable on the 30 psi gage.

Further investigation should be undertaken on finding the

effect of eccentricity on the vena contracta. With this information

a vena contracta tap could be employed, with an increase in

differential pressure available for control devices, for the same

flow rates. In conjunction with this, the author believes that the

pressure tap used for eccentric orifices should be located at the

vena contracta on the same side of the pipe as the eccentric position.

Study would be required to determine the flow coefficient for a tap

of this nature.

The investigation proved the feasability of using the

eccentric orifice in flow measurement. The orifices studied were

sharp edged and were in a thin plate. Further studies should now

be undertaken on the effects of eccentricity on rounded entrance

orifices and on thick plate orifices. In many instances a thick

plate "orifice" (in reality probably a short tube) may be necessary

for structural rigidity when high differential pressures are encountered.

30.

Another possibility worthy of investigation would be the use of

an elliptical shaped eccentric orifice with the major axis along a

diameter of the pipe. This shape would probably reduce the effects

of the boundary layer on the flow coefficient but still give high

differential pressures for control devices. This would incorporate

the good features of the large and small orifices, as brought out

by this investigation.

31.

V. BIBLIOGRAPHY

1. REPORT OF THE JOINT COMMITTEE ON ORIFICE COEFFICIENTS OF THE AMERICAN GAS ASSOCIATION Al·OOUCAN SOCIETY OF MECHANICAL ENGINEERS (1935), History-of Orifice Meters and the Calibration, Construction and Operation of Orifices for Metering, ASME, New York, N.Y.

2. SCOFIELD, G.L. (1964), Static Test Complex Requirements for Secondary Rocket Testing, Douglas Aircraft Company, Report No. TU-24931.

3. JUDD, H. (1916), Experiments on Water Flow Through Pipe Orifices, Journal of the ASME, New York, N.Y.

4. PO~JER TEST CODES (1940), Flow Measurement, Chapter 4 of Part 51

ASME, New York, N.Y.

5. AEROSPACE PROPULSION DATA BOOK (1961), Section 4 -Materials, Fuels and Oils, General Electric Company, Cincinnati, Ohio.

6. STEARNS, R.F., JOHNSON, R.R., JACKSON, R.M., AND LARSON, C.A. (1951), Flow 1·feasurement With Orifice Meters, D. Van Nostrand Company, Inc., New York, N.Y.

7. BEITLER, S.R. (1935), The Flow of \vater Through Orifices, Ohio State University, The Engineering Experiment Station, Bulletin No. 89, Columbus 1 Ohio.

8. URQUHART, L.C., Editor (1959), Civil Engineering Handbook, McGraw-- Hill Book Company, Inc., New York, N.Y., 4th ed., p. 4--36.

9. REPORT OF ASME SPECIAL RESEARCH C01-1MITTEE ON FLUID METERS (1937), Fluid 11eters, Their Theory and Application, Part 1, ASME, New York, N.Y., 4th ed.

10. KING, H.W., \fiSLER, CO., AND WOODBURN, J.G. (1948), Hydraulics, John Wiley and Sons, Inc., New York, N.Y., 5th ed.

ll. SHAW, G.V., AND LOOMIS, A.W. (1951), Cameron Hydraulic Data, Ingersoll-Rand Company, New York, N.Y., 12th ed.

12. SHAMES, I.H. (1962), Mechanics of Fluids, McGraw--Hill Book Company, Inc., New York, N.Y.

32.

VI. VITA

The author was born December 30, 1936, in Quincy, Massachusetts.

During the early years of his life he moved quite frequently and his

primary and secondary education was received in no less than 11

schools in 11 years. He graduated from Port Clinton High School,

Port Clinton, Ohio in 1953. In November of 1953 he entered North

eastern University, Boston, Massachusetts, on a co-operative education

program. In June 1959, he received the degree of Bachelor of Science

in l~chanical Engineering.

In his co-operative work program at Northeastern University,

he was employed from August 1954 until April 1957 by Watertown

Arsenal, Watertown, Massachusetts, as a draftsman in the Plant

Maintenance Office. From the period August 1957 until November

1959 he was employed by Buerkel and Company, Incorporated, Boston,

Massachusetts, as an air conditioning systems designer.

In November 1959 he entered the United States Army as a

Second Lieutenant and has now attained the rank of Captain in the

Regular Army. As part of' his military career developnent program

he returned in June 1963 to the Nissouri School of llines and l.fetallurgy,

Rolla, Missouri, to pursue f'urthur study. In May 1964, he was granted

the degree of' Bachelor of' Science in Civil Engineering and is presently

pursuing a program leading to a degree of' Master of Science in l.fech

anical Engineering.

The author is married to the f'onner Mona Lou Feeley and they

have two children. He is a registered Professional Engineer in

the State of' Missouri.

33

VII APPENDIX

The following Tables 1 to 16 contain the data taken with the

experimental apparatus. On Page 50 is a sample calculation showing

how the data was reduced and the desired parameters calculated.

Figures 1 and 2 are the differential pressure gage calibration

curves. Figures 3 to 11 are a series of curves for the four

orifice sizes, each in four positions in the flow. The reader is

reminded that in using Figures 3 to 11 the symbol, e, stands for

eccentricity as defined on Figure IX.

TABLE I

DATA FOR DETERMINING FLOW COEFFICIENTS FOR ORIFICE PLATES IN A 1" LINE, DIAMETER - o .3002", ECCENTRICITY - O.

RUN NO. 1 2 3 4 5 6

LINE TEMP ( .. F) 64.5 65.5 66.0 66.0 66.0 66.0

p1 (psi) 2.0 4.0 10.0 15.5 20.0 24-5

AP (psi) 3-75 8.0 14.75 20.5 25.25 29.75

TAP NO. 1T 1T 1T 1T 1T 1T

LBS WATER 100 100 100 100 100 100

TIME (sec) 243.29 161.10 116.56 98.60 88.80 81.91

LINE TEMP ("'F) 65.0 65.0 66.0 66.0 66.0 66.0

PJ. (psi) 2.0 4.0 10.0 16.0 20.0 24-5

AP (psi) 3-75 7-75 14-75 20.5 25.25 29.75


LBS WATER 100 100 100 100 100 100

TIME (sec) 242.80 163.0.5 116.21 99.01 89.04 81.73

LINE TEMP (• F) 65.5 65.0 66.0 66.0 66.0 66.0

p1 (psi) 2.0 4.0 10.0 16.0 20.0 25.0

~p (psi) 3.75 7.75 14.75 20.5 25.25 30.0


LBS WATER 100 100 100 100 100 100

TIME (sec) 244.90 162.98 ll6.(f7 99-C17 88.63 81.52

35-

TABLE II

DATA FOR DETERMINmG FLOW COEFFICIENTS FOR ORIFICE PIA TES m A 111 LINE, DIAMETER - o. 3002", ECCENTRICITY - 1/3.

RUN NO. 1 2 3 4 5 6

LINE TENP (° F) 67.0 66.0 66.0 65.5 65.0 65.0

p1 (psi) 2.0 4.0 10.0 16.0 21.0 25.0

AP (psi) 4.25 8.5 14.0 19.75 25.25 29.75


LBS ~'lATER 100 100 100 100 100 100

TIME (sec) 227.72 152.61 116.70 98.53 88.09 80.71

LINE T.E1{)? (oF) 67.0 66.0 65.5 64.5 65.0 64.5

P:l. (psi) 2.0 4.0 10.0 16.0 21.0 25.0

~p (psi) 4.25 8.5 14.0 20.0 25.0 29.75


LBS WATER 100 100 100 100 100 100

TIME (sec) 227.87 152.72 116.38 98.49 88.01 80.91

LINE TEMP (oF) 67.0 66.0 66.0 65.0 65.0 64.5

p1 (psi) 2.0 4.0 10.0 16.0 20.5 25.0

AP (psi) 4.25 8.5 14-25 19.75 25.25 29.75


LBS WATER 100 100 100 100 100 100

TIME (sec) 226.30 152.71 116.92 99.02 87-49 81.48

36.

TABLE III

DATA FOR DETERMlNING FLOitl COEFFICIENTS FOR ORIFICE PlATES IN A 1" LINE, Dlli!ETER - o .3002", ECCENTRICITY - 2/3.

RUN NO. 1 2 3 4 5 6

LINE TEMP (°F) 70.5 70.6 70.0 69.5 70.0 70.5

11. (psi) 2.0 4.0 9.0 13.5 20.0 25.0

LlP (psi) 4-5 8.25 12.75 17.75 24.25 29.5


LBS WATER 100 100 100 100 100 100

T:mE (sec) 206.97 151.65 123.33 104.37 89.80 80.91

LINE TEMP (•F) 71.0 70.5 70.0 69.0 70.0 72.0

Pl (psi ) 2.0 4.0 8.5 13-5 20.0 24-5

1!. p (psi) 4.5 8.25 12.5 17.75 24.25 29.25


LBS "ltlATER 100 100 100 100 100 100

TIME (sec) 207.52 151.22 124.04 104.89 89.51 81.18

LINE TEMP (*F) 71.0 70.0 70.0 69.0 70.0 72.0

P.1. (psi) 2.0 4.0 8.5 13-5 20.0 24.5

tip (psi) 4-5 8.25 12.5 17.5 24.25 29.25


LBS ~vATER 100 100 100 100 100 100

TIME (sec) 207.07 151.69 124.97 104.99 89.94 81.65

37.

TABLE IV

DATA FOR DETERMINING FLO\Y COEFFICIENTS FOR ORIFICE PlATES IN A 1" LINE, DIAI.mTER - o.3002", ECCENTRICITY - 1.

RUN NO. 1 2 3 4 5 6

LINE TEMP (°F) 72.0 69.0 68.0 68.0 68.0 66.0

p1 (psi) 2.0 4.0 15.0 23.5 27.0 24.5

6p (psi) 3·75 7-75 12.0 17.25 25.25 29.25


LBS WATER 100 100 100 100 100 100

TIME (sec) 232.13 157.02 129.90 108.72 89.01 82.01

LINE TEMP (.,F) 71.0 68.5 68.0 68.0 68.0 66.0

P:t (psi) 2.0 4.0 15.0 23.0 25.0 24.5

6p (psi) 3-75 7-75 12.0 17.25 25.25 29.75


LBS WATER 100 100 100 100 100 100

TIME (sec) 229.80 157.27 130.51 107.62 89.48 83.28

LINE TEMP (.,F) 70.0 68.5 68.0 68.0 68.0 66.0

P:l (psi) 2.0 4.0 15.0 23.0 25.0 24.5

6p (psi) 3-75 7.75 ll.75 17.25 25.0 29.25


LBS WATER 100 100 100 100 100 100

TIME (sec) 229.95 157.20 130.42 108.49 89.90 82.68

38.

TABLE V

DATA FOR DETE~ITNING FLOW COEFFICIENTS FOR ORIFICE PlATES IN A ::L11 LINE, DIAMETER - o.4000", ECCENTRICITY - O.

RUN NO. 1 2 3 4 5 6

LINE TEMP (° F) 64.6 65.0 65.0 65.0 65.0 65.0

P:t (psi) 4.0 6.0 :12.0 16.0 21.0 26.0

6P (psi) 5.0 10.0 15.5 19.75 25.25 29.75


LBS vvATER 100 100 100 100 100 100

TIME (sec) ll0.93 77-54 62.59 55-39 49.12 45-48

LINE TEMP (•F) 64.5 64.5 65.0 65.0 65.0 64.5

1\ (psi) 4.0 6.0 :12.0 16.0 21.0 26.0

/lp (psi) 5.0 10.0 15.5 20.0 25.5 29.75


LBS vlATER 100 100 100 100 100 100

TIME (sec) ll0.89 77.63 62.ef7 54.88 49.36 45.68

LINE TEMP ("F) 64.5 64.5 65.0 65.0 65.0 64.5

P:t (psi) 4.0 6.0 12.0 16.0 21.5 26.0

A p (psi) 5.0 10.0 15.5 20.0 25.5 29.75


LBS WATER 100 100 100 100 100 100

TIME (sec) ll0.58 77-98 62.:14 55.61 49.29 45.81

39.

TABLE VI

DATA FOR DETERMINING FLOW COEFFICIENTS FOR ORIFICE PLATES IN A 1" LINE, DIAMETER - o. 4000", -ECCENTRICITY - 1/3 •

RUN NO. 1 2 3 4 5 6

LINE T.E1-!P (°F) 65.0 65.0 65.0 66.0 65.0 65.0

P:L (psi) 2.0 6.0 ll.O 14.5 20.0 25.0

li.P (psi) 4.75 9.75 14.5 18.75 24.5 29.25


LBS ~vATER 100 100 100 100 100 100

TIME (sec) 114.92 79.48 64.15 57.67 50.95 45.80

LINE TEMP (oF) 65.0 65.0 65.0 65.5 65.0 65.0

p1 (psi) 2.0 6.0 ll.5 15.5 20.0 24.5

6 p (psi) 4-75 9.75 14.75 18.75 24.5 29.0


LBS WATER 100 100 100 100 100 100

TU1E (sec) 115.24 78.63 64.55 56.96 50.21 46.69

LINE TEMP CF) 65.5 65.0 65.0 65.5 65.0 65.0

p1 (psi) 2.0 6.0 11.0 15.5 20.0 24.5

/). p (psi) 4-75 10.0 14-75 19.0 24.25 29.25


LBS ~vATER 100 100 100 100 100 100

TD.fE (sec) 114.68 78.23 64.33 57-30 50.65 46.00

40.

TABLE VII

DATA FOR DETERMINmG FI..0\'1 COEFFICIENTS FOR ORIFICE PlATES IN A 1" LINE, DIAMETER - o .4000" 1 ECCENTRICITY - 2/3.

RUN NO. 1 2 3 4 5 6

LINE TEMP (° F) 66.0 65.5 65.5 65.5 65.0 65.0

p1 (psi) 4.0 6.0 9-5 13.0 19.5 26.0

A p (psi) 4.0 7-5 13.0 17.75 24.0 30.25


LBS \'lATER 100 100 100 100 100 100

TIME (sec) 140.95 94-92 69.81 59.27 51.05 45.13

LINE TEMP (°F) 65.5 65.5 65.5 65.0 65.0 65.0

p1 (psi) 4.0 6.0 9.5 13.5 19.5 26.0

.ip (sec) 4.0 7-5 13.0 18.0 24.0 30.25


LBS \'lATER 100 100 100 100 100 100

TIME (sec) 140.29 95.01 70.08 59.17 51.12 44.21

LINE TEMP c·F> 65.5 65.5 65.0 65.0 65.0 65.0

1\ (psi) 4.0 6.0 9.5 13.5 19.5 26.0

tl.P (psi) 4.0 7-5 13.0 18.0 24.0 30.25


LBS WATER 100 100 100 100 100 100

TII..m: (sec) 141-72 95.11 70.4J_ 58.89 50.94 45.64

4l.

TABLE VIII

DATA FOR DETERU[NING FLOW COEFFICIENTS FOR ORIFICE PLATES IN A 1" LINE, DIAHETER - o.4000", ECCENTRICITY - 1.

RUN NO. 1 2 3 4 5 6

LINE TEMP (6 F) 66.0 66.0 65.0 64.5 64.0 64.0

I\ (psi) 4.0 6.0 9.5 15.5 21.0 26.0

~ p (psi) 4.0 8.25 13.5 19.0 24.75 29.75


IBS HATER 100 100 100 100 100 100

TIME (sec) 134.75 87-54 66.64 56.28 49.02 44.65

LINE T.Elv1P ('"F) 66.0 65.0 65.0 64.0 65.0 64.0

P:L (psi) 4.0 6.0 9.5 15.5 21.5 26.5

A p (psi) 4.0 8.25 13.75 19.0 25.0 29.75


IBS WATER 100 100 100 100 100 100

TIME (sec) 137-40 87.70 65.98 56.38 49.50 44-39

LINE TEMP c· F) 66.0 65.0 64.5 64.0 64.0 64.0

pl (psi) 4.0 6.0 9.5 16.0 22.0 27.0

A.P (psi) 4.0 8.25 13.5 19.0 25.0 30.0


LBS ~'VATER 100 100 100 100 100 100

TINE (sec) 135.72 fr/.62 66.32 56.48 48.49 44.44

42.

TABLE IX

DATA FOR DETERMINING FLOW COEFFICIENTS FOR ORIFICE PlATES IN A 1" LINE, DIAMETER - o.5013", ECCENTRICITY - O.

RUN NO. 1 2 3 4 5 6

LINE TEMP («'F) 64.0 63.0 64.0 64.0 63.5 64.0

P:L (psi) 5.0 6.0 14.0 19.0 20.5 28.0

~p (psi) 4.0 8.0 12.0 16.0 21.0 25.25


LBS VlATER 100 100 100 100 100 100

TIME (sec) 74.80 54.60 45.05 39.10 33.75 31.05

LINE TEMP ("'F) 63.0 63.0 64.0 64.0 63.0 63.5

p1 (psi) 5.5 6.0 14.0 19.5 20.5 28.0

AP (psi) 4.25 8.0 12.0 16.0 21.5 25.0


LBS 1rfATER 100 100 100 100 100 100

TD-1E (sec) 75.25 54.85 44.60 39.00 32.91 31.05

LINE TEMP (oF) 65.0 63.0 64.0 64.0 63.0 63.5

~ (psi) 5.5 6.0 14.0 19.5 21.0 28.0

A p (psi) 4.25 8.0 12.0 16.0 21.75 25.0


LBS WATER 100 100 100 100 100 100

TllfE (sec) 75.45 53.76 44.78 38.50 33.27 31.60

43.

TABLE X

DATA FOR DETERMINING FLOW COEFFICIENTS FOR ORIFICE PlATES IN A 1" LINE, DID!ETER - o. 501Jl', ECCENTRICITY - 1/3.

RUN NO. 1 2 3 4 5 6

LINE TEMP (°F) 63.0 63.0 63.0 72.0 63.5 63.0

P:l. (psi) 5.0 9.5 14.0 17.0 17.0 24.5

AP (psi) 3-75 s.o 12.0 17.0 17.25 21.5

TAP NO. 1T 1T 1T 1T 2B 2B

LBS WATER 100 100 100 100 100 100

TD!E (sec) 77.15 53.60 44-35 36.36 36.90 33.61

LINE TEMP (°F) 63.0 73.0 63.0 69.0 63.0 63.0

p1 (psi) 5.0 9.5 14.0 17.0 17.0 25.0

A p (psi) 3-75 8.0 12.0 16.75 17.25 22.0

TAP NO. 1T 1T 1T 1T 2B 2B

LBS \iATER 100 100 100 100 100 100

TIME (sec) 76.95 53-58 44.05 36.56 36.84 33.41

LINE TEHP (oF) 63.0 63.0 63.0 68.0 63.0 63.0

~ (psi) 5.0 10.0 14.0 17.5 17.0 25.5

~p (psi) 3-75 8.0 12.0 17.0 17.25 22.25

TAP NO. 1T 1T 1T lT 2B 2B

LBS HATER 100 100 100 100 100 100

TIME (sec) 77.20 53-75 44-35 36.21 36.73 32.50

44..

TABLE XI

DATA FOR DETERMINING FLOW COEFFICIENTS FOR ORIFICE PIA TES IN A 111 LINE, DIAMETER o. 501Y', ECCENTIUCITY - 2/3.

RUN NO. 1 2 3 4 5 6

LINE TEHP (oF) 64.0 64.0 64.0 64.0 64.0 64.0

p1 (psi) 4.0 5.0 10.0 15.0 18.5 24.5

IJ.P (psi) 3.75 8.0 12.0 16.5 19.75 25.25

TAP NO. 2B 2B 2B 2B 2B 2B

LBS \"lATER 100 100 100 100 100 100

TIME (sec) 87.55 56.81 45.28 38.85 35.05 31.10

LINE TID1P ( • F) 64.0 64.0 64.0 64.0 64.0 64.0

P:L (psi) 4.0 5.0 10.0 15.0 19.0 24.5

LlP (psi) 3-75 8.0 12.25 16.75 20.0 25.25


LBS ~-lATER 100 100 100 100 100 100

TllfE (sec) 87.70 57.00 45.21 38.66 34.85 31.18

LINE TENP (oF) 64.0 64.0 64.0 64.0 64.0 64.0

PJ_ (psi) 4.0 5.0 10.0 15.5 19.0 24.5

AP (psi) 3-75 8.0 12.25 17.0 20.0 25.25


LBS lvATER 100 100 100 100 100 100

THIE (sec) 87.26 56.88 45-34 38.34 35.41 31.35

45.

TABLE XII

DATA FOR DETERMINING FLOW COEFFICIENTS FOR ORIFICE PLATES IN A 1" LINE, DIAME'I'ZR- o.5013u, ECCENTRICITY -1.

RUN NO. 1 2 3 4 5 6

LINE TEMP ( .. F) 65.0 64.0 65.0 64.5 64.0 64.0

p1 (psi) 4.0 s.o 10.0 14.0 22.0 24.0

AP (psi) 3.25 s.o 10 .. 75 14.25 21.25 23.0


LBS VlATER 100 100 100 100 100 100

TD-lli (sec) 82.07 51.52 44.75 39.48 32.41 31.15

LDrE T1!.11P (• F') 65.0 64.0 65.0 64.5 64.0 64.0

p1 (psi) 4.0 8.0 10.0 1h.O 24.0 24.5

Ap (psi) 3.25 8.0 10.75 14.25 21.75 23.0


LBS \'lATER 100 100 100 100 100 100

Tll:!E (sec) 82.51 51.52 45 .. 12 39.68 31.53 31.32

LINE TEMP (oF) 65.5 64.0 65.0 64.5 6h.O 64.0

P:L (psi) 4.0 8.0 10.0 14.0 24.5 24.5

~p (psi) 3.25 8.0 n.o 14.25 21.75 23 .. 0


LBS HATER 100 100 100 100 100 100

TD-IE (sec) 82.30 51.72 44.45 39.60 31.34 31.33

46.

TABLE XIII

DATA FOR DETERMINING FLOW COEFFICIENTS FOR ORIFICE PlATES m A 1tt LINE, DIAMETER - o.6005", ECCENTRICITY - O.

RUN NO. 1 2 3 4 5 6

LINE TEivlP ("'F) 67.0 67.0 66.0 66.0 65.5 66.0

PJ_ (psi) 4.0 7.0 11.0 14.0 17.0 19.0

Ap (psi) 2.25 4.5 7.0 9.25 10.75 12.25


LBS WATER 100 100 100 100 100 100

TIME (sec) 66.10 47.57 38.80 34.35 31.52 30.09

LINE TEMP (• F) 67.0 66.0 65.5 65.0 64.5 65.0

p1 (psi) 4.0 7.0 11.0 14.0 1s.o 19.0

l;).p (psi) 2.25 4.5 7.25 9.25 11.25 12.25


LBS WATER 100 100 100 100 100 100

TIME (sec) 61.63 47.73 38.35 34.05 30.88 30.15

LINE TEMP (o F) 67.0 66.0 65.0 65.0 64.5 65.0

P:l (psi) 4.0 7.0 11.0 14.0 18.0 19.0

ap (psi) 2.25 4.5 7.25 9.50 11.25 12.25


LBS ~'lATER 100 100 100 100 100 100

TIME (sec) 65.83 47.63 38.28 34.05 31.20 30.15

47.

TABLE XIV

DATA FOR DETERMINDlG FLOvl COEFFICIENTS FOR ORIFICE PLATES IN A 111 LINE, DIAMETER - o.6005", ECCENTRICITY - 1/3.

RUN NO. 1 2 3 4 5 6

LINE TEMP (•F) 65.5 64.0 63.0 62.5 62.0 62.0

P:L (psi) 4.0 6.0 10.0 12.0 16.0 18.0

AP (psi) 1.75 4.0 6.25 8.25 10.0 ll.5

TAP NO. lT lT 1T 1T lT 1T

LBS \'WATER 100 100 100 100 100 100

TIME (sec) 71.85 50.45 41-15 36.10 32.50 30.40

LINE TEMP (• F) 64.0 63.5 63.0 62.5 62.0 62.0

P:L (psi) 4.0 6.0 10.0 12.5 16.0 18.0

AP (psi) 1.75 4.0 6.0 8.25 10.5 11.5


LBS \'lATER 100 100 100 100 100 100

TIME (sec) 72.45 47-75 41.00 36.22 32.22 30.70

LINE TEMP (°F) 64.0 63.0 63.0 62.0 62.0 62.0

I'J. (psi) 4.0 6.0 10.0 12.5 16.0 18.0

Ap (psi) 1.75 4.0 6.0 8.0 10.5 11.5


LBS \'lATER 100 100 100 100 100 100

TH1E (sec) 72.38 51.30 41.50 36.00 32.10 30.70

48.

TABLE XV

DATA FOR DETERMINmG FI..O\v COEFFICIENTS FOR ORIFICE PlATES IN A 111 LINE, DIAMETER - o.600511 , ECCENTRICITY - 2/3.

RUN NO. 1 2 3 4 5 6

LINE TEMP ("F) 66.0 64.0 64.0 63.5 63.0 63.0

p1 {psi) 4.0 6.0 9.0 13.0 15.0 18.0

AP (psi) 2.0 4.0 6.0 8.0 10.0 11.75


LBS WATER 100 100 100 100 100 100

TD1E {sec) 69.65 51.12 41.50 36.25 33.00 30.75

LDffi TEMP (oF) 65.0 64.0 64.0 63.5 63.0 63.0

~ (psi) 4.0 6.0 9.0 13.0 15.0 18.0

tl.P (psi) 2.0 4.0 6.0 8.0 10.0 11.75


LBS \vATER 100 100 100 100 100 100

TllfE (sec) 69.95 51.09 41.45 36.25 32.55 30.40

LINE TEMP (• F) 64.0 64.0 64.0 63.5 63.0 63.0

~ (psi) 4.0 6.0 9.0 16.0 18.0 18.0

~p (psi) 2.0 4.0 6.0 8.0 10.25 11.75


LBS WATER 100 100 100 100 100 100

TIME (sec) 70.15 51.00 41.62 36.30 32.30 30.85

49.

TABLE XVI

DATA FOR DETEmn:NING FI.Dvl COEFFICIENTS FOR ORIFICE PlATES IN A 1" LINE, DIAMETER- o.6005", ECCENTRICITY - 1.

RUN NO. 1 2 3 4 5 6

LINE TEMP (OF) 63.0 63.0 63.0 63.0 63.0 63.0

PJ. (psi) 4.0 6.0 10.0 14.0 16.0 18.0

~p (psi) 2.0 4.0 6.0 8.0 10.0 ll.25


LBS WATER 100 100 100 100 100 100

TIME (sec) 69.70 49-90 40.92 35-38 32.10 30.68

LINE TEMP (•F) 63.5 63.0 63.0 63.0 63.0 63.0

~ (psi) 4.0 6.0 10.0 14-0 16.0 18.0

AP (psi) 2.0 4.0 6.0 8.0 10.25 11.25


LBS WATER 100 100 100 100 100 100

TUm (sec) 70.55 50.10 u.os 35-50 32.00 30.88

LINE TIDfP (•F) 63.5 63.0 63.0 63.0 63.0 63.0

p1 (psi) 4.0 6.0 10.0 14.0 16.0 18.0

bP (psi) 2.0 4.0 6.0 8.25 10.25 ll.OO


LBS \'lATER 100 100 100 100 100 100

TDiE (sec) 70.48 49.90 41.65 35.00 31.68 30.80

50.

SAMPLE CALCULA. TION

Data taken from Table XIII -- D2 = o.6005tt, e ::::. 0, Run no. 1.

66.10 + 61.63 + 65.83 t = avg

6P -avg-

3

2.25 + 2.25 T 2.25

3

T = avg 67.0 T 67.0 + 67.0

3

• w =

Now:

K =

=

100

64.52

o.691

= 1.550 lbsm I sec

• w =

• w

= 64.52 seconds

= 2.25 psi

1.550

from which the following can be found from tables:

p = 62.3 lbsm 1 ft3

jU = o.0006S lbs I ft-sec m

1.550 Re 15.28 :: ::: 15.28

D2 o.0006S (o.6005) ~

= 58,000

These values of K and Re will be found plotted on Figures 7 and 8.

ACTUAL PRESSURE (psi)

30.0

20.0

ACTUAL PRESSURE (psi)

~o.o

0

51.

~o.o

s.o

0 s.o 10.0

GAGE READING (psi)

FIGURE 1 GAGE CALIBRATION CURVE- 1: 10 psi DIFFEREliTIAL. GAGE

i I I I I ' ' '

-· ' ' I I I

II l I I I 1 ! I -+--+--! I I I I

I I T r ' I I I I

I I I I I i I I I I

' I I I I I -++ I I I I I I ~ ' ' ' ' I I : I I I 1_ I I

' I I I I ·/f I I i

'+·~: I ' I I I __ j /. I I I _ _:_! I I I I

I I I l_l I I ~~

1 : I '

' I I I I 7 !

-·---+-+ I i I I I 'T i I ~J ----1-~--! I W---W-- ----::/ I i I I ' I ' I I I 1 0 ' r I i I ! H++ I

-+~ 10- L-h r-+~~+-i ;--:-:n-

t-'-; -t---+-I I I ~- +i' , , I -+-Lt- -r-1-t-- -;--t- I I I=-1=R-i- --t-• .- I 1-1-' 11- 1- -+---+ I

!--r--1-h-- ' I T -· 11 t- -+-, -t ' ' I [.;7'1 I ~~:

I I ' ' I I~ ~ I '

I I I

~--H- ' I r--t-H+ :l I i ' I I 1-f-r-t- -h1 i I I

' I

--r+-1± I I --L-+- 'T I

I I I I

+-H--: -;k~ I I ·IT I I 1---L ' ' I ~ i I I I ' I I I 1 I

1---"--+-' I I / I i T I ! I ! I f I I i;-4 I i ' I I I

' ' I 1 I i I ' '

I

I I I ' I '/ I I ' I r I ' ' I :

L/ I I I I , r I I I I

I. i/ I I I ' I I ; ! I I

i/ I i ' I I I I

t l '/: ' I I ! i ' I J I I i

I i t+t- --1- ! I '/: I i I I I I I

IV l ~ _j _j I I I I ~ -tJ J I l I

~o.o 20.0 30.0

GAGE READING (psi)

FIGURE 2 GAGE CALIBRATION CURVE "!: 30 psi DIFFERENTIAL GAGE

6 I 0

~

=fEfPiP++=t+H~~;fHfH±i=±±tii:~{jR=+~~H==H±1 r 1 - 1 1 1 ' , ~ , ,--·-::_ r 1 , 1 1 , 1 ' 1 1 I ·-tt---o • 70 1 I ~r-.)- l I ' I I I I I i ·. I -~ i --t++ _.__ "" I 111 11 i •11 1 lt+---!-A..~L___j___j. I I I i l ; I ! I i I I r- 1 i -~ r:--.~. I ~ • .... , I ~ I I • 1 1 I - j_ .. i I I - -·"". ·---·- 'T I i I I ! . Oo65 1- T + _ , I I : : :. •-· -;--C :_w_ \o_C , , • I < ~ · : · .

J ! - 1 i---+-+ '-- ~ : ~:- r-:--":- ;.. '\:J A -- . -·- •. +--- ... -- --· TTt ~- ~-~+h--ili__ ..... ,&..-.ioo- ·- t .,.._, • - .......

o.60 i

o.50

o.45

. 20' 40 60

FIGURE 3 - FLOW COEFFICIENTS FOR SHARP EOOED ORIFICE PLATES IN A 111 LINE, ECCENTRICITY - 0

(AT REDUCED VERTICAL SCALE)

C!J - D2 • o.J002" e. - D2 = o.4000"

G - ~ = o.5013" - D2 "' o.6005" •

• I ' 80 100 120 140

REYNOLDS NUMBER (in 1000's)

160

~ •

ti § 0

~

• 1 1 1 1 1 1 1 1 1 l+ii. -l-t--+~. ~~- 1 1 1 i 11-"---'-+Ln~i--; I i i I W :Lilillll H·t-ti+!t-:-+ 1-~ r+tt-+--H·t-+-n-7~_-1-r-rr · I I ' i i I I - I I I I ' I - -~ - ~ -- -- -- - - - - ' ' - ' - • I I I - I - - '

I I I I I I I I I I I +-+-+-++-H-+H---H--t-t-+-+++--t-t~-t++t+t±tj_-~_tl I I I 1+++-+-1---H-l-----+~ I ~l:i', .0 I ,~ ~ -~ -I ~ + _,_;_ H-t-' l 1 "' ' ,+-~~ •l' , 1

~1 ,_._ r -0 - ~ ~ ' ·~ '-:-- ~ -~ . I :-'-+- ~ ,_J .f!1 : 1 - ! l ~-~- - 1---1-- I I I .

+-+~

~TTl I : t! I I I Tllt~ -l t- I ' ·-~,- ; ·--·-

- ~ 1------f---' -1--- l[j_[ --1-LI-L .. +--++ r +~j- -r-:= ~i~-j[_~-j - ~ ~~H~ I ' '

! I It 'T, _ 1 ~!] II I I I I I I I I I I H--++++++- --t-+-+-++++++H I I I I I I I I I-t I I I I H-t+ t~-

T I I! J-+- -·- ~t-+-+- ±H--I--~------- ~~-~-~ --j ~~ ~-~ , I • IT 1- T • 1---+- 1 l t-+- · · -- t-'-1·--. I ' ' - ,-• - ~ • H-;- L 1 ' ..0 ' : , i l (- _L I , • I I I I - ·- :

0 • ' 1- ~ ~ I > I H-1- 1- ~ I '

·: ~- I 1 ,

IT ' ' .• I

~ ~ .. i- .

I I I 1 1 i I 1- - r+ 1+H ~i-r ! r, 1• I

1-·-, !--1--+-1 ! L.L.I 1--:--+- +· 1-

H-+--+-- _,_ ~ ---+- =r.TJJ 1 r -r : i ; 1 I 1 , :! --~··! ·t :- t ~ !

I - --~-- -+r- ___ , ' , .. --! • I L' I I I I ' ' . I --- ~ ---j- - --!--_,_-,_+_ -·-r, .

; I ' I ' . I I I

.-1--rt~~w +t Lf , - .

I I - ~-+-- I -t- ·t·J --r~t t r T i -j 1

N I I I _j I I ! I ' I ' ' ' ..0 I H- ~ _ _.__ --1 - ~ • - -l- ; j·;

• I 1 ' l t· --1---- ---j~T-t+ +f- --i o - - _ -1-----1- - -·~r--· , __ , __ ! , I ' I t;::_: I I I I : --+--:---r I "I · . 1---1-- ___ . , ..:. 'l!/'J. .• , , - ' • · 1 1 ~r.y 1 1 , , e - *"/__.L___

_ • , ; , m I • -;..._ 1 , , 1 _ ~ • .:.. : , ~ 1

1 , ~t~r --- --- ~~TT 1 'I i ~ · - ·"iT,_ 1 1 ~ · ·il ~ ~·~-~____;_~ 14i- i-t-1_-i' · ···;···-: 1--;-t··t~r •l[fB l:f , 1 11 ~~t~4 1 r 1 1 1 r 1 1 ·rT ";'i -:t~ it' _ _, _ ~~.+----- 1 -r-L-t !-:-+_j --'---t-Tf r--t- - - II I I 1 1 T 1 I I f l 1 1 ~- . 0 - -+ 1 ;- 1 T , 1 I '- I I I I , :r T I I ·

il-~ ' ' ' I , I • , . _ , '

...c IF ., iE . I , ·x' l L • .. : I.:...'-,~·--_+ --H !---+- -++- ~--i---+t+--",''~-r---+--1 i· .,,,,-H-i t-r, 'M--;-• ~-+-~--= tl' -. . . . ~ ' . --. --- . -- ' ' ' ' I ]'_ - -f-tJ- 1 11+1 ~ -A TT ll I I I I ri I I I I I I I I I I I I I I I I . tr;r: L Y .c .•.•.

0 '- f-t+ -f.~~ - -t-· m· -- .... ": I r T . . . . i I I 1 r i i "i I , ~ I ii t' ' ! ' -~-,---+ •. r.

" 1 1?n j 121:: -~ -t-t~ iiJJJIJ IJll JJll lllJ ll-l.Jllll Jll-l. JJll • 1 I • 1 • I ' · · !1 ~ · ~e 1 J P-- 1111111111111111 I 1-t±tt_I_ 1 111 H±t _J • , . _ lllll11$r~""' 111 ' ;;_..~i-+- +- J~J_j J j_J_U J ~ I . - ,_, L[ 1 I I-f I t--'- Lt--1 _, --r-.

lR.It ilTTl~-H--+ ,+ ~ . - '' ' '· 1

• ·!. I

•~ '+ I I , FIGURE 4 - FIDW COEFFICIENTS FOR SHARP EOOED ORIFICE PlATES IN A 111 LINE, DIAMETER-o,J00211 •

0 --~1 ~1--- ~--1 I • c.l -1-----t-- - '

r -Ll-t-!t+-H-1--.R fMt:ttl--ututttt1 IIIII Hlttt1tt-t ' -·-1

'•' ,, e =- 2/3 e = 1

0 ++-H-H-+t-f--t-t-1 ~t +l+t-t-t-t-t-t~t-i t-+i--t-. I I ' I ' I ' ' ' ' I ' .,-- I

3 4 5 6 7

~ •

~ a ~ ~ 0 o;.. t> ~

l-+

-·-nmtmt=t~mtHmtm·ttlwHnBn*JllEE3-Ift~~it111tMttttJttt11~~#+1-- -) : ll=~-~--c~n~~+~t=;-r~-: C[:f-1 I I I I I I I I I I I I I I I I I I

-+--+-+-+ I I i I I I I t--t--~ -~-

I 1111111111 mmffi-11111 H rrnrn-m IIIII 00~-ti!Utlf~=rtl+!tl

-i-; -t-

11111111! lftllllllllltlllllllllllllllllllllllllllllllllll#tiL~Lti~W .~f:Jt!Eh +iH -: .:.~-+- -,-~T+ ----;-; -R· .-~

• I ! ' ' ' ' I t I

l 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 I I I I I I I I I I I I I I I I I I I I I I I I I I I I I 1-+mt:ttti.U~r= : ~~i=~~~-:_T-tl ~itrr 1.::rr j t+-+-+- -i+f+H-H-r -:+i-t· --t-il7

~1111111111111111111111 tl IIIIIUIIIII11lllllllllllllliiJIIIITl--~1t-Hlf 1 1 1 1 1 IT r t rt 111 1 l~ l TTTTT 1 1TT N1' I iT f" T TT TT I 1 TT

1 1 TT

1 -<> f-l'' lTI!ITl!ITTI -j . o _lw .1=<' I I : l Tt +rift !!u i -' J ~-'-'!:;~~~Ill' !-I~IDJ Di ~i-,:11 I I,: ~ ... i-~ Lt~hl+!(i-l+t +~H -1-l· 0! -rt', , , ' ' r·i t·ft+t i ·~ . ' . ~r .. _,J_, '.Ui. ti~J; ·-·- J -- T .~ T~Cff'f t~lre" I,.J.j-L± h

4 ~ i ~' tit ·1 ·" - :-r· Lli };! f..' :j:J j+Lf-i~ ~: ~ ~ .; 1 · -~ ~~; T"~~~ J:litt-~ -tT11 :;::..L, f-lr~,;blt=J1111l.li- I T n ---~- . - ! , ~~L t:_i·_r l L ' ,_, ! ·T-'_ ~- .i '!?' I ' ~ n . !1-ft+-4 '+H+- t ~ I 11• ++1 ---· t l ~T;··-

• H+ e~ t1,' · .IJ'c..c~ • '".

H I_·~ ,_...,.., i+l_il I IT -!-!I --·- . '' ~~ I' 0 @FfJ~-+= 1- --+"'1 :;:::.T i-· ~~ • I I [I+ I I; i·L - '• ' . . --. ·.j. _:o-----I [-'_/ -LC ~ ' ' !' r -f "-+ '·".. i l -•- ' -(, i x+.•jj p T l li - =--"'I~<" (lt I +-H- ~ T L t T I .G:-r I,.. . ~~ I .

I ;'"I I ' I I I I I + ..... ~11~ i I I I I li 1 I 1-+- +l I I ' ' ' ' ...

I I I I . ' ~ + -+ I T i- il .. LU ,r:~ttt:~ ~ L H+n:ttJt'lll ,_ : , -"t •~ " J, 1 : LJ ~ ill±f± #it t~1 i:ti -~ I J J 12[ Jlitr:J+-!-..,Jtft::F-""=Li>T-'i~ ). H I ' I . ! I T Tt I ,~-,-: -~ !j ' ' : i ;:,ttl

! I 1 I -;'j/ r>fi-+-H . ·-o~c!J II I ITTT ' -.-++- --t <011 ·~ I L.lt =t 1-., U ' '

lot\ ·t-~-·- -H-II'l~~--- _:_!-t?'t~r+ -~

FIGURE 5 - FLO~·T COEFFICIDITS FOR SHARP EOOED ORIFICE PLATES IN A 1" LDlli1 DIAMETER-o.4000"

0 t~~~1 ~ ~~~~~~ =f:~Ct .:.HE J:t- ~- G> - e ; 0 -1- - e ; 2/3 , . tlT !/ i I I & - e :a 1/3 '•' - e = 1

++.-i/' -t-h--t- ~ttJ- I I - / ' ~J-t"?"; -L -h-V -+ -- ·t 1-H-- ~-,4~- r--· r- +--r--1- - - I I • T I t

40 50 6o 70 so 90 100 no 120

REYNOLDS NUMBER (in 1000'~)

~ •

N 0

E ~ 0

~

,- ·r-r~~;~~-"-j:-J_~--~1: ;-~iiTT~Tl ;--rt-nTriltTitiiTi~~jiTT--:itr;tt-JTi-r-1 r i 1-

I ' • ! . I ' , j ' · i t' 1' j • I I • ~-- ·i _;_tT'- tj'-1 - +r t+ ;- · ··t· l +·-t ~p -l ~~~ m ~ ~ mf li- lff+. mO ii··t-11 J~ ~-- ±J l

~ ~-- - ~t- t ~- 1 n ·r r- . -Tr , +- I ~d ~ 1 L ·- -~ --;- tt- +1+~- H~H + ++_j 0 ~-i- +--+. .:. -"-' -- .. t~r-~,-~- _; --r-~. -·- +++t: ~~~r-

: : I I ' f ' i I I ' ' ..:...+ ·-rl t -: n· ·1 rt- -r ·; ---:- , , , ~ ' -i·rr ; · :-t-;-- t- t t ·j ·--~ ·; ... _:...: e ·: l1 ~

J I

.I I ' I

1lF+t ~ · -~ I I ! ; ~~-- T ' ' ' ~ • -+-

.J

I .

j ! ' I I 1 , ~ t- ~ • ~ ~ 1~~ -~ ; t +h- l t -t + ! + l l 1' i + , . . •. ; • • • • ·• .• + ~t -·~ t ·i ' J..! . - ~! . I L.

. ~- ./ '\ ,-+ "t + +-~~ • • • • ' • ' !I' . '+f+' I I I: ; • -- _,..,......_.. __ •·. -~ .. !1. 4 I ' I' I: ·~ ~ lt LL ~•~-

• ~I I

0 7 ~ --·- -·· ...---

W1., ''I' , 1 · I' Cl - . ~--; ~ '. : . .. .. -- ~-.~ j- -r I i- ; - I • .

-Jii -~®;_:__ : : :_:~ ' : -~ : I I I i ' : I I ' I I i ' -+--t-t- .,. ·r~--~- -~ · -+-+ ~ + ~~--r-r- I--~--.. ··

. ' I i ' ' I i ' I i I I ! i I ~

Tft~f- _ 1 -t-J l J-f++- _p-iT~~ : .... ~ c-U-4-.+-1--t-J-++ ~-+'-4[Eg' +~ ++-. _LL _J_: I , -'-r ~ , 1.. ... . . . , !T. 1 L-L-~~~-t+rrn-;-~-t-·-- ~~-+·Ill'·. D. I __ -:•~'!--r···~-~-t--+T •-:-__; ____ , 1 1 · 1 .'· 1 I ;l=f· _ 1~~ -Lt+. ~ 1 1 1 1 .~,·-~-- ::q_ ·-~ ~- 1 '. 1 1 -r-~~ I : _, -·f· J.~- _j._1_tl-+- _ LL.:-~- .. 1 1! l.JT 1 L -H' ~+1---+-fe--L• ~.~ .;_,._,;_, ! .. : _:~J~_:___;.~.-~ ·-i-J...t- .J >--1

- L~H~f~t--J-+++J -~ oi . 1 1 1 1 1 , 1 1 1,, 1 1 1 I 1 .,..,., ~ --- . I • 1 1 , 1 1 'T I

~" i ' .. I fll R=fft' I i i HJ ''.>"" I' I I I.' 'I ! I ! I I I ~ -+-+-+-+1-l m=l I I t- -~ . ~.~c-t.i '-t--t-··-· ! ....... ,-:-.- ................ ; ; .. ~t:·-:. ~-r-t"',.....,- T l . T ir-·+-'-.1· -~-.·-~ .... · .... r·· + o \ -t - ·t ,:-, crr:::c+~~·~i· ~-~~ ~:---:--;- -~rr·: 1 f~ , , 1 1_.±±~'- ·:· · · ·- ~.., : ! ,,- 1- I I 11' ~.r·: ,-~+1--rl, ... tr TT I i! I TT-r-·· T ; ±:t I ~--~~· ~- --·--;-·-·-• .)....,... ~ -+-l · r I I I I j )-- ' ~·- -+- t- ~r-+- .. · ·• ... · ,. · ' I I I ' ' ---· i ' I . i 11 11 . 1 ~~: I . I I I • '

' '

T :ni' ,qm-, . __ ._ . +=Lri- __ I: ~ ; I -w~~-~~~ too·_;___!_i I ~-~++-~t-r- ;~ I I ' . --H-l-- -~+-- - -T' +~-; . 1 -rr: 1, t: . : , .

1- ' ' ' 1 i_[I"~T i_L, ~~. ' i I l-t 11 i I JII i IIi .u f t±fll' Lt-+fUJJ ___ H ,_; :-~ .l . • I I L ~~ rt~t-l_l I~-.--~+ J_ __ •. ' ., I. ' . I i ' I I I I jj__JJ + l ~_J _.~Ll! ... !.-1..! : . • . I

•TTTT · rr 1 1 1 · I ~ , 1 1 : 1 1 : _J •

. 1 .

~·

l. ' . .

_ .. - .. -l.-

'

+- l I d.:JT ~-~ i I I : 1 I ! I I ! I

co i 1 i 1 ' 1 ' ,_ v_ . . . I : , , 1 , 1 , ~ ! ~ 1 I I ! l.t'\ 1 1 1 i _j_ I _ _! /_ . -r _;---"--...,--~ J 1 f -i~ ! I i ! ...l.....L.L. !-- -+-~ • ·,·W' L IT 7;:::f1I:I ' I ! I I I I I I I ITT"' I I I I _j_ 0. ~· -~· . ...., :·,1 Ill I /1 I I I I I J_ - ---1.. -+-\- _!. I I I... J_L .. ~-r-- --1--

-+-l..--f.-.+- -- -·1 •. ·-t · -~ l-t--f~ -;-.; ~-·~ 1 1 ..L,.. ~-;i--- 1-i~r--r- t-,...-·-,~ - ·

FIGURE 6 - FLOW COEFFICIENTS FOR SHARP EDGED ORIFICE PLATES IN A 111 LINE, DIAMETER- o!501''

----r--:, \ Jl t••t fTTI I II, 1

~

Jl i I,, I .j: j, ---r-T:: I• I

R=8 ' /I ! I ; I I i '±±:' I I I ' ; i+ ' i I ! ' i

IJ1?r-i+~LH=F -~n=r:r= ~t=h--f.- hr=tlli:-r~t -q:,:: +-'=~m+~~--1~~ j ;-t)-rTTI ·- H- ~- -t .. r---;--r- 1 1 1 J 1 r+- ~ : ; , •. _..._ ,-·-- -~ -t--r. t- , ...... _..., __ ,....,... , -r-t-+-t--- -+ --t-~- ~ I_.._ -·

~ ' . ! ' ' ' ; I . 'I T

s6 66 76 so J

110

0 e = 0 e ~ 1/3

' -·-' ~< • 0

96 1(~0

e c: 2/3 e = 1

I

120

REYNOLDS Nm.ffiER {in lOOO~s)

130

\It \It •

~ ~

~ 0

~

0 d±i ±it . ; I ' . ~~+++ - ' - - - --- ,. _,_.._, .. -· . . ·--· . • ·-· . ; • . ~ ·- +-' -j- . _;~~-~;i-~-4-~-+~ m=·m· . ~._,_,,; m~•~M- i , ; , I I I .-H-n-t ++· . I ,,, +- . _ ~t _- ~ ~~ ::::= =r Ll jJ:IT __ ,_,_, __ . --1-~ --· _,_,._ -·----1 -· -· - - - - .J ~-~ ·-cn_L-r I 4 ::::., - -+- - :-+ -; -~ : . :-~- LT~ - -: ; . --r-t-t-t-:r:m:r - t . (.) ·- iii-. I I ~- _ _ _ _ _ _ _ _ ft i ! I • · ' ' · ' i ; I

I !

i I' I ' . :~:~ -;_ -i -[ .;.: -~- -. :--t , .. -·--·-· --·-- -L-'---r'-- ·. I ( i ( I i . '

·r ... .... .;. l •

~ . : .

-· - --- - _ -__ -- -- '--- ·1 __ --~--:- -r_·_t--t-_- ~T -~- ]-- -_- - f-'-'-- !-+- . • . ___ · • __ -_-- __ ___ -'~-t i L~- 1 L ~~- I I 4 I I : ' I I M' . { i . . . - - - - - --~------4-,------- ------ f- ++-- ·1t I __ -rJ- ---- - -r-- r-~- 1-t-L'--+-: 1-i- : .. ;-+. ;_ ___ ,_ ;_,, _ - _- ___ - _ : = - -- - · -t _+xrl J= ~ _ - " _ Y- -l-~- ~- -l--P + -:-r---r- .: 1 L ; ; 1

('l

1 ~r,'-- 11 -t f I t . , I , t -- I ! I I 4 ,_ --1- Tn-:- ___ i_ . _ _ . . .. _ 1 . .

..cJ rtltll 1 1! I I I 'J.'' I _[111 i' , I. • - c--y+-+-t-- -T -- r~- T -- -L+ ·tt - Hi- -rt - 1 - 1 H- -- - -r- ++-r_--~- --~r-_-: ~ · , -· • , -· -0 - - H-- -' -1- - -- . -~- - - +-- - - f-1- _ _,_ .. ~ I__ ' ' ' . . . ' I I ' =-Ltif- ~ -t-- q==~=- fm *==---~·Jr_tb= =- -t- f-1- _l__- - '--· B_L- -+H- tfT.rr T:=:-r.:: --:=:=:-. , .. ·--r- ; ;· r·] I I 'H I i ±_· I J::: I I ' I T II i ' I ' ' i . i ' ' . • ~ ··-· ·- ~-,-· -·

111 1 · - ~- - - · - T 1 -~ - 1 : 1 t ·r- I ·-r- r· 1 · · · ·

1 +~-- r-1f1 ' l f·l- ·t· -- ·t= +l{=- - lltH -f_- +1- +H : I I + ~ -t -r- T -+-- - . - -· - + I -ri - H-i_# '-- --y-1 - -r • - .... - . - - - . -+- - - ..J...L .l-1--+--+-+- - . -I I I I I ' I I I I I I I I

0 i- i ,-;·r ·1 r- ·t --- -- t· -~~1- '-~ ~- -t-,;--r- -r-d-~ Tt 1 -

..cJ .111 ,;;,I fliT ll'' :ill II I I • ·.--r· r· .• r· )_(_ . r··t-1 -+- -t-+ ·r·+--r t ( ri--+j_j·'---r-·. 0 ' I ! I I ' : I . 1 ' j I I . t r i r- i ·- -- - · · t -·- -· - - -i 1 : -~ ·t- -r '1- t ' -·-·-~ r ·1 +tJ .. lt [ ~. 1 +H- ···[- --ti- ·r-r_ ~--·- Tt r -t-f i4~f---l-l L I . . • . ' r ·r - c! i T j t ' ' .. - I_ - ,. --t --r-i -+ i - ·•

: I 1 • i I I ~ I 1 1 I I 1 • ' • I l 1 . I

T t! Ill! 111 ,.li' '•,1 l:it :li

FIGURE 7 - FW.'l COEFFICIENTS FOR SHARP EDGED ORIFICE PLATES m A 111 LINE, DIAMETER-o.600511

@ e = 0 ~ e = 1/3

I -·-1 '•' ~'

e = 2/3 e = 1

~· • -· ........ ·-·-·-·· • ... ·-•. ·- ·-·-· .. ·-··' I

4 56 66 76 sd 9o 100 T no 120

REYNOLDS NUHBER (in lOOOts)

~ •

§ ~ ~ u

~

--1-+--+±fliill ifi1f"-0J ~-H-·-j';; ;hTtiti;·;~-~-· FIGURE S - FLOW COEFFICIENTS FOR SHARP EDGED ORIFICE PLATES IN A 1". LINE, ECCENTRICITY - 0

0 - D2 = o.3002" b:. - D2 = o.4000"

m ~

- D2: o.5013" - D2 :. o.6005"

-t I I I I 1-H-1-++-+H-H-t-t-t·t-t-t+i t--H·"i-t I i I I I I I I I I I i-t-t-i·i·t-t-t""iT"l~' : I t i : i I : : I ' t I . i -P-1-++11 I I I 1-H-H-1 ~:=:=:=t=U-t++---H 1 I I I 1++1 I I ! I I +-+-+

t --~ . -~-- . i I

~ • ' i I I : i j I I r r • _ _ . ±f ,,~J~r'] 1111 _ ..• ,, - •. • · - ....).._ -'--+-+- - - -- -, -• • I , "i -~--:-;- ~ ·t-rr · --t-+- 1 r- -r-r- 1 . . , 1

o _ 1-_ ~---- ... __ 1 __ u_ _ . ______ , . .. . ....... , , . __ , ,....._ . ..~_ . -· .. +!-+-H- --H+ """""-Hi-+Uit- -++l±_ H-~l 1-- +:-f+~i-r -~ ,_ ., __ :_ .. ~-: . . j Ll -:H- .:. : ~ D-;=·•>•3002'--+---H---r-- · 11 =jtl-;_:- _ '--=ttf+-jr- .. 7 1 :.. -:-: 1-t-r-J -' __ -+ y .. i __ ,_ i -~ u.. ·2-: ~ -·-t ..,. 1-1-+-- J I , ,1 1 :_ +- .... , - r 1 -+ , __ , ____ ;_~-,- : -: .. .... ...... , . 111 , r .v 1 r , -I , , . I • I l 1 . . -' .. , . . . ,

IPrl --~Lt-t= -~- -.. i_J-±+ , ~ . - +_-J--UJ'i-~-m~--~t....c I tj! 1-Fm ::~-:I-FF --l il-~Ei-= _.i. L ... L.,+ L H- ------t- + ~--r~~- 1-LL~-~'~·++ «> . ''" : _J ;_ +- f-n-+-+--1-+- -!-- ------- ----·- -- -r 1-- , .... u .. ..L . , _ _;_ &1'\ ........ ·t'_' 1 , i1+! '-" +-·-t 1-....lf-r-t---~j-1--~.-l-l--l-,~-1----r+·tL ... f ......... ! ... l ......•. • ' ' ·t ' 0 40 50 66 70 00 90 100 llO 120

REYNOLDS NUHBER (in 1000's)

"' -...] •

~ 0 H

~ 0

~

::r - . - -- . - - -- .· ·-· :~ -·- , - ~-rr : 1 T I ~iTl-T-Tii- -:·-r--;--r- ~~ ;·n· . '(Oi .. ]I I i It I r-: 1·1-~' - ' . . ' ; . . ' i t+-1- ; J--h 1---h--;c..i= -·t'*t W' t' t ! --t--7--;--.-- -:·: .. ..a 1 1 1 , ! 1 1 1 11= -~~~:----- · ' 1 +-l---+ · ~-·-: .JJ .... 1_1--t ·++- X1 I • t14L -T +-t- -h-;-r '::_-: ~

• .. , . !TTl ~~~± , · , , I • • _ 'liT- -f-f-1r~ ··.- , ·++_: -'7 n2 = p.6oor --r--r--l--i 1-- 1 -- -+- - 1---r-,.-,_- • . o .. -'-++++-1-++ j ~ : : , : I , I i ++~:i-ll::- r:, ;- I I ,' :+ -;t'J :;:·

-IIIII I lllll! :::I ! I I; :I . l_ijJ ,_._0. !--H---§t---1--t--i-+- ~---=-- -~=L~;Lrl: r_I_JI t '

-+-+--f .. 1 ·~· -11-t~+f= H 1 1 r ~-~ ~-L-1- ~! ·-•--H - +--+-- -f- r- J \ 1 , j t I r rt- i--11>--+--+-+11 ' , . -H T"'' I I I~· +-- ~-.-- - -- ~-t-h- --~1-· .. ~t- ~~- 1 1 ~--=: 1- ~-: :-+~ ~~--t-t- -t-, 1 1 Ltl i--1-rtxr=r=v~ =~-~-+- -+-- --- - ~- -n -H- --,--~ . t I r~ __,. _l I lJ I + ~ • -r+ '1 t-r-..;__h .. r I fT: ' ' m-- I I l j ' ' ' i i ' ' ' '

-.o 1 ~ ~ I I' ' I ' ' I I I I ! -·-I __ -""" ~-+=i'~--- ~-l-_ ! \1 rJ ~ r ; ; ..a 1 1 , • I

1 1 1 __. 1 1 • • ' ++J ~ !--t- 1--1 _, • J_ 1-+-L . . . - . _. , • 1 -; ' ' : ··' : · · • ++- -H-~; f;.. ~,--t"j= ~ ~-t- Tit-+ t-+-r--f-t-rl--r-- H+H-1 -r-u_ . ~ i~--+~: 1 -i H-r -, :-o tt -t-t-t-'-'~ -W-1-f-L' . t r-n-· T I I I ' ,_ +•-H '-r+ 11 ~- . . , .. n-- -t-t-t-t-- 1 K_.· ·-- .-: -+-+--f--+-l-~ I 1 1 t 1 -~ 1 1 T , · · · !i-+-111 1 rr~ · · ·

- - t- t-1---- ~ ·- ..• ~ ~-r~~ ' I I I -I I I I I I I i- - r ~ . - , :tt -± - :~.: ·~l!il II I Ill I I I , /.\~~

- i- -:-~,-,-,--·; · r I ! , I ] I ] I J ·-t + -/--;- ; t ·' ~ · <e) - - -- - ---- ~ ~--; ~-~-- - I , I ! I I I i I I I -r t . T 1 • i .. . . - '

4 -t- - - r-t -· -:--;- ~-: ~ • ~~-:- ·-- t+ -H-r-: 1 - -l ' 1 H- -t -t-f---)-1-r -· ,-. · · · · ~ -.o ! . ' I ' ±I ' ' I ~ I : I ' I I I I I I D' ' ' ... 1 5013 t' ~ ' I I • _I ·--' .. :-\--+-+- --+-+--- -'-+-t-+- ·+-, ;--t--t--r-+- ~--+-•- - ---:::-~·· . j-f-f--- -1-t-- H!--t-- 1- --' .. LT:-

J ! I l I I ' I I i I ' I I I J I • I ' I I I I ' ' o 1 r- r-L~ ·--r-ro· ~- I iT'" +r-tt-~...;;.::-·-r~---· _-·- -: 2.+--+-r-J-, .. T ~~~:- rrr- JJ_l. -•·-·:-'· 1 I -[-t--1 1- -;-n--+ . Tjt~--rt·H-1- -i+t=t-+------. - ---r-·•- T . . + -h-U I -r- - 1+--+- -~ ~- ; :

f- __). I --t-_Lj_~ _L,--;- -t T l -- -·- -; i - L ..... - ·-r-t -Hj -T -~- - - - - - +- H -T -- ., ...

I ! I ' I I I ' ' I ' ' I I ' ' I I . I --.e.t. ' ' I ' ' •I ' . ' I I '

• I , I • , I , 1 1 -~--~r--.:.l-L --~ :.; : __ u :: .. l •• : , 1 ' 1 I+ I . '-~ I I l__j_ _l I I ' I ' ' -+--r--t- -'--+--+--t___,__,_,~ . I r---+--' -,-r - -j- -t I • i- rrt i I '_l J ' I -L+..l_L s--+"""!'-:-=a· 1--. I • I . : . - ; : - - - . t----tn -t-t-t-r- Ttil_ ' -H ! I I _ll r T I '. -++' --- ·q=· ,\!I ·--·--;.--r - .... t-+--1-- 1-1 - -mi -rt--n-- 1 II] I I -;_~ I _ _ .L!.- --1-l-· _l1 -~..l....!- ~-I-·

. ]!)

N l · · -- ··--til 1 · I 1 ~ n 1 1 1 1 . ,,, _, n J.Ml' 1tt , 1 1 1 1 1 1 , I

..0 I I I ' : I ttm ' ' I I '-~-' ,• IT ' ' I + I ' ' • I - - -' t:IJTI t- h-++7"" !.-+- I r ++ i •• ' .1£ __ 1 _· _}__t- 1 til I++ I+ "1r_LLL J~-:-. 0 I +-LL ,--t- --r--i-+--+-11'. ~L . . I I I 11 ' I I ' ' i i r c- r-- Iii ITT I IT.]_ -~- . . 1~--tl-+- --1----,--+-t-- -t-r--- ·-·;_-·_·~ -·. ~ .. r ~ II tl II~ I ., ,, I

t- ' L r--r- f"l i j__' ' I : I I I .L r~ - - ... - H--+-- , .. 1,...,._ ----~ I -·--;--r-----+ t·~ •· . ---c- ·- . i - ·• : . rt- 1 r- · - t7' . 1 1 , 1 : • ~ · 1 • , 1 1 1 r-- . 1 • 1 , --· . __

• 1 , ' ' • ~ I ~ ~-~~- '-~· '-i--t-~ _j~- -++H--~ . -- ..... ;_,: . -fjj-·-:.~-·;-·- f"""""".·: :-r·r-J:::: --1-IJ..i __ :t'_j__['( _L[t. 1. t:J.~..L.I:t---..;_w··· ~'--•---.-. ib.'LL-:--~.-~-----· ~-- . : ... ~ -- - -- ... .. ·-·--,-........._,__ f- 1-- t- -t I i : I ' I I Lc I 1 I ! I I I Cl. I ' i

I I -~ 1 , J ,_, -- ..... ·•- -~- · .,;.._ _L .. , __ ; -•- -· -;--· "-' .... • --·- --'----r----- ·:· ·~:r. !--- · · ---- -· -- ---- --, : ' I I I - . L " ' I I I ' I - ' ' 1.-t-t--•f=t_t--t- - r- · - 1 ~ 1 . _ _ , · 1 .... n2 . --- o. 300~ -· · 1 --l---+--t-+~ r--..:.. . . . - - .. . r--:-Oii--· ~--- +-t- --+-+-. ve~ ~ ·-·-:-------- -;--TiT I , ~~ • . , , , , 1 I 1 . 1 i 1 I I I I I---

_,.. I I ' ' ' I ' ' ' ' ' I I I I i I i I + 1..1 : t-t' I ' --_, I I I • I I ' ' ' I I ' ·-- . ' ' I H '. ~- i -l. . -:-- ~--- • - -· :-, - • • • _.1. ~ -·--· -- -·+--... ~--- -+---------- ' I I t I I I L I 1 ~ I •

] ' .. '. -Yr .-~. . , , L : 'LL -~-~- 1 -++~ ·--'-·--- ..... L.... .-:!:IT ·- .LL, __ L .... -. . . . ... I . O '-I--f- 0··~ _,r, ··--+--·- . ·--,-1 - --,-::j:II '1 1 I , I I ~··

r r : 1 . , 1 1 1 • • • ----i-- • · -+- · r r-f-t--t - r-· --,-·-' -r-;·-t --j----;· , ...,-- 1 1 · 1 1 1 1 ' -;- ; ' "t' : "t: ~+ ' :: ; · : ~~ ->-r -n-FF, I FIGURE 9 - FLOH COEFFicmrrs FOR SHARP EOOED ~~.~t Jyrl~}~ ~~--~~j-1~ :£8i : ~.-+~- +} j -l T +ir. ORITICE PLATES IN A 111 LINE, ECCbiTRICITY-1/3

1 I I ' i -t l ' -:--r- -~LLLH-.L -L '-!--1-- .J- --,-!--+-- -.L.J+-~ . ~-- ~--- . ·- __ , __ j_. -- ·-+-+-+- I T i I I I I I I I i I I I VJ i I I I I I ' ' ' I ! I ' . D 3002" D 501

1 1 , 1 : i 1 _J l. j .J-.U-' , I I I I ~-; H-t--. -+- _ t-f--+- -±! . G,) - 2 : Oe t!) -- 2 : Oe 3" 0 ~TJ _~1:j_[r'=Lrl·; .. ·f·f-t-_+-t- -1-t--4- ! I ~=~b-H. J-it-fr I i _;_J_;_~ ~ -- D2 ~ o.4000" <:> - D2 = o.600511 r'- ---+ J_ L I t --! j t • --r .. L +-H +- -· . ! ' fl I J 1 ! .

' ' ~ I 1 -f ' I I I I ; ~~-- - . - . ---- . -~ - , ... --~ -t-+- . -·--·--·~ ·-~--r--~--r- r-~ ~··1 .-~~-r- -. · · :. -·~ 1 1 1 1 1 ---------------. •

. • . .I ~ .{ 70 sO 90 100 110


\1'1 0) •

fi ~ ~ u

~

t :--r · -+-+++--t-H-H--I~ <:J--- ---,=~ ~-~_;__._H.l1 · r~~~1 ·mm,m 111111it~--~--~~-t+l jln-· j- , ·, · -~- - ' LL _ _J I I - _J__ - - - ·- - l - -L -- -t -I-t , - ; - • . •

1 1 1 1 ' ! 1 1 1 1 1 -H""i ~ LJ \-- 1 1~ t-~l~, .~ -1..- --1-- T lt -r f-!-: i ' I i · •• l . I I . ~~m~=1:llitEarn~ li+j--., i p-1 l --

'ill II! II H::tttt:t:llb1~~J~: ~J-tt+_tttt_e_=~_____:~ ~~ ill~ hiT l· 1 \,£)

~ I jj~ -+-+++++-+ H-H I I I I I t-+-H-t-t-+-+~ff~t . i_.__: •. -\ j lj_j __ -- --f-1-i{ ~-~-Lt- -~~~±· _LJ_I+~--1-! ' ' - ~ ; -. -t j - -, - --++,- -i -- -- ~j-1_ h . ! : ' - - ' ·-- e- - :-+ -- - -r. ,_ -r- ··-t·i-+-t- t-t· ' • ; =tllU illllt!W:W:11111ilt+1+1=1- ~I + ' tit ll~ i + i I I i ; ' ; : '

~- -1-+- -~1---t- -t-t-t--+-1-++-~-+--+--'---41--+~~-L ; I 1 ~ . ' ' . • • - I I I I H-T+. + --1-H- ' -t ~~t-+-k.::f -· --_f -_ \ J f ; --~.~ : -~- .. _ , . J , .' ..:t r-+-- f- 1 r I i ~;....· · · · - - - , . 1•- -t-+-+- -~~~ __ ,_--~ lL,.jti t;~: , ~. :·: : : ~ : '-D I ' , I ' , ,__ . ' • - -r- -- - - - - -rj I . ~__.___;____ o -+-+-+-H-+-+T-~~---- ~--- - L -- .. ~ f- - - -r~-~ ·: -: : : ,r... - . ;-.;...:_· .

t-- - T- - - - ' I v I - :~ -l--l---l--+--l---l-l--l--1---l- !- ~--~ - t-- 1- - - 1- - -- - f = = = : -t = -t . • : i . . : . -

1 j ! t I. I ' ! - 1

. i

; .

j -·- -~-•-+- -- t-t-t- -- - H- fll!l- l_ i-t· + . -t H -,' 1 ; -+---+-!-+ l H-- - t- . . !'r 1- : ' : r . l 1-t+- -- ~~ ~~-- -- - 1 ·j. I " i·t T -: r ; : C'll I t I . -·+ - . . . . t-. ~ .

\,£) I t I I I ' I ' I I I • ' :~ • 1-1-1- 1 1- ' - H-- t- - - - - - ~-- .L j_l __ ~ • . • ; i i ; '

o ri t-- -- --·®-- -~ -t-'- 1-1- - --- -+-t-t- -t-- - -f- r- -tt t_J -· _j 'T - i : _; : : ' -~--~- rt+-.-t-: ;-1--1-~ D- -.o,300T2"r+- ~----~- -~- 1-- !---~ --1- _ · u_ 1 !.l! ·_ i-· -+---+--+-++-·- Lt-H--1-1- -Vt- _il2- -f·ti-~-- ., -·-~-- ·-' --_I - ' . • . I .I 1 I I · I I 1 I ,- I · -; ·: -· 1..,

""- I ! I I I , , ' I ""'\!.t -c.:~-n+-...-.-~..-1-...:_;.....t:. " ' I ® A

r-++- -- -~--1--r- -+- J.;:-::_J_Jl-=-i---l----i---+-1_1-_+-.--1-,...--l-l-~-H--{-+---~-j,-+-+--++-+--1H'--t ~ CL~~~~ · .. ~11],. , , . . , .

~-4---J-~- -~ - T T_L_IJ_ _: _ '--~ ,-1-, £--~-t- l.!..;. -, ·, .. ,_J

- ---,--:-- - f- -f- l + LL. -~ ~ i • -·-··- -i-+-Lr- ! - _j_ ;-n- -~-[ ++- ; '.; . -r+ ~ - t f---t-5~,.~,.~3-,t-, -1- f-+-~ ~~-~- ~~Ft-·-- -~---~m".~--ij'-+ -l--H -1_~+-\-r o - 2--.:~f~ffi~.). ;JI...J..=t;±t?~~-. ·' ~-.~:-+---+ 1- - f-1-~ - =lJ:J.:: =ti-Lj - ·t·;.::p

I T II/ .I .l tl -- 1-l- --- -l-----~---·---·-·-L+----1-j_ t··'-··· --t--1-+-++-+--t-+-H-++-t-t-t- .- -1 - , - - ~..,./" · · r - r 1 , r • , , , , 1 ,

' L' ' ' !"".....-: I I I I I I f--f-- -l--ll-+-+-+-1-+-+[b~ "- T fT i- -+-- I I I I

1-H-t-t-. I I I ~ T. :=r= 1.:: 1, ++++-+-.I _ l-l-:J_~~f:::])2+1 = -O•J QQ<L+-+-+-H-

((1 i H- r=w~/;-- ; , I +I : I I : I i-l·f +-+-H-';; r:~;t~~=~-~- -- -~v, ~--;~-1+T~~ :~~:-t:- ~--+ ··/:·_. ~ -~-~~: =+--in ~t·_::t'-fq~ ~Jl_[l- : :_+-!_:: -+~-H+++-f-H-t · I , l , 1//_i·~- r • 1 ! ! • • _j_

I ' ~- I' ' ' ' II +' ' i i 1 ' I 1' I j' i=i·~·iitif-t=±t=ti! ' ... - . -T : . : I f- T '· -' j -~~--- .. -- -~~- ! ' • ·±. t-tti-+,-L,._ L I - - • -- . i 40 50 60 70 80

FIGURE 10 - FLO~T COEFFICIENTS FOR SHARP EDGED ORIFICE PLATES IN A 1" LINE, ECCENTRICITY- 2/3

G> &:l

D2 -= o.J002" D2 = o.4000"

8 ~

----~~----~------~ 90 100 110

D2 ::. o. 5013" D2 : o.6005"

,··---' 120

REYNOLDS NUHBER (in 1000's)

\.11 '-()

•

~

i ~

-:t~--t+++tr-H+-t-+-i t-+ -~_;_-:f -~ t ;_ ; H+-·-H11 I i I I I I 1 ! r ,_ ~ • \!]

~ I r II -·-L+--1--r--f-+-i-d--t--:-J•--r' _;_j·j~--i--J-Ht >---,- -r---- + >--t_·_-- ----+---- 1-l~~-- ;-:·r'--·_:IT 0 JJJJ I I I I ____,_ ___ ,_ J_ -r-l- _J_ - -f- -_ -• f- -f--r-- -- I - H-- --- -1 ~-- --1-1 -t·-f- ---,- --+ 'I ' I 1 ' 111 ' ' 1 1 1 , '

f-t- _L f--- - - . - -- -~ i-L -+-j~t- -1, 1 +- ; i- l -f-- j -~- - H-+--- , -- -r- -j :- f --; •· 1 1 1 1 1 , -r 4 ++±± +H-;- _-t t -d 1-tlF ·- 1 -H- ±-r ·'-~~-~- f- --r· :-nHr Ht , .. ·•

h..

11-ul I '+. __ LJ_L{_ I 1-tJ . . I J i J l- ±±r+ -H _ I LL I I I I : : i I I

--++-t-----t-t-t-----t+-f _:_- l =H-=tt -H~-Y_ -~ i: _i ___ : lJ ~~---t ±i±± __ -: - ~~lJ_L :tff+=H·+ -H=i+-u_ ±tli=~FTn.++- -! u_,~- J;.-1: o 1-H- _)+1~ ~---~-- t.IJ+=r-~~-:-~q+l+H f- 1 -f=tty-n~!~-o.3oo~n-:~,q=- _L__ -+f-+-+1--fT- T-·-:-; t+: ·-·-· ~,... -H- ® ' ! ' I I - _,__ I ' / ... ' ' ' ' I I I I I I I J I i II : : I . : -...., ' I ' ' ~ ' ' I I I I I I ' ;~&'' ' - -· : - ___ ;_,_ _ro:-'--' -·-·----r -· t -!---_ -~ ' '-·- ., . ..,.. ..•• , -- ~ •• ° C+-i :fi~ll :1% :;n;~ rll~~~F~;fH t• . . . . . . . .... ·~c._... -·

' r-- t---- w-+-: V, __ t+ L -t +:-f ~+t- f--f-- I f-- ;--+ Ll +_ : 1-i-i ~-+--'--t j ' I

+- ,_ _:-s . L -l! -·-t- -n-H- # +-- r--1-++ J~ ~ 1-t-t----+-1-++-+-+--r-- -~ I , ..., l~ - ---r--- _,____ t '- - -t--+-+-w 1-t-t- - t- - .. . 1 l l ' I I I 1 : I I I I I I ; '

~ I I I ' I : ; ,~: _f'- __ :- (_: '-- l 11 II' 1- - + +t·.L· -! o -t-t- ·T ,_%; ; : 1 l L_- _L1 - ~-~-.Il -~_-r- - -t--.- -r- i- i --i---H--1 I: 1f1 11.-f-'.11--l-t---- .-tt--'--·•--·

1-t--t-_ ·i·l- . : t iTj -t 11 i t I ; I --- l; '-l- __ l_;;)t-~ -H- . ~-; r t - -· ·--t -·----~ ;--~- :--- t··t· i · r, r, ~ _: i I I . !...,t __ -

4b 50 6~ 70 sb

FIGURE 11 - FLOW COEFFICIEl'ffS FOR SHARP EOOED ORIFICE PlATES m A 111 LINE, ECCENTIUCITY - 1

G> &

9b

D2 = o.3002" D2 = o.4000"

16o

t!l 0

rio

D2 = o. 5013" D2 = o.6005"

120


~ 0 •

Documents

The eccentric orifice as a flow measuring device in small