Q~

University of Illinois

*NA^ Engineering Experiment Station

^—* Technical Memorandum No. 6 UJ

Q C/D CALIBRATION 07 IMPACT TUBES

by

Arnold Kivnick and J. W. Westwater

Issued in Conjunction with the Final Report on the Program

"Mixing of Pluid Streams"

Contract No. IborM)71(ll)

Office of Naval Research, Department of the Navy

H. ?. Johnstone, Technical Director

Urbana, Illinois

September 30, 1953

41

• Distribution List

Technical Memorandum So. 6

Copies

15 8 1

Government Agencies i • 11 i • *] i ii

ONR. Washington, Attn: Fluid Mech. Br. (Code 426) Biological Dept., Camp Detrick, Attn: Dr. J. B. Bateman

(Code 3*00) Diehl (AER-23)

, Wa8 8erman,

Dr. T Theodorsen

ONR, Boston 10, Maes, 1 ONR, New York 2 ONR, Chicago 1 OKI. San Francisco 1 CNR, Pasadena 2 ONR. F.P.O. 100, New York 1 ONR, Washington, Attn: Mechanics Div 1 BuAer, Washington, Attn: Capt. W. S. 1 BuOrd, Washington, Attn: Code Re9 3 Wright Air Dev. Cen., Dayton, Mr. L.S

Flight Res. Lab 1 Air Res. and Dev. Command, Baltimore, 1 BuAer, Washington, Attn: Mr. J. S. Attinello 1 Director, David Taylor Mod. Basin, Washington, Attn: Dr. Brode 1 Air Material Command, Dayton, Air Doc. Div (MCIDXR) 1 Ballistic Res. Lab., Aberdeen, Attn: Mr. R. H. Kent 1 Army Chemical Center, Attn: Dr. D. MacRae 1 NACA, Washington 1 NACA, Langley Aero. Lab., Langley Air Force Base, Va. 1 NACA, Ames Aero. Lab., Moffett Air Force Base, Calif. 1 NACA, Lewi6 Flight Proculsion Lab., Cleveland 1 Dr. Francis H- Clauser, Johns Hopkins Univ., Baltimore 1 Dr„ Arnold Kuethe, University of Michigan, Ann Arbor 1 Dr. Hans W. Lippmann, GAL. CIT, Pasadena 1 Dr. G. B. Schubauer, Nac'l Bur, of btas., Washington 1 Dr. R. J. Seegei*, NOL, bilvtr Spriug, Md.

Copy No.

1-15 16-23

24 ?5

?6-27 28 29

30-31 32 33 34

35-37

38 39 uo Ul U2 43 uu u5 U6 U7 hs UQ c-0

51 <S2

1 1 1 1 1 1 1 X

1 1

1 1 1 1 1 1 1 1

Universities and Research Organizations

Atlantic Res. Corp., Alexandria, Atfyi: Dr. A. C Scurlock Polytech. In3t. of Brooklyn, Prof. R. P. Harrington GAL, CIT, Pasadena, Attn: Dr. C. E. Millikin Jet. Prop. Lab., Cal. Tech., Pasadena, Attn: Librarian Urlv. of Calif., Berkeley, Attn: Dr. R. G. Folsom Cornell Aero. Lab., Buffalo, Attn: Dr. J. V. Foa Cornell Univ., School of Aero. Lng., Ithaca, Dr. W. R. Stars

Reiuirowi \z Uciv . of Del., Eirvard Univ.,

Attn: of of of of

K. Wohl Chero. Eng. Dept., Jitward, Attn: Dept. Ann. Phys. Engr. Sci=, Prof. H. W- Emmons

Illinois, Attn: Dr. H. F. Johnstone Illinois, Library Illinois, Eng. Library Iowa, Inst. Hydraulic Res., Attn: Dr.

Johns Hopkins Univ., Dept. Aero. Ing., Prof. S. Applied Pby6. Lab., Silver Spring, Attn: Supervisor,Tech. Repts. Arthur D. Little Co., Attn: Dr. P. V. Kleinschmidt MIT, Gas Turbine Lab., Attn: Prof. A. H. Shapiro MIT, Guided Missiles Coram., Attn: Supervisor, Tech. Repts.

Univ. Univ. Univ. Univ. H. Rouse

Corrsin

53 54 55 56 57 58 59 60 61 62

63 6U 65 66 67 68 69 70 71

tr

i

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5

,

CopleB

Distribution List (Cont'd)

Universities and Research Organizations

MIT, MIT, MIT, MIT, Univ Frinceton Princeton

Aero. Chem. Math. Mech. Eng. of Mich.,

Univ. Univ.

Eng. Dept., Attn: Dr. J. C. Hunaaker En/;. Dept., Attn: Prof. G. C. Williams Dept.., Attn: Dr. C. C. tin

Dept. Dept. Aero Gugg

Attn: Prof. M. , Attn: Prof.

Attn: Prof. J. H. Keenan Aerc. Eng., Attn: Prof. E.W. Conion Eng. Dept., Attn: Prof. L. Lees Jft. Prop.Lao., Attn: Prof. J.V. Charyk

J. Zacrow . A. Leighton

Copv So.

7? 73 r« 75

Stanford Univ Univ. of Texa6, Attn: Dr. M. J. Thompson UnJv. of Wichita, Aero. Eng. Dept., Attn: Mr. K Appd. Phys. Lab., Silver Spring, Attn: Dr. F.K. Pu^due Dr. T. Dr. Mr. Dr. Dr. Mr. Sat.

Univ. Dept. of Chea. Baron, Shell Devel.

Razak Frenkiel

E.W, Comings ,Met. Lng., Attn: 2 Co., Emeryville

E. Weller, Battelle last., Columbus C. Hsu, Iowa Inst. of Hydraulic Res., Iowa City I. Pai, Univ. of Maryland, College Pk .

Irvin Glas6aan, Guggenheim Lab., Princeton Univ. Frank Kreith, Dept. Mech. Eng., Univ. of Cal., Berkeley Ren. Corp., Cambridge, Attn: LiDrarian

A. R. 5.

Mr. G Prof. Prof. Prof. Prof. Mr. S James Dr. Dr.

R, . Maslach, Dept. W. McCloy, Univ

Mech. Eng., Univ. Cal of 111., Dept. Aero.

, Berkeley Eng.

Paul Torda, Univ. of 111., Stillwell, Univ. of 111., H. E. Korst, Univ. of 111, F. Oilman', Univ. of 111.,

Dept. Aero. Dept. Aero. 2 , Dept. Mech.

x>ne.

Dept, iorrestal Res.

Am >ld Kivnick, L. G. Alexander

Center, Princeton Penn. Salt Mf--. Co

Mech. Er.g. Univ., Attn' Librarian , Philadelphia

Oak Ridge, Tennessee

7c 77 7S 73 30 SI 62 &3 su

86 37 SS S3 30 91 9?

9h

37

99 100

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1 -

Calibration of Impact Tubes

Consider a tube placed in a fluid stream, with ite axis parallel to the

flow, its one open end facing into the flow. Such a deTice causes the flow to

stagnate at the tube opening, and there is developed within the tube a pressure

srproxinately equal to the sun of the static pressure in the stream at the tube

opening and the pressure developed by stagnation of the flow; viz..

(1)

where H is the pressure developed within the tube, Fg is tho static pressure, 2

P che fluid density, u the stream velocity, and C^ an empirical constant.

In using such a device—called an impact, tube—to make measurements in jet

systems, one connects the end of the tube not facing the flow to one arm of

a manometer, the other arm, of which is open to the ambient pressure. The

manometer reading is AP:

AP - H - Pa

' c: AP-P8+ -£$- -Pa (2)

'f

where Pfl is the ambient pressure. For the free Jet systems the assumption is

usually made that Pa « Pas in such systems,

AP« ~eiL (3) 2 Of

It is usually sufficient in crude measurements to assume that Cf is unityj

thus the manometer reading may be translated immediately into information

dealing with the momentum flux density of the flow, ?£ the stream density is

>. '

- 2 -

knows, and the flow may be anauned substantially free of fluctuations, the

velocity is calculable. If the measurements are to be considered precise,

however, there must obviously be obtained some description of the quantity C^.0

An extensive literature survey, cohering more than UOO references dating:

from the l?th century to the present, has disclosed few studies of the calibration

characteristics of impact tubes, Goldstein (3) reported that at speeds varying

2 from 20 to 6C ft./sec, l/C* did not vary from unity by more than + 0.1 percent.

<^

At speeds from 6 to 20 ft./sec=B l/C^ varied from unity by no more than + 1 per-

cent. These calibrations were performed by mounting a tube at the end of a

long radius, which was rotated about a center s.t various carefully measured

speeds^ The tangential velocity cf the tub? w*e thus subject to reasonably

precise measurement.

It was recognized early in ^he p-o^r^m en ;iis* ^ .ract that impact tube

measurements would provide a lerge portion of the experimental data. Calibrations

vere therefore attempted in order to improve the accuracy of the measurements,

2 Values of C^ appreciably less than unity were observed. The study described

hers was undertaken in order to ezplain the apparently low values of the cali-

bration coefficients. * -

There appear in the literature two causes for calibration coefficients

less than unity. At low velocities,, Barker (2) showed that impact tubes of

small radius are influenced by a viscosity effect„ which may be taken into ac-

count by the equation

« 2 AP - -£* • j t u (U)

2 2 r

where \x is the fluid viscosity and r the internal radius of the tube. Combining

Equations 3 and k, the calibration coefficient predicted at low velocities is

given by the equation

- 3 -

2

\L u (5)

Below are tabulatod values of C^ predicted at several velocities,

for r • 0.50 inches, in air at 70° 7. and atmospheric pressure.

u ft./sec.

U 10 20 50

0.971 0.988 O.99U 0.998

For flow at high velocities, L4 pmann and Puckett (5) relate the

pressure drop and the kinetic head by the equation

gjfig

pu» 1+*-,**"**lfe"'*" (6)

where M in the Hach number. Combining liquations 3 and 6 one obtains

•s- -l+h'+i-H4* 1 - Ms + .. c" U i+O lbOO (7?

Tabulated below are values of Cf at various velocities calculated from

Equation 7>

u ft./see.

100 200 300 400

0.999 0.995 0.990 0.983

- U -

XL

ft./sec. C f

In figure 1 are plotted the calibration coefficients listed above

and those obtained experimentally by Grimmett (U) early in the program.

There is obviously a serious discrepancy at low velocities. The technique

of calibration must now be considered. Air was allowed to flow through a

carefully built nozzle with an A.S.M.I, elliptical approach contraction.

The temperature and pressure upstream of the nozzle were measured. By

means of a calibration of the nozzle, previously shown to be correct to

0.1 percent, the mass flow through the nozzle was determined. An impact

tube was located on the centerllne of the nozzle, its open end about 1/U

inch from the noztle exit. The assumption *as made that the velocity

was everywhere the same in the plane of the nozzle discharge. On the

basis of the known area of the nozzle discharges the assumed uniform

velocity profile* and the measured flow rate, the velocity at the cen-

terllne of the nozzle could be computed. The impact head, as measured

by the impact tube, was recorded. The impact head and the kinetic head,

so determined, were compared, and values of C^ calculated, according to

liquation 3°

The obvious flaw in this procedure lies in the assumption of a

uniform velocity -file in the plane of the nozzle discharge. Two

questions must be raised: Is it reasonable that the velocity profile

be uniform? If not, how should that profile vary as a function of the

velocity at the centerllne?

» 500 0.975 6oo 0.963 700 0.9U9 soo o,93**

-

- 5 -

Consider a momentum balance between two sections through the

discharge nozzle. These sections are perpendicular to the centerline

of the nozzle, with Section 1 upstream from the nozzle contraction,

and Section 2 coincident with the nozzle discharge. Let ut be the

velocity at the centerline at 1, u, the velocity at the centerline at

2, Tj the mean Telocity across Section 1, and Ya the mean velocity

across Section 2. By Bernoulli's theorem,

ua - uj AP

Similarly,

vS 21

AP

where B* is the skewness coefficient required to extend Bernoulli's

theorem to the mean velocities. At 1, Vx and ux are related by the

equation *4 • (7\Ui where cK i* * constant characteristic of the flow

in the nozzle at Section 1.

If the variation in density between 1 and 2 is small, then by

a material balance, ?\SX • VaSa where S& and Sa are the areas of the

two sections of the nozzle at 1 and 2, respectively. Then

?

and

•«•<[(*)"•* Replacing vj with its equivalent in terms of 7a,

1

6 -

*»

Only when the quantity in the bracket is unity is the mean velocity

across the nozzle discharge exactly equal to the velocity at the cen-

terline.

JOT the flow nozzle used in the impact tube calibrations, the up.

Btrean diameter was 1.610 inches and the discharge diameter was 0.932

inches. The ratio B9/Sx is O.35. The value of B is usually close to 1;

and is a function of the flow rate through the nozzle. If the flow at 1

were normal turbulent flow in a pipe, the value of OC would be about 0.8.

In that case, the quantity in the bracket would have the value 1 •* [(O.35)

(I.56 - 1)1 or 1.0b8. As the velocity increases, the velocity profile up-

stream of the nozzle should flatten, and <^* should approach unity. The

mean velocity at the discharge then should be equal to the centerline

velocity. Conversely, at low velocities, 0s is leas than 0.8, and the

mean velocity at the discharge should differ still more from the center-

line velocity. Thus, it should not be expected that the velocity profile

which existed under t&e conditions of calibration at low velocities should

have been flat, as assumed in the calculation of Cf.

In order to obtain an estimate of variation in velocity profile as

a function of centerline velocities the following assumptions are made:

When the centerline velocity is u0 in a nozzle of radius ra, the i

velocity profile is flat at the value u across a circular area of radius i

ri# located ^n the center of the nozzle. In the annular region for which \

the inner radius is rx, and outer radius ra, the velocity varies from u0

- 7

when r • rx to 0 when r * ra. The variation is parabolic, such that

iS • 0 when r * rx. dr

The above assumptions can be used to obtain analytic expressions

for the velocity as a function of r. Since the velocity variation has

been assumed to be parabolic,

u - a + br + cr*. (g)

By employing the assumptions above, the constants of Equation 8

can be evaluated to give

u • u. [ L r* " rJ / (9)

Let the volumetric flow through the nozzle be q; then q • f 2fTrudr o

q * 2TTU0 f rdr •*• 2nu£

Evaluation of Equation 10 gives

rdr (10)

q - TTU0 rj - 1 (3r, + TX){T9 - rx)

How let ra - r4 • O , where Q is the film thickness. Then

(11)

3ra + rj « Ur8 -0 (12)

Substituting in Equation 11

q ""UQ rS - \ (Ur, -cf) c/ -TT u0(r5 -| raCf) (13)

ignoring the higher power of Cf .

When the impact tubes were calibrated at first, on the assumption

of a completely uniform velocity profile, the centerline velocity uj,' was

- 6 -

obtained from the equation

q • « r| u0' (lU)

yollowing the derivation above, assuming a finite boundary later of

thickness Cft the centerline velocity u0 was described in Equation 13.

Eliminating q between 13 and lU and rearranging,

"ti. . i. i J_ (15) u0 3 ra

The impact tube coefficients are proportional to the measured

velocities according to Equation 3. BO

2L . i- ! £C (16) Of 3 r,

where C*! and C* ere the impact tube coefficients obtained from the as-

sumption of flat and variable velocity profiles, respectively. Using

tlie impact tube coefficients measured by Grimmett (U) for the C-' and

the values calculated from Equations 5 and 7 for the Cf, it is possible

to compute the value of & at several velocities. These are tabu- la

lated below, as well as the values of £7 corresponding to Qrimmett's

measurements.

*o Oj^it (Grimmett)

20 ft./oec. .131 .086 in. 50 .151 .072

100 .120 .057 200 .091 .0U3 Uoo .0U7 .023 600 .023 .011

Experimental

The ultimate purpose of experimentation in this field was the

construction of an apparatus euitable for the calibration of impact

tubes, and thus to corroborate the equations already obtained and

experimentally verified by Barker, (2) and by Liepmann and Puckett (5),

A suitable apparatus could have the following characteristics:

(1) An orifice flow meter with a precision of + 0.5 percent at all

points in the velocity range.

(2) A calibrating nozzle with a contraction ratio euch that 1 £s )

as is Equation 7 would be less than 0.001, and of such a diameter that

the film region would be appreciably thicker that the impact tube used

to traverse the nozzle.

(3) A traversing mechanism capable of positioning an impact tube

to withis 0.QQ1 inch, immadiately downstream of the nozzle discharge,

without blocking the flow.

A prototype for such a calibration system was built. The orifice

aeter consisted of nine brasB plates, ea'.h with a stainless steel disc

at its center, in which was drilled an orifice following the recommen-

dations of the A.S.H.I, (l). Photomicrographs were made of the plates,

and the orifice areas were measured by a planimeter with the assistance

of a scale which was part of each photomicrograph. The orifice plates

were then calibrated according to a flow nozzle previously found to be

correct to + 0.1 percent. The precision of the orifice meter was within

the liraite set.

It was decided that the calibrating nozzle should have an upstream

diameter twelve time* the discharge diameter; thus

(*)"•(*)•

well within the stated limit. The largest pipe available wae standard

six-inch pipe; hence the nozzle diameter was fixed at 0.500 inch. The

smallest tubing available for the impact tube was 1/32-inch o.d. stainless

steel hypodermic tubing. The traversing device consisted essentially 01

- 10 -

two screws arranged perpendicular to each other, permitting adjustment

in planes normal to the nozzle geometric axis. Each screw had a pitch

of 0.05 inches and a hand wheel whose circumference was marked off in

fifty equal divisions.

The experimental procedure started with locating the center of the

nozzle with respect to the traversing device. A plug with a l/6U-inch

hole at its center was held by spring action in the nozzle; thus the hole

was believed to be at the center of the nozzle. Air was admitted upstream

of the nozzle and escaped through the hole. The impact tube, mounted in

the traversing device, was moved until the point was located at which the

pressure was at a maximum. Repeated trials showed that the reproducibility

of the centering procedure was + O.OO5 inches.

The nozzle center being known, the centering plug was removed from

the nozzle. The upstream pressure was adjusted to provide the desired

volumetric flow through the nozzle. At this point, the object was to

determine the extent of the region of constant impact pressure imaedi-

ately downstream from the plane of discharge of the nozzle. Obviously

no measure of velocity could be made, either in the region of constant

pressure or in the film region where the pressure fell off, for the

impact tube used in the measurements had not been calibrated. Thus no

exact calculation could be made of the velocity distribution across the

nozzle, nor was any iutended.

The impact tube traversed the nozzle in two direct ior.8, and a

pressure profile was obtained. This procedure was repeated at each of

several flow rates. In each ease, a large region of constant pressure

was noted about the noztle center, and close to the edge the pressure

was observed to fall off. The "film" region was presumed to begin at

the T)oint at which the pressure was 3 percent below the average value

- 11 -

measured in the constant pressure zone.

The observed "film thickness" at each velocity and the value of

t OfTa corresponding to it are tabulated below. The observed /ra is

compared with the 7»lue of 0fra calculated from Equation l6. The

experimental data of Grimr»ett were use*•+» Squat ion l6. -

u C/r, (Bq. 16)

20 ft./aec. 0.181 50

100 0.151 0.120

200 UOO 600

0.091 0.0U7 0.023

Cf/r. (Measured) ^(Measured)

0.2*4 0.06 inch 0.10 0.025 0.088 0.022 0.070 0,0175 0.060 O.OI50 0.060 0.0150

The agreement between the recently observed data and those

obtained from Grimmett's measurements by Equation l6 is not sufficient

to confirm beyond question the hypotheses presented earlier. The recent

measurements do indicate the presence of a slow-moving boundary layer,

of which the thickness diminishes as the gas flow through the nozzle

g&es up, This ooaf?.«?.§, in gR.isral, the explanation previously offered

for the unusually low Impact tub* calibration coefficients observed by

Grimmstt, However, the discrepancies between the computed cf\r% end the

measured values <io preolude the use of the current apparatus for cali-

bration a* impact tubes. The disorepanoite way be explained in part as

follow*,

First, it should be noted that at velocities higher than POO

ft./see. 1 ^changis only slightly. The Talus obscrvsd is ,019 inohesj

the impact tube ussd had an outside diameter of 1/J8 inch or about

,0313 inohssj the tubs opening was about half that, or .015 inches.

Thus the magnitude of ths film at Tslocitiss beyond 300 ft./seo. is of

the order of the diaseter of the tube opening, and therefore measure-

- 12 -

merits of a smaller film thickness are not possible. Moreover, in view

of the total film thickness even at the low velocities, the relative

error is an appreciable part of the total thickness.

It appears that Equation 7 does not apply quantitatively. Sven

though (Sa/Sj) is small, the centerline velocity us 1* appreciably

greater th»n the mean velocity calculated from the integrated velocity

distribution piven by Squat ion iU. The ratio X as a function of uc *o

is tabulated below.

u0 (ft./sec.) ?/uo

20 0.3U 50 0.93

ioo o.94 200 0.98 Uoo 0.98 600 0.98

Conclusions

It may be concluded that the hypothesis regarding the existence

of a : latively slow-moving film close to the wall of the flow nozj}^,, is

reasonably well substantiated. This explains the unusual impact tube

coefficients which Orimmeit observed.

As to the use of the present apparatus for the calibration of

other impact tubes, it must be concluded that this is not possible, Tha

nozzle diameter is too sioall, relative to the diameter of the tube used

to determine the presftur* profile. Since that tube is already as small

as practicable, the else of the nossle must be Increased. Squat ion 7

is apparently a gross overslapllfloat ion, since a far larger boundary

layer vas observed than the equation would Indicate. It is therefore

probable that the 12/1 contraction ratio is not neceasary.

There is at hand, therefore, no device which permits calibration

- 13 -

of impact tubes with the requisite precision. Two alternatives are ap-

parent: (1) to assume that Cf « 1.0; or (2) to accept the validity of

the coefficients predicted by Barker, and by Liepmann and Puckett; i.e.,

the coefficients calcualted from Equations 5 *r'd 7. The latter course

was adopted in most of the work in this program.

nomenclature

a An arbitrary constant in Equation 6.

b An arbitrary constant in Equation 6.

B Skewness coefficient in Equation 7.

C An arbitrary constant in Equation 8.

Cf Impact tube calibration coefficient. Equation 1.

Cf' Coefficient based on the assumption of uniform velocity across flow nozzle.

E Pressure in impact tube.

M Mach number, dimensionless.

p Ambient pressure.

Pfl Static pressure.

AP Pressure difference indicated by impact tube .

q Volumetric flow through nozzle.

r Radial coordinate.

rx Inner radius of slow-loving film.

ra Badius of flow nozzle.

Sx Upstream area of flow nozzle.

Sa Downstream (contracted) area of flow nozzle.

u Velocity at a point in the discharge of a flow nozzle.

u0 Velocity at the centerline. *

u0' Spurious centerline velocity, q/Tir£« /

- lU -

Uj Velocity at r • rl.

t ua Velocity at r • r8. j

V Mean velocity In a transverse section. t

G^ Relationship between centerline and mean velocities.

c Thickness of the slow-moving film, r8 - r*.

j M> Viscosity of fluid.

P Density of fluid. t

Bibliography

1. American Society of Mechanical Engineers Research Publication "Fluid Meters, Their Theory and Application" Uth Edition (1957).

2. Barker, Muriel, "On the Use of Very Smell PUot .Tubes for Measuring Wind Velocities" Proc. Roy. Soc. AlOl. • >UU5 (1922).

3. Goldstein, S., "Modern Developments in f*,.-''! >yaaoiic8,n Oxford- Clarendon Press, London (193&).

U. Grimmett, E., "Intrainment in Air Jets," Ph.D. Thesis, University of Illinois (1950).

5. Liepmann, E. W., and Puckett, A. £., "Aerodynamics of a Compressible Fluid,H J. Wiley and Sons (19U7).

I

1.00

20 kO 60 100 200

Velocity, ft./sec.

U00 600

figure 1

Calibration Coefficient* for Impact Tubes

i I

\

)