Quadrant-edge orifice-modification for better performance

Cr :

CDl!'l"!")

d Rn :

QUADRANT-EDGE OR'IFIC:E-MODIFICATION

FO'R BETTE'R PERFORMANCE

This paper presents the results of an experimen- tal investigation to extend the upper limit of Rey- nolds number for the eonstant discharge coefficient of a quadrant-edge orifice meter. The perfor- mance characteristics of this type of meter in the high turbulent zone is explained for the first time.

The results show that the upper constancy limit of this meter with

0 =

0.500 can be increased from RD

=

200,000 to 450,000 hy cutting ofI the dc)"wn- stream tip of the quadrant edge by abou t 10 degrees.

Some more methods are also suggested for possible similar extension of the constancy limit.

Nomenclature

ratio of c!iameter of orifice to the <1iam- eter of the pipe;

coefIicient of clischarge;

drag coefIicient of a cylincler in a infi-

nite fluid; .

drag coefficient of a quadrant-edge orifiee plate;

l' : radius of the quadrant edge;

cliameter of throat;

pipe Reynolds number;

coefIicient of contraction;

cocflicicnt of velocity.

* Scientific Ollicer, Civil and Hydl'aulic EIlgg. Dept., 1n- dian 1nstitute of Science, Bangalore-12, 1nclia.

* * Associate Professor, Civil and Hydraulie Engg. Dept., Indian Institllte of Science, Bangalore-12. Illdia.

BY M. V. RAMAMOORTHY * AND K. SEETHARAMAIAH* *

Introduction

The quadrant-edge orifice meter has been retained for an International Standardisation hy the International Standards Association sin ce 1939.

Investigations are heing carried out in many coun- tries based on the results of Koennecke(1) [1], and his recommended values are shown in Table 1.

Table 1

UPPEH

[:1 -^l' C CO;-':STA"CY LDIIT

d OF HEYNOLIlS

NU~I!lEH

: 0.225

i

0.10 0.7G9 5G,000

0.400 0.11 0.782 140,000

0.500 0.135 0.804 240,000

().(jOO 0.208 0.842 250,000

0.G25 0.285 O.85H 250,000

: :

Table 2 furnishes the results of other investig- ators regarding the upper constancy limits for 0=0.5.

(1) Numbers in parenthesis rcfer to similar]y numbel'ed references in hibJiography nt end of paper.

313

INVESTIGATOH

be related to the drag coefficient of a cylinder, Cu, in an infinite fiuid medium by the following relationship :

ANALYSIS OF THE HIGHLY TUHBULENT ZONE

(RD> 100,000).

This zone is characterised by the steep upward curve artel' the eonstancy region and a break off at the end of the rising ctll've. This phenomenon of the rapid increase in the discbarge coefficient is explained in the following paragraphs.

There are two evidences to show that there is a contraction of the jet issuing out of the throat of the quadrant edge or in other ,vords that Cc is less than unity.

1. In the constancy region, though the overall losses of the quadrant-edge orifice for various ~

ratios are Just the sa me as that of an il..S.M.E.

Flow Nozzle [6] the discharge coefficient of the former varies from 0.77 to 0.885 for ~ ratios of 0.225 to 0.630 respectively, while the discharge coeflicient of the latter is of the order of 0.97 and above, This indieates that, though the val ues of Cv are the same for both the meters, the value of c for the quadrant-edge orifice is far less than that of an il..S.M.E. Flow Nozzle. Since C= Cc X Cm it can be concluded that the value of Cc for a quadrant-edge orifice is less than that for a nozzle Cc of which is very nearly unity.

2. Figure :3 shows the typical fiow around a cir- culaI' cylinder kept in an infinite Huid medium.

This figure has been reproduced from reference [8]. This figure indicates that ,vhen the laminaI' boundary layer becomes turbulent, the separation point moves from upstream of the diametral axis perpendicular to the direction of the How to {he downstream of the axis, with the increase in Reynolds number. Ey this the portion of the wake reduces in size and consequently there is a reduc- tion in the drag coefficient. This is why the value of the drag coeflicient suddenly falls down when the Reynolds number is of the Ol'der of 200,000 and the lowest value of CD is attained at about RD = 500,000, when the boundary layer becol11es completely turbulent. It has been already establish- cd by the authors [7] that a quadrant-edge orifice especially with~ = 0.500 exactly behaves as a cylin- der in an infinite fluid medium. This indicates that the contraction of the jet which existed when the pipe Beynolds number is of the order of 200,000 is eliminated as the Heynolds number is increased further.

It is clear now that the steep ri se in discharge curve is only due to the elimination of the contrac- tion or in other words, due to the increase in the value of Cc with the increase in Beynolds number artel' the constancy region. The value of Cv has already been shown to be constant at these values of Re,;nolds numbers and also independent of the latter' [6].

Table 2 (2)

RD MAX'j

(upper

c eons- HEFEHENCE

taney limit)

i i ! i

---i--[--I--I---

' - - - 1

Koennecke: I i i . . i . 1

(ac~ual).. '[ (J.50 10.13510.8041.. 240,000^!.:... [1]

" (a~Jw;ted).^,0.:0 iO.135Io.80:J!2~'0,000i ^[1]

FerrogllO . . . i0.,)1010,14 10.813

I^{1.l0,000i [2J} Jaumotte and_{Van Dijck} i()).<>cO ¹lU'13('1 0ll'·f

~9,)r

~i 1.)~,^{c') OOOii r:J} Brand ^j'0.50 i.! 0.135 1.. 0.8021230,0001 [4]

: ' i ¹ [5]

R~n~~moorthY

^1.,0.480!i 0.135Io.8241;OO'00o)..

unZ~~t~li~~ed

Seetharamaiah\ 0.483 0.138

1

°.808, _00,0001 authors

l ' ⁱ ! ^f

The upper constancy li mit is mainly guided by the steep upward trend in the discharge coeflicient curve. This paper offers an explanation for this steep upward trend and based on this rational explanation, some l11ethods are suggested to delay this upward trend to OCCUl' at a higher Reynolds number and thus extend the upper constancy limit.

One of such methods is undertaken for an experi- mental verification and the results show that the theoretical expIa nation has been proved to be appropriate and rational.

SPECIFICATIONS OF THE QUADHANT-EDGE OHIFICE.

Plates lIsed:

PLATE r :lJANO~!ETEH

No. B _il TAPPING

3-1 0.4834 0.l:J7G D-D/2

:J-2 0.4873 0.13GO D-D/2

A sketch of a quadrant-edge orifice meter is shown in figure J.

Experimental set up:

A detailed description of the set-up has already been reported by the authors in reference [6J.

Disc1wl'ge coefficient curue:

Figure 2 shows a typical discharge coefIlcient curve of a quadrant-edge orifice meter of ~= 0.5.

The charact,eristic shape of the discharge coeflicient curve is due to the faet that the quadrant edge behaves Just the same way as that of a cylinder kept in an infinite fiuid medium. Il has been demonstrated by the authors [7J that the drag coefficient of a quadrant-edge orifice, CD1"l,,!e)' can

CD(lllate) = Cl

+

^~2)

C2 (1)

el

On1y the results or those investigators whose equip- ment did not 'l)ose any limitations to reach this limit arc listed.

Elimination of the l'ise in disclwl'ge C/lrue:

From the discharge ctll've of a quadrant-edge orifice with ~= 0.500 il is seen the constancy

80undary layer laminar Couche lirmte laminaire (i)R= 162,500

~-r,·:;

1 Separation

---..,~...

i

Décollement

~~~C=.

^~

A

1

f

1 - ' - - - ' - - -D - - - 1 ' i

>\ 7

/

.

r t---d~

SECTION - COUPE_ A-A

Boundary layer turbulent (Measurements by flachsbart in air)

Couche lirmte turbulente (Mesures dans l'air par f/achsbart) li A quadrant-edge orifice plate.

Diaphragme en quart de cercle.

3/ Flow around a circulaI' cylinder.

Ecoulement autour d'un cylindre circulaire.

0-81 0-84 083 0-82 086

c

0-85 0-87

•

•

•

- - - - + - - - \ - - - 10-5 -.---11-0

l ,

i 1

-t-·-~--·---i--·~--4 -.J+-J~Turbulent

----+-

High turbulent

! Turbulent 1 Très turb lent

---:----.-.--,,-.-,~- ---t-_·_-~---

=0-500---~~---

CD --'l'<.---\·----·---+---·----\---I----·---11- 5

-+

Lom;""

~t;;,)~~;,~ ^--

- - Laminarre

-+---

^---~­

1

1 2 3 5 \ - - - -

al

d

CL

"' Reynold' s number -Nombre de Reynolds du cylindre

~

^1A45IrO

~-_T_-__,:__---.:-10r3---1::;0~4---1:.;0~5---

^{_ _1:,;06}2-0 -<::~

~ê} 1-375 -...~---.-.--

la

L - --'-:- "-::- -'---, -'--:- ----'0-80

10² 10 3 10⁴ 10 5 10⁶

Pipe Reynold's number-Nombre de Reynolds du tuyau

C, Cn, Cn(!'lato) curves /2/ Courbes de C, Cn , CD(dla""rag,,,,).

region extends upto RD

=

200,000± and the peak point occurs at Bl) = 500,000±. This means that the contraction of the jet which remains unaltered till RD reaches a value of 200,000±, gets completely stabilised at RD = 500,000±. If we visualise the contraction of the jet gradually fading away \Vith the separation point moving downstream as in Figure 4, it is possible to suggest some methods of eliminating such a change in the jet and thereby making the value of Cc unaltered, even after RD reaches a value of 200,000.

The methods suggested are:

1. Cut off the downstream tip of the quadrant edge to the point \vhere the separation point existed at Rl)

<

200,000 and thereby providing no surface for the separation point to move downstream any further, along the curved edge. Since this position is not known exactly, lrial and error method has to be adopted to find this position exactly. The modi- fication upto this position will not alter the dis- charge Clll'Ve in the constancy region, as long as the flow is turbulent.

2. Make the surface of the edge as smooth as possible and hence delay the point of separation as far downstream and closer to the outlet tip as possible. This will enable to delay the rise in dis- charge coefficient curve to a higher Reynolds number and thus exlend the constancy limit. This ll1ay pose a problem as to how to standardise the smoothness of the surface.

;3. The existence of the laminar boundary layer itself could he destroyed by creating turbulence using a mesh j ust upstream of the plate and making the houndary layer remain turbulent even before BD= 200,000. This may h'owever incl'ease the

discharge coefficient even at conslancy region, since the contraction of the jet is completely avoided except for a thin turbulent boundary layer. But the disadvantage of this method would be with regard to the standardisation since this method involves the difficult maintenance and control of the similarity of turbulence.

4. By the boundary layer suetion with extraneous ll1eans to make the separated jet stick to the hound- ary. This method can only serve for a theoretical interest and by no means adoptable in practice.

The first of the four methods has been success- l'ully tried and has been reported here.

EXPERIMENTAL DATA ANALYSIS.

Since the position of the separation point cannot be exactly located by any theOiretical analysis at present, a trial and error ll1ethod has been adopted.

Referring to Figure 4 if the portion of the orifice plate beyond the point 3 is cut off, the movement of the separation point will be stopped upto the point ;3, since there is no surface provided for further movement. This means that diameter of the jet cannot increase any further beyond d;< and the peak of the discharge coefficient curve will be lowered to that extent. Since the stabilisation of the jet boundary is complete only at RD= 500,000, the peak point even when lowered has to he at this Bevnolds number only. This will try to flatten out th; discharge coeffici~ntcurve. By Vtrial and error the optimum amount of cutting off the downstream tip reqlüred to ohtain the flattest curve may he round.

In the experiments conducted two types of culs were made as shown in the inset block diagrams

Plate-Dlaphragme- 3-1

• Without any modification }(3= 0.4854 Sans modlflcatlan

(3004842 (300-4842 (300-4851 (3004857

=0·1376

° 1° downstream t!p eut } 0=0-4840 Bord aval coupe;8=1° 1-'

1°

• 42

+ 6°

°

8r

il

9r

088

0·86 0·87

0·81

a80~_=::r:6b>o P-"-_...L_-'-_L..l....-'..::....::..:.::.w

la 4 10⁵ la.

Pipe Reynold'5number -Nombre de Reynolds du tuyau 0·831' --- -

0·84

0'821-- - - __^o• • _ - - . . - - - -

51

0·851"--···-··· ---;= ---.• ---.-. ----j--... ---

II III N 4

Jet boundary

• Limite du jet

~~::

. Flow Ecoulement

...

4/ ?v[ovement of separation point and the inercase of jet diameter.

Déplacemenl du poinl de décollemenl el II/I(Jmenlalion du diamèlre dl! jet.

4/

5/ Consolidated test results.

Ensemble des résullals d'essais.

-'-=0-1376 ,

d i

- - - ----T---

1

Piete -Diaphragme - 3-1

Cl Without modification }f3~0 -4834 Sans modification

+ 6⁰ downstream tip eut o}[3~0- 4842

Bord oval coupé;8=6 __

---~---

0'82 0-85 0·87

0·86

0-81 0-88

0-83

0-84 -- --- ---.--

1 -tI _______________ __..J1 _

• 1

-- 1

---,'-1,'--.1

^---1

,

/

• /+

---~-··-r_-L--'-+---:i1'/-.Jllr'---·/

• ,h-+--..,+

i of eo

---~~---1

At

+.. . .. .

^{1' }}

- - - -++--F- ....

O'80,L04;---'---'--.L....+..L-Ll.-LLI0'--,';---'---'--.L...L-l-l-LW10.

Pipe Reynold' s number -Nombre de Reynolds du tuyau

8/

} f3~04834 Plate Diaphragme- 3-1

a l' downstream tip eut } f3~04834 Bord aval coupe;8=1⁰

• Without modification Sans modification 0·88

086 0·87

0·831 - - - . - -

084 o851----

a 82~--- ---

O' 80;'-04;;---'----'---"---'-.L..JL.L.L I .L 0

""5- - - L - - L - L - L - L - l - L U IO '

Pipe Reynold's number-Nombre de Reynolds du tuyau 081

6/

1/

0-80 '

'-04;---'----'--.L...L-l-l-LL I L O

5,----L--L--L-L...L.L.L..LJ 10

•

Pipe Reynold' snumber-Nombre de Reynolds du tuyau

-'-=0-1376 d

do"tnstream tip eut

, 8 810 } f3_~4851 coupe; = '2

- Diaphragme· 3 - 1

0·81

10⁵ 10' 1

Pipe Reynold' s number -Nombre de Reynolds du tuyau

9/

Plate -Diaphragme - 3-1

• Wlthout modificotion }f3=0 4834 Sans madlflcatlOn

A 4

r

downstream tip eut _ Bard aval coupé;8=4

f

^{0 } f3 -O·4842}

-'- = 0-1376 d 0·88

0-86 0·87

0·84

0·83 085

0·82

0·81

0,851-- --- --

Pipe Reynald' s . Plate -Diaphragme - 3-1

• Without modification } f3~0 4834 Sans modification

l '

'/i 9'2 downstream tip eut1

0}[3~^0-4857 Bord aval caupé;8=9 '2

O' 8 8r--- ---

086

0·82

0-831 -

0·81

Ç')

- - -'/i'/i-·f-rm;.--r,-'7--7I ---"'-=---=--_--..---">--i'lj-0 '/i'/i '/i /'/i

• ,---4J'0--- - 0'805

}Ç1I Ç1I /.// /

8 // /

0- 80

1':-04;;----=-=="""'=="'=-=:.:1"'=~="'=10' 5 -- 0- 5% 10' number-Nombre de Reynalds du tuyau C

0-87

10/

6/ to 10/ Effeet of downstream tip eut.

Effet de la coupure du bord aval.

of Figure 11. In plate 3-1 sbraight cuts ,vere made so that

e

is madeequal to 1 ", 4~o, 6°, 8~o and 9:\-".

Artel' each eut the calibration tests were made.

Care was taken to note the change in the diameter of the throat artel' each eut and hence in the value of ~ ratio and the corresponding new value of ~

was usecl in the computations of the values of C.

In Figure 5 the consolic1ated results are shown. It can !Je noticed that the peak point gets lowered consistently at Hl) = 500,000 and with 9:\-° cut, the constancy 'limit is extended upto Hl)

=

^450,000

allowing a ± 0,5 % tolerance.

In order to have a clearer picture of the change in performance with cutting off tips to various degrees, figures 6, 7, 8, 9 and 10 are furnished. In or der to check for the reproducibility, another plate (plate ;~-2) with a Hlo inclined cut was made and tested. The results of tests on hoth the plates (3-1) and (3--2) are shown in Figure Il. lt can be seen that the results are amazingly consistent.

As predicted hy the theOl'y, the cuts made at the downstream tip do not affect the discharge coeffi- cient in the constancy region beyond the allowable

317

Acknowledgements The authors express their deep gratitude towards Prof. N. S. Govinda Rao for his encouragement and guidance throughout this work. The useful dis- cussions with Messrs. Ramaprasad and Sanna who are lecturers in this department are gratel'ully acknowledged.

2. Four methods have heen suggested for increas- ing the upper constancy limit.

8. Results of tests conducted on hvo plates

~ "" 0.500 show consistently that a downstream eut of 9io to 10" extends the constancv limit l'rom RI)= 200,000 ta 450,000. .

4. Scope for fmther work on the extension of the constancy limit has heen suggested.

IilQ

·+

^{0 ' 5%}

_%JJ1i

Q~

-0·5%

-a-

⁼⁰¹³⁶

~l· ¹⁰

/18'9 2 I l 1 : Cut-typel- plate3-1 _J

Coupure du type t - diaphragme 3-1

-1--

iZSt1

re~~"""""""'- 18=10'

~1 . . . .._.__

: Cut-type 2

..J.plate3-2 Coupure du t;p.e 2 diaphragme 3-2

Plate3-1 r

iZS Dklphragme 3-1 } (3 '0-4857 d'0 1376

9·r

dowstream tip eut Bord aval coupé;8' 9-j⁰

Plate 3-2 }

.. Diaphragme3-2 (3'0-4873 10⁰downstream tip cut Bord aval coupé;8'100

0·86 ---

0·84 - 0·85 -

0'82~-

0·83 ---

0·81

0·79 c

O· 78 t"'0""4--....L-....L---'---'---'--'---LL..l.

tO...,5---'---'--.l..-.l.--'--J-'--LJ,06 Pipe Reynold's number-Nombre de Reynolds du.tuyau 1II Com'parison of test results on plates 3-1 and 3-2.

Comparaison des részzltats obtenzzs avec les diapllrag- mes 3-1 et 3-2.

tolerance of ± 0.5 %' It remains ta be seen the effeet of this modification when the whole flow is laminaI'.

Scope for further work:

Experimentsare heing conducted for checking the validity of the other tluee methods suggested herein and the results will he reported saon.

The optimum amount of 10° eut may be peculiar ta the case of ~= 0.500. The optimum values for other ~ ratios are still ta he 1'00Uld out.

Experiments are necessary ta study the effect of cutting off tips when the whole flow is laminaI'.

Conclusions 1. A rational theOl'y has heen suggested for the steep rise in the discharge curve of a quadrallt-edge orifice at very high Reynolds numbers.

References

[1] KOENNECIŒ (W.). - Neue Düsenformen für kleinere und Mittlere Reynolds Zahlen. Forschlwg V.D.l., May- June 1938, pp. 10\1-12'5.

[2] FEHROGLIO (L.). - Boccagli e Diaframmi pel' Piccoli Nu- meri di Reynolds. L'Energia Elettrica, vol. 19, 1\142.

[3] .TAUMOTTE (A.) and VAN DI.ICI( (G.). - La mesure des débits aux faibles nombres de Reynolds par tuyère en quart de cercle. Revlle Générale de l'Hydrazzlique, No. 67, janv.-fév. 1!J52.

[4] BOGEMA and MONKMEYER. - The Quadrant-Edge Orifice.

A Fluid Meter for low Reynold's Numbers. Paper No.

59-A-140, ASME, December 195!J.

[5] RAMAMOORTHY (M. V.) and SEETHÀHAMAIAH (K). - Qua- drant-Edge Orifice. Performance at very High Rey- nolds Numbers, Trans. A.S.M.E., .Jollrnal of Basie En- (fineering, Series D, March Hl 66, p. !J-13.

[6] RAMAMOOHTHY (M. V.) and SEETHAHAMAIAH (K). - Losses in Quadrant-Edge Orifice Meters. La Jlouille Blanche, No. 2-1!J65, mars-avril, pp. 12!J-1:l5.

[7J HAMAMOOHTHY (11'1. V.) and SEETHAHAMAIAH (K). - Drag characteristics of Pressure DifferentiaI Metering De- viees (under publication in the Journal of the lnsin.

of En(frs., lndia).

[8J RouSE (H.). - Engineering Hydraulies. Text Book, John Wiley and Sons, lnc., N.Y., Chap. J, pp. 121.

Résumé

Diaphragme à bord amont profilé en quart de cercle Modification lui assurant un meilleur fonctionnement par M. V. Ramamoorthy * et K. Seetharamaiah

* *

Le diaphragme débitmètre il bord amont profilé en quart de cercle a été retenu pour une Normalisation Internationale par la International Standards Organisation dès 1939. Les limites supérieures de la constance des coefficients de débit, préconisées par Koennecke [1 J, sont indiquées au tableau 1. Le tableau 2 présente les résultats obtenus par d'autres cher- cheurs, en ce qui concerne les limites supérieures de cette constance, pour ~ = 0,5. Le présent article propose une explication de la montée raide de la courbe des coeflicients de débit à partir de la région constante, ainsi que certaines méthodes pouvant permettre d'étendre cette zone de constance jusqu'à un nombre de Heynolds plus élevé.

La figure 1 représente le schéma d'un diaphragme à bord amont profilé en quart de cercle. La figure 2 montre une courbe type des coeflicicnts de débit correspondant à un tel diaphragme-débitmètre, pour lequel ~ = 0,50. Dans une étude antérieure [1], les auteurs avaient démontré la possibilité de relier le coeflicient de traînée d'un tel diaphragme, C_{D (1l1)} à celui d'un cylindre Cn' maintenu dans un milicu fluide infini, par la relation:

(1

+

~2) ^__21<2

C2 " ⁽¹⁾

D'après cette équation (0, la montée raide dl' la courbe des coe1Iicients de débit correspondrait à la brusque chute des valeurs du coeflicient Cn, correspondant à un cylindre. On sait que cette chute soudaine est due à la fois à la tran- sition de la couche limite au régime turbulent, et au déplacement ainsi provoqué du point de séparation de l'amont vers l'aval, et enfin il une réduction des dimensions du sillage. La figure 3 représente l'écoulement type autour d'un cylindre, dans un milieu fluide infini.

La figure 4 montre un phénomène semblable, il l'intérieur du diaphragme à bord amont profilé en quart de cercle.

On voit, d'après cette figure, que lorsque la couche limite passe du régime laminaire au régime turbulent, le diamètre du jet augmente, ainsi que la valeur de Cc' Il a déjà été démontré que la valeur de Cv reste constante, pour ces valeurs du nombre de Heynolds, et qu'elle reste également indépendante de ce nombre [6]. Puisque C= Cc X Cv' la valeur de C croît en fonction de la transition.

Il est possible d'éviter cette brusque augmentation de la valeur de C, et ainsi d'agrandir le domaine de constance, à l'aide des quatre méthodes suivantes:

1. Si nous coupons le bord aval du diaphragme jusqu'à l'endroit où existait le point de décollement correspondant à Hn

<

200 (JOO, de sorte que nous enlevons la surface qui aurait permis à ce point de décollement de se déplacer plus vers l'aval, nous pouvons empêcher la croissance du diamètre du jet. Il s'agit ici d'un procédé à tâtonnements, puisque nous ne connaissons pas la position exacte de ce point de décollement. Nous avons recoupé les bords du diaphragme n° 3-1 il 1",41/2", G", 8 1/2⁰ et9 1/2"; l'extension de la limite de constance ainsi obtenue est montrée sur la figure 5. Les figures G, 7, 8, H, et 10 montrent plus nettement l'élimination progressive de la courbe raide et montante.

Dans le but de vérifier la reproductibilité de ces résultats, nous avons recoupé le bord d'un diaphragme n° 3-2 (sem- blable au n" a-l) en fonction d'angles différant de ceux du cas précédent, et allant jusqu'à 10". La figure 11 montre la comparaison des résultats obtenus, et ceux correspondant au diaphragme n" a-1.

Une caractéristique intéressante de cette méthode est qu'elle ne modifie guère le coefficient de débit à l'intérieur de la zone de constance.

2. En rendant la surface du bord du diaphragme aussi lisse que possible, dans le hut de retarder la transition de la couche limitc vers un nombre de Heynolcls plus élevé.

3. On pourrait détruire la couche-limite laminaire par la création de turbulence, à l'aide d'une toile métallique placée juste à l'amont du diaphragme. Ceci augmenterait éventuellement le coeflieient de débit, même à l'intérieur de la zone de constance, étant donné l'élimination complète de la contraction du jet.

4. Par aspiration de la couche limite, à l'aide de dispositifs extérieurs, afin de «plaquer» le jet décollé contre la limite.

Ces difIérenfes méthodes devraient permettre l'extension de la zone de constance jusqu'à Ol = 500 000.

Scientifie Offieer, Civil and Hydraulie Engg. Dept., Indian Institute of Seience, Bangalore-12, India.

Assoeiate ProfessaI', Civil and Hyclraulic Engg. Dept., Illdian Institute of Seience, Bangalore-12, India.