Half width and center-line velocity

RESULTS AND DISCUSSION 5.1 General

5.5.2 Half width and center-line velocity

The half width is an important geometrical dim en-

sion for length scale, generally used ,for explaining the

self-preserving flow. Dimensionless half width(2~/CdmL)

of the wakes are plotted against axial distances, which

are shown in Fig. 5.10. Half width pf the wake which are

calculated from the semi~empirical equation (3.2.13) given

by Schlichting [ 7J ^for two-dimensiotnal wakes are also

plotted in the same Fig. 5.10 to compare with that of

38

experimental results for plate -

1

and plaie-II. The axial variation of half width of the wake near the trailing edge of the plate deviate from that of semi-empirical results,but it agrees with empirical results after xjCdm L;50. The deve- lopment of wake depend upon the initial conditio~s which are already mentioned. Schlichting's[7] results are valid for a very thin boundary layer at the beginning. fig. 5.10.e~alsO present the fact that with the decrease of intial boundary layer for higher Reynolds number the experimental results spproach: towards Schlichting's equation (3.2.13). It is also to be noted that the effect of the initial condition exists only upto a certain axial distance and then the flow forgets its state of origin. Similar case is also explained by Islam [1 ] and Hussain and Zedan[31] for jets. This is pro- bably due to the nature of energy transfer from large scale

to. small scale eddies which depends on vortex Pairing. The' spread parameter for the wake is shown in fig. 5.10b which

achieves approximately a constant value "C= O.6'li5at 'Xi9=200 for the Reynolds numbers studied.

Dimensionless center-line velocity defect is plotted in fig. 5.11 again8t the dimensionless exial distanc~, x/CdmL. for the four different Reynolds number, the expe-

rimental value fallon a samB line except close to the trailing edge. T~e plot in fig. 5.11 also shows e comparison with the results of Schlichting's experiments • Near the tra- iling edge of the plate-I velocity defect

.

^, is less than that of Schlichting's experimental r'esults.'\But after X/Cd L> 40

, " m

the 'experimental velocity defect is gre~ter t~an that of Schlichting's experimental results. For the thin plate-II with thin boundary layer at the beginning the present results come closer to the Schlichting's Values. The center -line

, u

velocity is also plotted in a coordinate system (1~U£ )-2

, 0

vs.

x/e

in Fig. 5.12, which is a conventional plotting given by many authors[21, 22, 32J. TheoZletical results of Korst &:

Chow[22J and the experimental results of Chevray and Kovasznay [4 J are also shown in the s,ame Fig.' 5.12 to .compare the present experimental results. Near the trailing edge of the plate- I' the velocity increment at the centre~lin8 of the wake is gre- ater than that of Chevray and Kovasznay[ ~ and Korst and Chow [22]. After

x/e =

^120, the present results lie between Korst and Chow's [ 22J theo re tic al resul ts an d Chevray and Ko vasznay Is[4J 8xperiment~1 results. Korsl andChow[Z2J calculated the diffe- rential momentum and continuity equation using Prandtl's model of shear stress. For all calculations Korst and Chow 122] used a flat velocity profile at the beginning of the wake. In the near region Korst and Chow' s{22J resul ts agree satisfactorily with Chevray and Kovasznay's [4Jresults and it does not agree in the region after

x/e =

^{100. This is an indication that}

the Prandtl's model of shear stress is not applicable in the region after

x/e =

^{100. The present results with conside-}

rable boundary Iaye£ thickness at the beginning shows a devia~ion from both Korst &: Chow' s[22 J and Chevray and Kovasznay's [4 ]

\

40

results. It is already mentioned that the flow forget its initial condition with the increase of axial dis- tance due to its transformation to small scale motion.

So, at further downstream region the present wake will agree with Chevmy and Ko.vaszn,ay's [4JwakB.

5.5.3 Self preservation

Dimensionless velocity distribution for the wakes.

are shown in Fig. 5.13a, 5.13b, 5.13c, 5.13d and 5.13e corresporrding to the Reynolds number 2.18x103, 2.01 x 103,

1.90X103, 1.70X103 and 1.77x103 respectively to examine

their self-preservation. The heIr wiclth,V1,is used as length scale in the self-preservation plot. The velocity distribu-' tion in Fig. 5.13a-e do not show self-preservation, but it may become similar only at large distance downstream from £h~ trailing edge of t~~ flat plate. No similarity of mean velocity is observed near to the trailing edge of the plate. The semi-empirical equation (3.2.11) derived by Gar'tshore~6 J and Keffer [3J for similari ty profile are also shown in Fig. 5.13a, 5.13b, 5.13c, 5.13d and 5.13e for comparison. Deviation of the experimental results from the semi-empirical equation(3.2.11)may be expressed in rms ~rror.

This rms error was calculated. and" found to decrease gradually with the axial distance as shmwn in Table 5.3. The rms errors for the plate-II ( 0.159 cm thick) were calculated -to be

0.079 at X/D=16 and 0.057 at Xjo = 56. The least rms error is an

rms ERRORS AT VARIOUS DISTANCE FROM THE TRAILING EDGE OF THE PLATE-I

~

16 24 32 48 56

ReGe ~

2.18x103 O.OTI 0.074 0.0'9 0.062 0.058

2.01x103 0.0795 0.078 0.072 0.064 0.060

1.90X103 0.0830 0.081 0.076 0.071 0.068

1.70X103 0.1190 O. 110 0~099 0.098 0.096

an indication of self-preservation. Examining the rms error in Table 5.3

it

can be concluded that the flow achieves self-preserva- tion earlier with the higher Reynolds

rison of Fig. 5.13a ~nd Fig. 5.13d it

is

forR"

e"e

xlrJJ =

^{56. The values 0f}

number~ ReG '. From a compa- e

is clear that the flow

=

^{2.18x103 than}

in Fig. 5.13a

= 1.7x103 at that in Fig. 5.13d for R

, eGe nearer to rslf-preservation

rms errors for various Reynolds number)R" , are plotted in Fig.5.14

e"e

'to show that the rms error is less for higher Reynolds number at an axial distance. So. tha wake velocity profile becomes similar(self- preserving) earlier for higher Reynolds number. The flow is not self-preserving'in the range of axial distance covered in this in- vestigation as the least rms error is of the order of 0.058, which is considered to b~ high for self-preservation. The semi-empirical

self-presel:ving velocity p,rofile can also be expressed as:

where the. spreading

'U-u U-u. c

parameter, 6 ~ replaces 'a' of the equation(Z.Z.Z) •.

The spreading parameter,6', is already shown to be constent after x/G

=

^{200 for al~ Reynolds numbers studied here. Using} the constant

value of 'in equation(5.5~)it is plotted in Figs.5.13a,b.D &_~

to show a comprison wi th Garts~ore' s[6] " eqU'ation ( 2.ZZ:.) •

5.5.4 W~ke _drag

42

Drag-cD-efficient due to the wake is calculated from the moment~m thickn~ss equation (3~2.7) obtained-by neglecting pressure is plotted in fig. 5.15 against Reynolds numbers.

Fig. 5.15 shows that the drag co-efficient increases with the Reynolds number. Diag co-efficient is also calculated by app- lying equation (3.2.10) near the trailing edge of the plate considering the effect of pressure. The result is plotted in Fig. 5.15 to show a comparison. Drag co-efficient calculated by the above two methods are in agreement at each point. This- indicates that the effect of pressure is negligible.

5.5.5 Pressure in waKe

Fig. 5.16 shows the variation of pressure in wakes for

- 3 - -- 3 - - 3 - - 3

the Reynolds number 2.18x10 _, 2.01x10 , 1.9x10 and 1.7x10 • In fig. 5.16 the pressure at the free stream region is nearly cons-

tant, -and it varies only near- the trailing edge of the plate-I and within a very small region about the center-line of the wake.

Drop of pressure is higher for ~igher Reynolds number as shown in fig. 5.16. Pressure drop in Vicinity of thi trailing edge is also high for thick plate. There i? no pressure gradient in the transverse direction near the trailing edge of the plate, if the plate thickness is very small as shown in fig. 5.17~ Th~ Same case was also reported by Ch-evray and Kovasznay [4]'

The present investigation is on the two-dimensional turbulent wakes formed behind flet plates in a wind tunnel.

Two flat plates of different thicknesses were used for generating the wakes at four different

be.rs, i.e. Rege

= ^2.18x10,

3

^2.01x10,

3

exit Reynolds num- 1.9x103 and

1.7x103.

The boundary layers were turbulent at the trailing edge of.

the plate, and the wakes formed with these boundary layer

were assumed to be turbulent from the exit. The initial

boundary layer is identified to be turbulent on the basis

of the experimental values of velocities, which fit to the

universal velocity profile of turbulent bounda_ry layer. The

uniform flow that surrounds the wake is confined by the wall

of the test section. The boundary layer on the test-section

wall is also identified to be turbulent. The wall momentum

thickness decreases with the increase of Reynolds number,

but remains approximately constant wi~h the increase of

axial distance. This indicates that the development of the

wake at the mid o~ the test.section does not influence the

mean Parameter in the wall boundary layer within the axial

distance covered in the experiment.

44

For the same Reynolds numer the wake momentum thickness is found to be constant with the axial distan- cas, but it increases with the increase of Reynolds number and plate thickness. The shape factor of the wake decreases with the increase of Reynrilds number and with the axial distance from the trailing edge but it decreases with decrease of plate thickness. The decrease of the shape factor to uni ty is 'an indication of self-preservation of flow. The velocity distribution in the neighbourhood of the flat plate is unstable due to the presence of high velocity gradient in the axial direction and it decreases gradually to make the flow self-preserving. The flow is not found to be self-preserving in the range of investigation

upto X/f)

=

^{56. The} axial variation of half width of the

wake is approxi~ately linear except close to the trailing edge. But it is determined to be a linear function of axial distance by many authors, starting from the trailing edge con- sidering flat velocity profile at the beginning. The present results agree with the existing results after a certain axial distance x!CdmL = 50, where the effect of initial conditions are insignificant. The rate of increase of the central-line velocity is rapid in the near region of the wake

&

it becomes slow with the increase of axial distance. For thinner wake

,

(,

,

^-

(-

~-'

REFERENCES

.1. I sl am, S.1'1. N•• Predic tion an d 1'1easuremen t ⁰f Tu rbul ence in the Developing Region of Axisymmetric Isothermal

free Jets, Ph. D. Thesis, Deptt. of ~lech. Engg. ,Universi ty of viindsor, Windsor,O\H, Canada, 1979

2. Keffer.J.F., "The uniform distribution of a turbulent wake",J. Fluid ~lech.,Vol. 22; Part-I, 1965, P.135.

3. Keffer,J.F., "fl note on the eXPansion of Turbulent J. Fluid mech., vol. 28, Part-1, 1966, P. 1B3.

vlakes"

,

4. Chevray, R. and Kovasznay. l. S. G.,"Turbulence I"Jeasurements in the wake of a thin flat plate", AIAA Journal,vol. 7., fJo.8, August, 1969, P.1641.

5. Hiroshi, S. and Kuriki, K., " The mechanism of Transition in the Wake of a Thin Flat Plate placed paral~el to a .uniform Flow", J. Fluid mech., vol. 11, 1961, P.321.

6. Gartshore,I.S., "Two-dimensional Turbulent Wake", J. Fluid mech., vol. 30, Part-3, 1967, p. 547.

7. Schlichting,H.,"Uber das ebene Winds Chatten Problem", Thesis Gottingen, Ingr. Arch; 5, 1930,P. 533.

8. Hall,A.A. and Hislop .•G.S.,"Velocity 'and Temperature distribution in the Turbulent Wake Behind a Heated

Body of Revolutibn",Prac. Cambridge Phi. Soc.34,,]93B,P.345.

9. Swain,l.M.,"On the Turbulent Wake Behind a Body of Revolti- tion", Proc. Rilly. Soc.(london),A,135,799, 1929, P.647.

10. Reichardt,H.","Gesetzmassigkeiten der freien t~rbulenz"~

VDI- Forschungsh, 1951; p. 414.

.

co.,^\

11. Fage.A.and Falkner~V.M •• "The Transport of Vorticity and Heat Through Fluids in turbulent f"lotion",Proc.

Roy, Soc., (London), A, 13?, Appendix, 1932.

12. Goldstein.S.,"Note on the Velocit~ and Temperature Distribution in the Turbulent Wake Benind a Heated Body of Revolution", Proc. Cambridge Phil. Soc. 34, 193B, P.351.

13. Demetriades, A., "f-JeanFlow. ~leasurements in an Axisy- mmetric Compressible Turbulent Wakes", AIAA Journal,

vol. 6, No.3, 1958 , P. 482.

14. Taylor,G.I •• "The Transport Dr Vofticityand Head Through Fluid in Turbulent Motion",PrDc. Roy. Sec;,

(London), A. 135, 828, 1932, p. 828.

15. Hussain,A.K.M.F. ,t1.CoherentStructures", Aerodynamics.

and Turbulence L~boratory,July,1921,P.6.

16. Townsend,A.A •., The Structure of Tufbulent Shear Flow, Cambridge U. Press( 195~).

17. Meller. G.L. and Herring, B.J.,"Two methods of

Calculating Turbulent Bo.undary Layer Behavior Based on Numerical Solution of the Equation ~f Motion", D.J. Cockrell, eds stanford University C.1969,P.331.

18. Peyne,F.R.

&

Lumley J.L., Phys Fluid Supple , 10, 5194(1967) •

.19. Brown, G.B. ,Physical Sec. 47, 1935, P.703.

20. Anderson, A.B.C., J. Acous. Sec. Amer, 26, 1954, P. 21.

46

i

I

21. Launder,B.E., ~'iorse->A., Rodi \'1. and Spalding B.B.,

"A comparison of the performance of six _turbulence models", Proc. Hypersenic Aircraft Fluid Mechanics Branch, NASA Langley Research Center, Mampton, Virgine, 1924-1972.

22. Korst, H.H. and Chow.,\-J.L.;' On the Correletion of Analytical and Experimental Free Shear Layer Simi- larity Profiles by Spread Rate Parameters", Trans.

ASNE, Ser D. J. Basic Engg., Vol.93, No.3, Sept.

1971, P. 377.

23. Schetz, Joseph.,A. ,"Some Studies of the Turbulent

\-Jake Problem", Astronant. Acta, Vol. 16, No.2,Feb.

1971, p. 107.

24. Abr'amovich,!JI G.N., The "theory

or

turbulent M.I.T.Press; MQssachusetts Institute of Cambridge, Massachusetts

jets, The Technology.

25. Islam, S.f'l.N. ,'Design Ii Construction of Closed Circuit

\.Jind Tunnel, I-1.Sc. Engg. Thesis, Department of tiechanical Engg. BUET, Dhaka, 1975.

'26. Khalil.,G.t'i., The initial region of plane turbulent

mixing layer, Ph.D. Thesis, Department of Mech. Engg.

BUET, Dhaka, 1982.

27. Lugwieg, H. and Tillmann,W., Ingn.Arch,17,1949,P.28B.

28. Klebanoff, P. S. and Diehl., Natl advisC'ry comm Aeronaut.

Te~~h'.,NotesNo. 2475, 1951.

29. Schultz-Grunow~ F., LuftfahrtForsch,17, 1940,p.239.

30. Duncan,W.J., Thorn A.S. and Young,A.D.,An Elementary

Treatise on the Mechanics of Fluids, The English Language book Society and Edward Annold Ltd. F.L. B.S. Ed.1967, P. 307.

31. Hussain, ~.K.M.F. and Zedan. M.E.," Effect of the Ini tial Condition on the Axisymmetric ,Free Shear layer", Physics of Fluii.ds,Vol. 21, No.9,Sept.1978, P.1475.

50

32. Thomas,t'i",Torda.,T.f'.and Bradshaw'P'.f "Tur~ulont..

Kinetic Energy equation and Free Mixing" Proc. Hyp- ersonic Air-Craft Fluid Mechanics Branch, NASA

langley Research Center, Hampton, Virgina, 1924-1972.

i

•

FIGUReS

••.,J;

" .~~,'

Y

X

u-

^Uc

MIXING REGION WAKE GENERATING BODY

...".•..•...70. '.;";;;i;c:,( i':; •.. i.

061"' •...••. " ';',- ".. ~,.;2~/~""

U

U

o

U

U

o

•

FIG.'.' WAKE GEOMETRY AND NOMENCLATURE

Ul IV

.0;.

x

Lr>

0

"

"I;' ^••

::J::J W

~

~

LL 0

:::;:

b

^>-

^w

.0 ^l/)

LD >-

l/)

~

w

.z >- ^>-

>- Z 0::

«

«

^.0

«

^z

-'

^{0:: 0 0}

-' ^w

^{~ z}

« ^w

^0::

~ ^Z 0::

::J.

⁰

W 0 •

~ ^{LD 0}

-' ^w.

^u

-w w

^{~ 0:: ~}

Z ~

« ^w

^M

z

«

~ ^>-

::J

_~

::J

~

>- 0 _LL

I

•

,

PLATE ':~":-:::, BREATH

I WOOD 45-72

em

[NO. I WOOD ]

1I. 45-72

em

. NO, 2 M,S, SHEET PLATE - I

TRAILING EDGE 1,905

em

,

LEADING EDGE

, , , , , , , , C' ' ,

't

~ls'24~.. _em 76'2

c:m

.1

,

•

EDGE 'PLATE. II

NO-2

TRAILING

(LEADING EDGE

I -

^{J ," Ill' .}

^t h ^I

.• .. 71 '12

em ••

20,32

:-1

em

U1 -t-

FIG,4,1. SCHEMATIC._ DIAGRAM OF THE WAKE, GENERATING PLATES

."

\ !

-,

-

,

3.PERSPEX DUCT O'762mxO'457mxO'457mj:, '7. AXLAL FAN ..

4. PERSPEX DUC,T (O'762mxO'457mxO.457mVil AXIAL FAN 9. WIRE NET (MESH SIZE: 6 HOLES/em)

\-1'524 m -+O'9~ +O7*'7~2+O1~21 -- 4.725m '1~1110 'l1-:"

(m)( m)

'''. A(7)IIA(B)

( 1 )

_{\I {2J ( 3) \I (4) I 'iJ II I 6}}

""~ lff3

,-

^{II II II}

t--E --

^\i

\D

0 ^,

-*- I ""

^Q

o':~":f,g

^{0"0 '.:"} oo'oo:O'.P,o"b~ .•o'o:<;i',<1O'.ci,o.tr<2< 'o',\l'OO:';"fO'~o:"o'~',o<,,:o'<:i^{, Q •}

.o.;,'."l."

0," O;o.~~ Q'QI>:~~"':<i9;o:, '0,~o"'0' '96." h?a-O:O;O0Q'.iO I:lb1a...oQQ(I:o<>.,.:a'~b:o'. 'O'O.Q d-Q.(j.u a.ot~, :t). b,o''P''?,().o'Q'~''o:o.Jo~"O. .. htCJ..~o.P,oO:..;i ~~o

"

T 'f'E

-L

-

FIG.4.2 SCHEMATIC' DIAGRAM OF THE WIND TUNNEL

U1 U1

.FrG:O SCHEMATIC. DIAGRAM OF THE EXPERIMENTAL SET- UP

_.

^".

,

WIND TUNNEL TEST-SECTION

STAND

WAKE REGION d

j/

TUBE

DRAFT GAUGE

,

lJ1 0'>

tTl

....,

''',

80

50 60

70

F0R CALIBRATION

30 . 40

--- ••- u (ft/see) TUNNEL TEST SECTI.ON 10

20

FIG 4.4 VELOCITY DISTRIBUTION IN

D:f:Red' ' 0 '"

D I> '"

21.0

-

D:5'48xlO~O", ,,' . ~ ~ MEASURED

'l ' , "'" •• IS)

L . ,E

",g "

^{",ox: 5.08 em}

190 ^'U

,>c-

^D x : 1.2192m

I 19.0 ^{ID (J 0 II>}

.'

J

10

^{D 1I 0' 'ID}

) OD

, _,I' I. I

,

^' _I 1 ,

3.0 6'0', . 9.0 •• 12.0 , 5.0 18.0' 21.0 'lJ. .~

-1'0 ••• ^u(r'n/see)

) , ','

•••

^{9 . D IS)}

) -19.0 0

III

.

^Q

^.,.;

-20'0

C - ^{IIIIS)Q II>lIDD D}

••• •• '" '"

^III

- 21.0 ^D ~

"

^III

II> II>

• ^•••

) _-220

•

II>^{DIf> II II.III}

•• "

^IDl1li

"

^IS)

'II> 0 ⁽⁾ 'II>

J

-

_0

••

^.1

"

^{I 0 , I I}

o

0.50

-~.oo_

0.0

-8'0

-7.5

-8.5

- 0.5

>c-

7-5 :I: 8.0

u

z

o o

I

D o

MEASURED

oX =5.08cm c x =1.2192 m

-7.5 - 8.0 -8.5 -

o

o

.0

o

0._- 0

o

Red = 5.48 xl 0 Red =4'17x105 Red =3'01xl05 Red =2.31 xl05

•

- 9.0 L..

0.0 0.0 0'0 0'0 -0.5 -1.0 -1.5 -2'0 -2.5 -300 -)-5 -4'0 -4.5 -5.0 -5.5 --- ....•••-P(PRESSURE IN INCH OF WATER)

FIG.4'5 PRESSURE DISTRIBUTION IN THE TUNNEL TEST SECTION FOR CALIBRATION

U1 0)

:'20:0. E

u

\]:';.~

_o

• ..~_:-,':0 . _•

^'

-2'0.

• •

..::t-3' • ^a

-;/-'20:0

• •

•:-I

721'.0

•• -1- •

22.0

•

1

II

OJ :-

^,.'

3'0

^",", >-

• • 2.0

:'-0.' I

•

;: 200 •• -,'

60. ,"'J60 _{• 80}

___ u (m/s~c) 10'0., 15.0.

,\ !

40.

- u (fl/s~c)

0.Q,L 20

8.H

_o

'.16Xlo'~

o 2.a1X1a3

<l 1'9aX1a3

8-0~

^{l>. 1'70}

X

103

~

-

1'0. ~

.-

^;.77

^X;

^{03] ,}

0..5

r

- 0.5

PLATEI- II (0..15 9

cm.~

THICK) - 1:0

(5

z

r

•• ••

• •

8

•

•

t> <1 0 0

t> <1 C 0

t> <1 0 0

t> <1 C 0

t> q 0 0

21-0f- 20.0

-3

^'Of-

2:0:0f- ~

q 0 .•

I -8'0

t> <1 .0 ,;0

21 0'/ ~ ~ g ~L:'

- . :,'_{. . ~}~ q_~ ,₀0 -,.. _o. _8.5 l-

t> <1 0 '0 ".'y

-22-0 ~

q"' 0 :':" .

, .... ~ q 0 .' _ ,-_

-90

" ~. "ft ..., . n _ . .

8.5

-1.0

- 8'5,..

- 9.0

- 0..5

-8'{)

:r: 8-0

u

z ~ 0.1- ~

- 'f3-" ~q 0

- 1-0 u' ~ q 0

"'"I ;::

2-0

^~_~

~ ~

^q_q

~

⁰

0

0-5 '1-0 ^{~q ,0}

. t> q 0

, I

^{_u(mls) t> ~ <1q ,'0o. -0}

- - . ~ S-O '. 1a-O". 1S'O",

a-a

0'0 ~ 2'0 ⁰ 40' • , _

eo I ,

t> <1 0 0

~,l'O

-u(ft/sEl:r~ _qq 00 ••

PL~~'d; ^(,.gOScm.; l! ~ ^j

THICK) ~ q 0 ~

t> <1 D 0

t>

g

⁰

FIG.5.',:;" VELaCITY DISTRIBUTIaN AT THE. TRAIL'INGi EDGE aF THE PLAT~S U1

\D

"oj'

-

eno

"

E

u

>-

!

1.00 2.00

- 1-00

o

0-0

-200

Reee: PLATE ^0-

075 ^l-

•

^{A 0 0 0.75} _{0 2.18 x}

103

l'

0

•

^{A 0 0 ~ 0 2. 01 x} 103

'"

^{::t 0}

~

190 x 103

<:c^u 0.5 t-

•

^{A 0} o ^U

z

_0.51- ^A'

103 ^III

z

^-~

•

^{1 .70 x}

-

•

^{A 0 0} .'77x 10 J

]1

~_o' o.

>-

>-

•

^{A' 0 '0 I}

! ⁰²⁵

!

^.0.25

^{• •}

^{AA 0'0 0 0 I-}

^•

^0'0

I I I I I I U.'C • 5.0

ttm/i)u,!Q.0

_{o '\5.0}

"."

^{' 10'0'}

^m/sL

^{u 15"0 20.q.}

','

,

_:"

_','

11111111 .u I

2J,).O(

tis

)0';'u40'Q, 60 ^II 00 (lis)' u400 60.0 • 80. (

•

^L

PLATE-!

•

^{A 0 0 PLATE-II}

•

A 0 ⁰

- 0 25t-

•

^{0 -025}

_.

,

•

^{A 0 9} 0

A 0 ^0-

•

⁰

- 0 50i-

A -0.50 ₀

•

^{0 0}

0

•

•

^{A 0}

•

- 0-75

•

^{A 0 0 -0- 75}

~ ~ _I

•

FIG. 51b MAGNIFIED BOUNDARY LAYER VELOCITY PROFILE AT THE TRAILING EDGE OF THE PLATES

120

-

PLATE - 1 (1905cm,THICK) 1.10

o 1.00

..•.. :::J ::J.

0.90

080

~D~D V

o

o

"vo

_o

o"v

_D.

Reee ,,0' 2.18 xl03

02.01 x 103

" 1.9

x

103

v

17

x

103

"v

_o

.f'

v 0 o

070

00

50.0 ^{100.0 150.0 200.0 250.0 300.0 350.0}

•• x/a

FIG.53 DIMENSIONLESS FREE-5TREAM VELOCITY AT VARIOUS DISTANCES FROM THE PLATE

'000

enN.

Q)

w

600

700

50"0

SECTION 30"0 40'0 20'0

OF THE

TEST