Boundary Layer Lab Report Full

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TITLE :

TITLE : FLAT PLATE BOUNDARY LAYER

FLAT PLATE BOUNDARY LAYER

OBJECTIVES

The objective of this experiment are as follows: The objective of this experiment are as follows:

•• To measure the boundary layer velocity profiles and observes the growth of theTo measure the boundary layer velocity profiles and observes the growth of the boundary layer for flat plate with smooth and rough surfaces.

boundary layer for flat plate with smooth and rough surfaces.

•• To measure the boundary layer properties for the measured velocity profiles.To measure the boundary layer properties for the measured velocity profiles. •• To study the effect of surface roughness on the development of boundary layer.To study the effect of surface roughness on the development of boundary layer.

INTRODUCTION

The

The coconcencept pt of of bobounundadary ry lalayeyer r wawas s firfirst st intintrodroducuced ed by by LuLudwdwig ig PraPrandndtl, tl, a a GeGermarmann aerodynamicist in !"#. The boundary layer concept provided the lin$ that had been aerodynamicist in !"#. The boundary layer concept provided the lin$ that had been mis

missinsing g bebetwtweeeen n ththeoeory ry anand d prapracticticece. . %u%urthrthermermoreore, , ththe e bobounundadary ry laylayer er conconceceptpt permitted the solution of viscous flow problems that would have been impossible through permitted the solution of viscous flow problems that would have been impossible through application the &avier'(to$es e)uation to the complete flow field.

application the &avier'(to$es e)uation to the complete flow field.

*s for

*s for flow in flow in a duct, a duct, flow in flow in a boundary layer a boundary layer may be may be laminar or laminar or turbulent. There is turbulent. There is nono uni)ue value of the +eynolds number at which transition from laminar to turbulent flow uni)ue value of the +eynolds number at which transition from laminar to turbulent flow occur in a boundary layer. *mong the factors that affect boundary'layer transition are occur in a boundary layer. *mong the factors that affect boundary'layer transition are pres

pressure sure gradgradientient, , surfsurface ace rougroughnehness, ss, heaheat t trantransfesfer, body r, body forceforces s and and free free strestreamam disturbances.

disturbances.

n many real flow situations, a boundary layer develops over a long, essentially flat n many real flow situations, a boundary layer develops over a long, essentially flat surface. * )ualitative picture of the boundary layer growth over a flat plate is shown in surface. * )ualitative picture of the boundary layer growth over a flat plate is shown in figure  below.

figure  below.

%igure .: -oundary layer on a flat plate /ertical thic$ness exaggerate greatly0 %igure .: -oundary layer on a flat plate /ertical thic$ness exaggerate greatly0

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THEORY THEORY

(ome measures of boundary layers are described in figure .1 below. (ome measures of boundary layers are described in figure .1 below.

%igure .1 : -oundary Layer thic$ness definitions %igure .1 : -oundary Layer thic$ness definitions

The boundary layer thic$ness,

The boundary layer thic$ness, δδ, is , is defined as the distance from the surface to the pointdefined as the distance from the surface to the point where the velocity is within  percent of the stream velocity. The displacement thic$ness, where the velocity is within  percent of the stream velocity. The displacement thic$ness, δ

δ2, 2, is is ththe e disdistatance by nce by whwhich the ich the sosolid bounlid boundadary ry wowould have to uld have to be dispbe displalaced in ced in aa frictionless flow to give the same mass deficit as exists in the boundary layer.

frictionless flow to give the same mass deficit as exists in the boundary layer.

The momentum thic$ness,

The momentum thic$ness, θθ, is define as the thic$ness of a layer of fluid of velocity, 3, is define as the thic$ness of a layer of fluid of velocity, 3 free stream velocity0, for which the momentum flux is e)ual to the deficit of momentum free stream velocity0, for which the momentum flux is e)ual to the deficit of momentum flux through the boundary layer. The -lasius4s exact solutions to the laminar boundary flux through the boundary layer. The -lasius4s exact solutions to the laminar boundary yield the following e)uations for the above properties.

yield the following e)uations for the above properties.

x x x x x x x x x x x x Re Re 664 664 . . 0 0 Re Re 72 72 . . 1 1 Re Re 0 0 . . 5 5 = = = = = = ∗ ∗ θ θ δ δ δ δ

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5ue to the complexity of the flow, there is no exact solution to the turbulent boundary layer. The velocity profile within the boundary layer commonly approximated using the 67 power law. 7 1













=

δ y U u

The properties of boundary layer are approximated using the momentum integral e)uation, which result in the following expression.

*nother measure of the boundary layer is the shape factor, 8, which is the ratio of the displacement thic$ness to the momentum thic$ness, 8 9 δ26θ. %or laminar flow, 8 increases from 1. to ;.< at separation. %or turbulent boundary layer, 8 increases from .; to approximately 1.< at separation.

EXPERIMENT APPARATUS

5 1 5 1 5 1 Re 036 . 0 Re 0463 . 0 Re 370 . 0 x x x x x x = = = ∗

θ

δ

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The experiment set up consists of: . *irflow -ench

1. Test *pparatus

;. Total and static tube pressure probes and multi tube manometer.

PROCEDURES

On-off switch Damper control rod Plenm otlet

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. The apparatus has been set up on the bench as shown on figure # uses the flat plate with the smooth surface for the first part of the experiment.

1. (et the pitot tube about <mm away from the edge of the central plate.

;. *djust the position of the central plate to set the measurement plane at the re)uired distance from the leading edge, say #"mm.

#. (witch on the fan and adjust the air speed to set the free stream air velocity at medium speed.

<. +eading of the total pressure is measured using the Pitot tube for a range of about " points as the tube is traversed towards the plate. nitially the readings should be almost constant showing that the probe is in the free stream outside the boundary layer. (hould it not be so, go bac$ and start further from the plate.

. *s the pressure begins to fall the increment of advance should be reduced so as to clearly define the velocity profile. The pressure reading will not fall to =ero as the Pitot tube has a finite thic$ness. * further indication that the wall has been reached is that the pressure readings will be constant.

7. +epeat the experiment to set the measurement plane at <" mm. >. +epeat the entire experiment for the rough surface.

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TABULATION OF DATA AND SAMPLE CALCULATION:

. (mooth surface with distance from the leading edge, x 9 #" +oom temperature: ;" ο? ρair9 .77 $g6m; ν 9 .;" x "'< m1 6s ρoil9 7># $g6m;

%ree stream velocity, 3 9

a o g h ρ ρ ∆ 2 m6s 9 177 . 1 10 22 !1 . " 7!4 2

×

−3 m6s 9 .! m6s +eynolds number, +ex 9 ν Ux 9 ₅ 3 10 30 . 1 10 40 "6 . 16 − −

×

9 <1>#.

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+oom temperature: ;" ο? ρair9 .77 $g6m; ν 9 .;" x "'< m1 6s ρoil9 7># $g6m;

%ree stream velocity 3 9

a o g h ρ ρ ∆ 2 m6s 9 177 . 1 10 22 !1 . " 7!4 2

_×

−3 m6s 9 .!m6s +eynolds number, +ex9 ν Ux 9 ₅ 3 10 30 . 1 10 150 "6 . 16 − −

×

9 !<!1.;

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a o g h ρ ρ ∆ 2 m6s 9 177 . 1 10 26 !1 . " 7!4 2

_×

−3 m6s 9 >.#;m6s +eynolds number, +ex 9 ν Ux 9 ₅ 3 10 30 . 1 10 40 43 . 1! − −

×

9 <7>.1

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a o g h ρ ρ ∆ 2 m6s 9 177 . 1 10 22 !1 . " 7!4 2

_×

−3 m6s 9 .! m6s +eynolds number, +e 9 ν Ux 9 ₅ 3 10 30 . 1 10 150 "6 . 16 − −

×

9 !<!1.;

TABLE:

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Table : Tabulation of data for smooth surface with x 9 #"mm @icrometer reading y mm0 (tatic pressure manometer, h mm0 Total pressure manometer, h mm0 5ifferential manometer height ∆h mm0 %ree stream velocity, U m6s0 +eynolds number _U u







 −

U u U u 1 " "" 11 11 .! <1>#.1 ".77 ".7! ".< "" 1 1 >.#; <7"7.! ".7"< ".1"> ." "" 1> 1> !.; <>>.<# ".>" ".1> .< "" 1> 1> !.; <>>.<# ".>" ".1> 1." "" 1> 1> !.; <>>.<# ".>" ".1> 1.< "1 ;" 1> !.; <>>.<# ".>" ".1> ;." "1 ;" 1> !.; <>>.<# ".>" ".1> ;.< "1 ;" 1> !.; <>>.<# ".>" ".1> #." "1 ;" 1> !.; <>>.<# ".>" ".1> #.< "1 ;" 1> !.; <>>.<# ".>" ".1>

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@icrometer reading y mm0 (tatic pressure manometer, h mm0 Total pressure manometer, h mm0 5ifferential manometer height ∆h mm0 %ree stream velocity, 3 m6s0 +eynolds number U u













−

U u U u 1 " "" 11 11 .! !<!1.; ".77 ".7! ".< "" 1 1 >.#; 11!;.; ".7"< ".1"> ." "" 1> 1> !.; 11"7;".> ".>" ".1> .< "" ;" ;" !.>" 11>#!.; ".<7 ".11< 1." "" ;" ;" !.>" 11>#!.; ".<7 ".11< 1.< "" ;1 ;1 1".#< 1;<!1. ".; ".1;1 ;." "1 ;1 ;" !.>" 11>#!.; ".<7 ".11< ;.< "1 ;1 ;" !.>" 11>#!.; ".<7 ".11< #." "1 ;1 ;" !.>" 11>#!.; ".<7 ".11< #.< "1 ;1 ;" !.>" 11>#!.; ".<7 ".11<

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





 −

U u U u 1 " "" 1 1 >.#; <7>.1 ".7"< ".1"> ".< "" 1> 1> !.; <>>.< ".>" ".1> ." "" 1> 1> !.; <>>.< ".>" ".1> .< "" ;" ;" !.>" "!1<. ".<7 ".11< 1." "1 ;" ;" !.>" "!1<. ".<7 ".11< 1.< "1 ;" ;" !.>" "!1<. ".<7 ".11< ;." "1 ;" ;" !.>" "!1<. ".<7 ".11< ;.< "1 ;" ;" !.>" "!1<. ".<7 ".11< #." "1 ;" ;" !.>" "!1<. ".<7 ".11< #.< "1 ;" ;" !.>" "!1<. ".<7 ".11<

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











−

U u U u 1 " "" 11 11 .! !<!1.; ".77 ".7! ".< "" 1# 1# 7.7 1"#;#!. ".7;# ".!< ." "" 1 1 >.#; 11!;.; ".7"< ".1"> .< "" 1> 1> !.; 11"7;".> ".>" ".1> 1." "1 ;" 1> !.; 11"7;".> ".>" ".1> 1.< "1 ;" 1> !.; 11"7;".> ".>" ".1> ;." "1 ;" 1> !.; 11"7;".> ".>" ".1> ;.< "1 ;" 1> !.; 11"7;".> ".>" ".1> #." "1 ;" 1> !.; 11"7;".> ".>" ".1> #.< "1 ;" 1> !.; 11"7;".> ".>" ".1>

*. (ample calculation for boundary layer thic$ness, , displacement thic$ness, , momentum thic$ness, and shape factor, H by using experimental.

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For smooth surface with x = 40mm i. -oundary layer thic$ness, 9 <mm ii. 5isplacement thic$ness, 9 * xδ

9 ". x < 9 .< mm iii. @omentum thic$ness, = *1 x δ

9 "." x < 9 ".!< mm iv. (hape factor, H 9

θ δ ∗ = "15 . 0 65 . 1 = .>";

For smooth surface with x = 150mm i. -oundary layer thic$ness, 9 <mm ii. 5isplacement thic$ness, 9 *; xδ

9 "."!; x < 9 .##< mm iii. @omentum thic$ness, = *# x δ

9 "."7 x < 9 ."< mm iv. (hape factor, H 9

θ δ ∗ = 05 . 1 445 . 1 = .;7

For rough surface with x = 40mm

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ii. 5isplacement thic$ness, 9 *< xδ

9 ".">;< x < 9 .1< mm iii. @omentum thic$ness, = * x δ

9 "."< x < 9 ".!7< mm iv. (hape factor, H 9

θ δ ∗ = "75 . 0 25 . 1 =_1.2!2

For rough surface with x = 150mm i. -oundary layer thic$ness, 9 <mm ii. 5isplacement thic$ness, 9 *7 xδ

9 "."!7! x < 9 .#! mm iii. @omentum thic$ness, = *> x δ

9 "."71 x < 9 .">! mm iv. (hape factor, H 9

θ δ ∗ = 0!" . 1 46" . 1 = .;#!

-. (ample calculation for boundary layer thic$ness, , displacement thic$ness, , momentum thic$ness, and shape factor, H by using theoretical.

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L *@&*+ -A3&5*+B L*BC+

For smooth surface with x = 40mm

i. x x Re 0 . 5 = δ mm m !76 . 0 10 755 . ! 62 . 521!4 04 . 0 0 . 5 4 = × = × = − ii. x x Re 72 . 1

=

∗ δ mm m 301 . 0 10 012 . 3 62 . 521!4 04 . 0 72 . 1 4

=

×

=

×

=

− iii. x x Re 664 . 0

=

θ mm m 116 . 0 10 163 . 1 62 . 521!4 04 . 0 664 . 0 4 = × = × = − i#. θ δ ∗

=

H 5"5 . 2 116 . 0 301 . 0

=

i. x x Re 0 . 5 = δ

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mm m 6"5 . 1 10 6"5 . 1 3 . 1"56"2 15 . 0 0 . 5 3 = × = × = − ii. x x Re 72 . 1

=

∗ δ mm m 5!3 . 0 10 !32 . 5 3 . 1"56"2 15 . 0 72 . 1 4

=

×

=

×

=

− iii. x x Re 664 . 0

=

θ mm m 225 . 0 10 252 . 2 3 . 1"56"2 15 . 0 664 . 0 4

=

×

=

×

=

− iv. θ δ ∗ = H 5"1 . 2 225 . 0 5!3 . 0

=

i. x x Re 0 . 5 = δ

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mm m !40 . 0 10 3"! . ! 2 . 5671! 04 . 0 0 . 5 4 = × = × = − ii. x x Re 72 . 1

=

∗ δ mm m 2!" . 0 10 !!" . 2 2 . 5671! 04 . 0 72 . 1 4

=

×

=

×

=

− iii. x x Re 664 . 0

=

θ mm m 112 . 0 10 115 . 1 2 . 5671! 04 . 0 664 . 0 4

=

×

=

×

=

− iv. θ δ ∗ = H 5"1 . 2 112 . 0 2!" . 0

=

i. x x Re 0 . 5 = δ

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mm m 6"5 . 1 10 6"5 . 1 3 . 1"56"2 15 . 0 0 . 5 3 = × = × = − ii. x x Re 72 . 1

=

∗ δ mm m 5!3 . 0 10 !32 . 5 3 . 1"56"2 15 . 0 72 . 1 4

=

×

=

×

=

− iii. x x Re 664 . 0

=

θ mm m 225 . 0 10 252 . 2 3 . 1"56"2 15 . 0 664 . 0 4

=

×

=

×

=

− i#. θ δ ∗ = H 5"1 . 2 225 . 0 5!3 . 0

=

T3+-3LC&T -A3&5*+BL*BC+

i. 5 1

$

%Re

370 .

0

x x = δ

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mm m 6!6 . 1 10 6!6 . 1 $ 6 . 521!4 % 04 . 0 370 . 0 3 5 1

=

×

=

×

=

− ii. 5 1

%Re$

0463

.

0

x = ∗ δ mm m 210" . 0 10 10" . 2 $ 6 . 521!4 % 04 . 0 0463 . 0 4 5 1 = × = × = − iii. 5 1

$

%Re

036 .

0

x x = θ mm m 164 . 0 10 640 . 1 $ 6 . 521!4 % 04 . 0 036 . 0 4 5 1

=

×

=

×

=

− i#. θ δ ∗ = H 2!6 . 1 1640 . 0 210" . 0

=

i. 5 1

$

%Re

370 .

0

x x = δ

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mm m !53 . 4 10 !53 . 4 $ 3 . 1"56"2 % 15 . 0 370 . 0 3 5 1

=

×

=

×

=

− ii. 5 1

%Re$

0463

.

0

x = ∗ δ mm m 6072 . 0 10 072 . 6 $ 3 . 1"56"2 % 15 . 0 0463 . 0 4 5 1 = × = × = − iii. 5 1

$

%Re

036 .

0

x x = θ mm m 4721 . 0 10 721 . 4 $ 3 . 1"56"2 % 15 . 0 036 . 0 4 5 1 = × = × = − i#. θ δ ∗ = H 2!6 . 1 4721 . 0 6072 . 0

=

i. 5 1

$

%Re

370 .

0

x x = δ

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mm m 65! . 1 10 65! . 1 $ 2 . 5671! % 04 . 0 370 . 0 3 5 1

=

×

=

×

=

− ii. 5 1

%Re$

0463

.

0

x = ∗ δ mm m 2074 . 0 10 074 . 2 $ 2 . 5671! % 04 . 0 0463 . 0 4 5 1 = × = × = − iii. 5 1

$

%Re

036 .

0

x x = θ mm m 1613 . 0 10 613 . 1 $ 2 . 5671! % 04 . 0 036 . 0 4 5 1

=

×

=

×

=

− iv. θ δ ∗ = H 2!6 . 1 1613 . 0 2074 . 0

=

For rough surface with x = 150mm (refer to data D)

i. 5 1

$

%Re

370 .

0

x x = δ

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mm m !53 . 4 10 !53 . 4 $ 3 . 1"56"2 % 15 . 0 370 . 0 3 5 1

=

×

=

×

=

− ii. 5 1

%Re$

0463

.

0

x = ∗ δ mm m 6072 . 0 10 072 . 6 $ 3 . 1"56"2 % 15 . 0 0463 . 0 4 5 1 = × = × = − iii. 5 1

$

%Re

036 .

0

x x = θ mm m 4721 . 0 10 721 . 4 $ 3 . 1"56"2 % 15 . 0 036 . 0 4 5 1 = × = × = − iv. θ δ ∗ = H 2!6 . 1 4721 . 0 6072 . 0

=

TABLE 5: Table of comparison for smooth and rough surface under experimental value

and theoretical.

%or smooth surface: #"mm  +ex 9<1>#.0

EXPERIMENT ( m )

THEORY

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δ < x "'; _{>."; x "}'# _{.1> x "}';

δ2 .< x "'; _{;.;;; x "}'# _{1.";> x "}'#

θ ".!< x "'; _{.1>7 x "}'# _{.<># x "}'#

8 .>"> 1.<! .1>7

%or smooth surface: <"mm +ex 9!<!1.;0

EXPERIMENT ( m ) THEORY LAMINAR ( m ) TURBULENT ( m ) δ < x "'; .<1> x "'; #.<< x "'; δ2 .##< x"'; <.1<7 x "'# <.>1< x "'# θ ."< x "'; _{1."1! x "}'# _{#.<1! x "}'# 8 .;7 1.<! .1>

%or rough surface: #"mm +ex 9<7>.10

EXPERIMENT ( m ) THEORY LAMINAR ( m ) TURBULENT ( m ) δ < x "'; >.17 x "'# .; x "'; δ2 .1< x "'; 1.7! x "'# 1."#7 x "'# θ ".!7< x "'; _{."7! x "}'# _{.<!1 x "}'# 8 .1>1 1.<! .1>

%or rough surface: <"mm +ex 9!<!1.;0

EXPERIMENT ( m ) THEORY LAMINAR ( m ) TURBULENT ( m ) δ < x "'; _{.<># x "}'; _{#.711 x "}'; δ2 .#! x "'; _{<.##! x "}'# _{<.!"! x "}'# θ .">! x "'; 1."; x "'# #.<!< x "'# 8 .;#! 1.<! .1>

DISCUSSION

• The micrometer reading y0 has to be started from ."mm as shown in the table , table 1, table ; and table #.

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• The value of displacement thic$ness δ2_{0 is obtained by the graph of} ∞ U u vs y δ .

• The value of momentum thic$ness θ0 is obtained by the graph of

      − ∞ ∞ U u U u vs y 1 δ .

CONCLUSION

This experiment, we can say that the various boundary layer velocity profiles such as boundary layer thic$ness δ0, displacement thic$ness δ2

0, momentum thic$ness θ0 and shape factor 80 are depend on the distance from the leading edge and the surface condition. *ll the result is as state in table <. %rom the table, the boundary layer property is increasing between smooth and rough surface. *nother facts that we can conclude are the micrometer reading y0 for the smooth surface is lower than the rough surface. t is because the free stream at rough surface occurs faster than the smooth surface. *lso as expected δ is increasing with increasing distance from leading edge for both smooth and rough surface. %rom experiment note that shape factor decreasing as distance from leading edge increasing showing boundary layer is changing from laminar to turbulent.

REFERENCES

1! FLUID MECHANICS, "! F! Doug#as$ "! %! &asiore'$ "! ! Swaffie#d$ hird Editio*$ +o*gma* Scie*tific , ech*ica#

-! INTRODUCTION TO FLUID MECHANICS, Ro.ert /! Fox$ #a* %cDo*a#d$ Seco*d Editio*$ "oh* /i#e , So*s!