Boundary Layer Labcomp

8/8/2019 Boundary Layer Labcomp

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Boundary Layer ENME 432L: Section 02

Lab Report Checklist:

_____ Have you included the raw (handwritten) data sheet? _____ Have you included your pre-lab report which has been signed by your TA or instructor?

_____ Have you typed the measured data and included them into your report? _____ Have you included enough data so that the instructor can calculate the final resultsherself?

_____ Have you included detailed methods so that your younger brother or sister can

understand what you did? _____ Have you included one or two figures for the experimental setup to help theinstructor

understand how you made those measurements? _____ Have you included a description of your experimental protocol? _____ Have you provided a table for all the parameters you obtained from other textbook?

_____ Have you performed the uncertainty analysis on at least one indirectly measuredvariables?

_____ Have each member of your group read the lab report?


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Objective

The objective of this experiment was to determine the shear stress and boundarylayer thickness along a plate. This was done using two different methods, measuring the

pressure at different locations using a pitot tube, and performing a theoretical analysis.

Introduction

Boundary layer thickness and the shear stress applied to a surface can be veryimportant in mechanical engineering design. In aircraft design the boundary layer thickness and the shear stress on the wing are very important to control. Both thethickness of the boundary layer and the shear stress have a large impact on the amount of drag experienced by the wing. The boundary layer increases the effective thickness of theairplane wing. An increase in the effective thickness will causes the aircraft to have todisplace more air and in turn increase the drag on the aircraft do to pressure. An increase

in the shear stress on the wing will increase the friction drag that the aircraft experiences.The shear stress and the boundary layer thickness will both be lower at laminar flow sothe best way to decrease both the boundary layer thickness and the shear stress is to

prevent turbulent flow. Figure one shows an example of a boundary layer. There is a

Figure 1

noticeable increase in thickness on the turbulent end of the boundary layer. A better understanding of how to control the shear stress and boundary layer would create the

potential for more efficient and faster aircraft due to reduction in drag.

Materials and Methods

In order to collect all of the necessary data for this experiment the air bench wasused. Figure 2 shows a picture of the air bench.


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Figure 2

A flat piece of metal was fixed in the center of the flow of air in order to create a surfacefor the boundary to be formed. Figure three shows the flat piece of metal on which the

boundary layer was formed.

Figure 3


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The air control on the air bench was first used to set the velocity of the air. Then pressurereadings were taken using the manometer for the static and total pressure above the testsection. All of the measurements to determine the boundary layer were made using the

pitot tube. The pitot tube is a small moveable tube connected to the manometer. Thisallows the pressure to be determined at different locations along the y axis. Pressurereadings were taken at 4 different locations along the axis of the flat piece of metal, xdirection. From left to right on figure the notches represent x1, x2, x3, and x4. The

pressure readings were taken at the surface and then at every .25mm in the direction perpendicular to the surface, y direction. In order to measure the distance that the pitotwas used for each reading a small caliper was used. This caliper is shown in figure 4.

Figure 4

Before beginning the experiment the critical Reynolds's number was used to determinethe first velocity to which the air bench would be set. This was done using equation one.

p

x

xV =Re (1)

Once the velocity was determined the wall tap for P total and the wall tap for P static wereeach plugged into one side of the manometer. Bernoulli's equation could be determined

what the difference in their heights should be at the desired velocity. This is shown inequation two.

212 2

1)( pair w V hh g p = (2)

Once the velocity was set then the heights of the water in the manometer were obtainedfor the P static wall tap and the P total wall tap individually in order to obtain the pressures at


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each of those locations. P static and P total were then calculated using equations three andfour.

( )total air water air static hh g P P += (3)

( )total air water air total hh g P P += (4)

In these equation water is the density of water g is gravity air h is the height of the

water in the side of the manometer open to air and total h is the height of the water in theside of the manometer hooked to the wall tap. After the total and static pressure weredetermined above the test section the upstream velocity could be determined for each of the cases using equation five.

air

staictotal in

P P V

)(2 = (5)

After determining the upstream velocity the pressures at each specific location had to bedetermined. This was done using the readings taken from the pitot tube. The pressure wasdetermined at each of the y locations measured for all four of the x locations. All of the

pressures were determined in the same manner using equation six.

)( total air water air yi hh g P P += (6)

In this equation yi P is the pressure at each one of the y locations measured, air P is

atmospheric pressure, g is gravity, air h is the height of the water in the manometer open

to air, and total h is the height of the water in the side of the manometer connected to the pitot tube. After the pressure at each location was determined the velocity of the air ateach location could be determined. The velocity of the air was determined using the total

pressure at each location and the pressure of air as shown in equation seven.

air

air yi P P y xU

)(2),(

= (7)

In equation 7 ),( y xU is the velocity at each location, yi P is the pressure determined

in equation 6, air P is atmospheric pressure and air is the density of air. After thevelocity at each location was determined a curve fitting method was used to determinethe boundary layer thickness and the shear stress at each location. In order to do this adimensionless quantity for the velocity had to be determined. This was done by taking thevelocity calculated at each location and dividing t by V p. V p is the velocity far away fromthe plate in the potential flow region. Figure 5 shows where V p is located in relation to the

boundary layer.


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Figure 5

V p is not always equal to the upstream velocity but in the case of a thin plate it is because

the effects of a thin plate on the flow of the air only affect a small area. After determiningthis the dimensionless quantity was then calculated using equation eight.

inV y xU

DQ),(

= (8)

In equation 8 V in is the upstream velocity, U(x,y) is the velocity at each location and DQis the dimensionless quantity. The goal of the curve fitting was to determine an equationthat would give the best curve for the experimental data. The equation used to do this wasequation nine.

01 y y

e

(9)

In equation nine y is the location of the measurements taken in the y direction from theflat bar and y 0 is a variable quantity that is used to fit the equation to the given set of data.In order to determine the correct value of y 0 the error between equations eight and ninewas determined with different values of y 0. This was done using equation ten.

2))1(),(

( 0 y y

in

eV

y xU

(10)

This equation was done for the velocity at each y location for each of the x locations. Thesum of all of the errors at each x location was then calculated. This process was done for different values of y 0 until a minimum error was obtained at each x location. With a valueof y 0 for each of the x locations for each flow rate the boundary layer thickness and theshear stress could then be determined at each location. The thickness of the boundarylayer was determined using equation eleven.


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)(6.4)( 0 x y x = (11)

The shear stress was then determined using equation twelve.

)()(

0 x y

V x p s

= (12)

After both the shear stress and the thickness of the boundary layer were calculated usingthe experimental data they were both calculated using theoretical methods to determinethe accuracy of the experimental results. In order to determine the theoretical results thedistance to each of the x locations along the bar was determined. Using this distance andthe upstream velocity of the air they Reynold's number could be determined at eachlocation. The Reynold's number was determined using equation thirteen.

p x

xV =Re (13)

In equation 13 x is the distance to each of the locations along the plate, V p is the upstreamvelocity, is the density of air, and is the dynamic viscosity of air. Once theReynold's number was determined the boundary layer thickness at each of the x locationscould be determined using equation fourteen if the flow is laminar and equation fifteen if the flow is turbulent.

x

x x

Re

5)( = (14)

51

37.)(

=

xV x x

(15)

In equation fourteen x is the distance to the x location where the thickness is beingdetermined and Re x is the Reynold's number at that location. In equation fifteen V isthe upstream velocity. After determining the boundary layer thickness for each of thelocations using the theoretical formula the shear stress was determined for each locationusing the theoretical formula. This was done using equation sixteen for the locations withlaminar flow. For turbulent flow there isn't a good enough understanding of the flow to

determine a theoretical equation for the shear stress. The shear stress at these locationsmust just be determined using experimental results.

xV

V x s

= 332.)( (16)


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After the shear stress was calculated for all of the trials with a laminar flow usingequation sixteen all of the calculations using both methods were finished. Listed below isthe experimental protocol used to complete the experiment.

Experimental Protocol:

1) Position the plate at the first notch.

2) Position the pitot tube against the plate.

3) Turn on air bench and adjust to desired flow.

4) Measure P total,in and P static,in

5) Take pitot tube manometer readings. After each reading, move the pitot tube awayfrom the plate in increments of 0.25mm and record the new manometer readings.

6) Repeat testing at other notch locations on the plate.

7) Repeat testing at a new velocity which creates mixed flow.

8) Turn off air bench.

Results

The first part of the results is all of the given values or parameters that wereobtained from the text book. All of these values are listed in table 1.

Table 1

air(kg/m 3 )

water(kg/m 3 )

g(m/s 2 )

p air(Pa)

air(Ns/m 2 )

air(m 2 /s)

1.204 995.7 9.8110132

5 1.82E-05 1.56E-05

Before beginning the experiment the critical velocity and the corresponding heightdifference when the static and total wall taps were hooked to the manometer had to becalculated. This was done using equations one and two. The actual calculation is shown

below.

)1056.1(

)255(.Re 5== x

V m xV p p x


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smV p /71.30=

2312

23 )/71.30)(/204.1(21

))(/81.9)(/7.995( smmkg hh smmkg =

mmh 58=

After determining all of the parameters needed from the text book and setting the air bench to the correct velocity all of the experimental data was collected. The first datacollected from each of the trials was the total and static pressure. From this the upstreamvelocity was calculated. Table two shows the total and static pressure for each of thetrials and the corresponding upstream velocity.

Table 2

Trial Pressure H air (mm) H total (mm) Pressure (Pa) V p (m/s)

1 Pstatic 100 96 101364.1 29.32503Ptotal 129 72 101881.8

2Pstatic 100 95 101373.8

32.64172Ptotal 133 62.33 102015.3

The calculation for the static pressure was done using equation three. The calculation for the static pressure for trial one is shown below.

( ) Pamkg Pahh g P P total air water air static 1.101364)096.100(./7.995101325 3 =+=+=

The total pressure for each of the trials was calculated in the same manner. After obtaining the static and total pressure for each of the trials the upstream velocity wascalculated for each trial using equation five. The calculation for the upstream velocity for trial one is shown below.

smmkg

Pa P P V

air

staictotal in /32503.29/204.1

)1.1013648.101881(2)(23 =

==

The experimental results collected for each of the trials using the pitot tube are shown intables three and four. Table three shows the results obtained from the pitot tube at each of

the y locations for all four of the x locations for trial one.


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Table 3

Table four shows the results obtained from the pitot tube at each of the y locations for theall of the x locations for trial two.

X1 (.105m) X2 (.155m)Y(mm)

Hair (mm) H total (mm)

h(mm)

Y(mm)


h(mm)

0 100 95 5 0 100 94 60.25 109 87 22 0.25 104 91 13

0.5 119 80 39 0.5 110 85 250.75 119 75 44 0.75 117 79 38

1 121 74 47 1 119 76 431.25 121 73 48 1.25 121 75 46

1.5 121 73 48 1.5 121 75 461.75 121 73 48 1.75 121 75 46

X3 (.205m) X4 (.255m)

Y(mm) Hair

(mm) H total (mm) h(mm) Y(mm) Hair

(mm) H total (mm) h(mm)0 103 93 10 0 104 92 12

0.25 106 89 17 0.25 109 87 220.5 111 84 27 0.5 111 84 27

0.75 114 81 33 0.75 113 83 301 117 79 38 1 114 81 33

1.25 119 77 42 1.25 116 80 361.5 119 76 43 1.5 116 80 36

1.75 120 75 45 1.75 118 78 402 120 75 45 2 118 78 40

2.25 121 74 47 2.25 118 78 402.5 121 74 47 2.5 N/A N/A N/A

2.75 121 74 47 2.75 N/A N/A N/A


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Table 4

Once all of the experimental data was obtained the pressure, velocity, and thedimensionless quantity needed for the curve fitting process could be calculated for eachof the y values at each of the x locations. In order to calculate the pressure at eachlocation equation six was used. The pressure calculation for the first y value at the first x

location for trial one is shown below.

)095.100)(./81.9)(/7.995(101325)( 23 mm smmkg Pahh g P P total air water air yi +=+=

Pa8.101373=

X1 (.105m) X2 (.155m)Y(mm)


h(mm)

Y(mm) H air (mm) H total (mm)

h(mm)

0 102 93 9 0 102 92 100.25 112 84 28 0.25 109 86 23

0.5 123 71 52 0.5 118 76 420.75 128 68 60 0.75 125 70 55

1 129 66 63 1 128 68 601.25 130 65 65 1.25 129 66 63

1.5 130 65 65 1.5 130 65 651.75 130 65 65 1.75 130 65 65

2 N/A N/A N/A 2 130 65 65

X3 (.205m) X4 (.255m)Y

(mm)

Hair

(mm) H total (mm)

h

(mm)

Y

(mm)

Hair

(mm) H total (mm)

h

(mm)0 106 90 16 0 107 89 18

0.25 112 84 28 0.25 114 81 330.5 117 78 39 0.5 117 78 39

0.75 121 74 47 0.75 119 77 421 126 71 55 1 120 75 45

1.25 126 69 57 1.25 121 74 471.5 128 68 60 1.5 124 72 52

1.75 129 67 62 1.75 125 71 542 129 67 62 2 126 70 56

2.25 130 66 64 2.25 128 68 60

2.5 130 65 65 2.5 128 68 602.75 130 65 65 2.75 129 67 623 130 65 65 3 129 66 63

3.25 N/A N/A N/A 3.25 129 66 633.5 N/A N/A N/A 3.5 129 66 63


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After calculating the pressure the velocity was calculated at each location using equationseven. The velocity calculation for the first y value at the first x location for trial one isshown below.

smmkg Pa Pa P P

y xU air

air yi

/006737.9/204.1)1013258.101373(2)(2

),( 3=

=

=

With the velocity at each location calculated the dimensionless quantity for the curvefitting could be calculated using equation eight. The dimensionless quantity calculationfor the first y value at the first x location for trial one is shown below.

307135./32503.29/006737.9),( === sm sm

V y xU

DQin

The results for these calculations for all four x values for both trials are shown in tables

five and six. Table five shows the calculated results for the data obtained at each of the ylocations for the all of the x locations for trial one.

Table 5

X1 X2Y (mm) P total (Pa) U(x,y) (m/s) U(x,y)/V p Y (mm) P total (Pa) U(x,y) (m/s) U(x,y)/V p

0.00 101373.84 9.01 0.31 0.00 101383.61 9.87 0.340.25 101539.89 18.89 0.64 0.25 101451.98 14.52 0.500.50 101705.94 25.15 0.86 0.50 101569.20 20.14 0.690.75 101754.78 26.72 0.91 0.75 101696.18 24.83 0.851.00 101784.09 27.61 0.94 1.00 101745.02 26.41 0.901.25 101793.86 27.91 0.95 1.25 101774.32 27.32 0.931.50 101793.86 27.91 0.95 1.50 101774.32 27.32 0.931.75 101793.86 27.91 0.95 1.75 101774.32 27.32 0.93

X3 X4Y (mm) P total (Pa) U(x,y) (m/s) U(x,y)/V p Y (mm) P total (Pa) U(x,y) (m/s) U(x,y)/V p

0.00 101422.68 12.74 0.43 0.00 101442.21 13.95 0.480.25 101491.05 16.61 0.57 0.25 101539.89 18.89 0.640.50 101588.73 20.93 0.71 0.50 101588.73 20.93 0.710.75 101647.34 23.14 0.79 0.75 101618.03 22.06 0.751.00 101696.18 24.83 0.85 1.00 101647.34 23.14 0.791.25 101735.25 26.10 0.89 1.25 101676.64 24.17 0.821.50 101745.02 26.41 0.90 1.50 101676.64 24.17 0.821.75 101764.55 27.02 0.92 1.75 101715.71 25.47 0.872.00 101764.55 27.02 0.92 2.00 101715.71 25.47 0.872.25 101784.09 27.61 0.94 2.25 101715.71 25.47 0.872.50 101784.09 27.61 0.94 2.50 N/A N/A N/A2.75 101784.09 27.61 0.94 2.75 N/A N/A N/A

Table six shows the calculated results for the data obtained at each of the y locations for the all of the x locations for trial two.


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2))1(),(

( 0 y y

in

eV

y xU

= 094332.)0307135(. 2 =

These two calculations were performed for each y 0 value selected at each y location for each of the x locations. Table seven shows how the minimum error value was calculatedfor the first x location for trial one.

Table 7

1-exp(-y/y 0)(y0=.25)

Error 1-exp(-y/y 0)(y0=.26)Error 1-exp(-y/y 0)(y0=.27)

Error

0 0.094332 0 0.094332 0 0.0943320.63212056 0.000147 0.61769573 0.000705 0.60383557 0.0016330.86466472 4.74E-05 0.85384344 1.55E-05 0.84305374 0.0002170.95021293 0.001529 0.94412372 0.00109 0.93782348 0.000714

0.98168436 0.001602 0.97863826 0.001368 0.97536787 0.0011360.99326205 0.001734 0.99183332 0.001617 0.99024163 0.0014910.99752125 0.002107 0.99687784 0.002048 0.99613408 0.0019810.99908812 0.002253 0.99880639 0.002226 0.99846846 0.002195

Sum 0.103751 Sum 0.103401 Sum 0.103699

The results from table seven show that the sum of errors that is the lowest is for y 0=.26 sothis value was selected for the first x location for trial one. The following eight graphs,figures six through thirteen show the line created by the curve fitting versus the points

obtained from the calculation of pV

y xU ),(. Table 8 shows the y 0 values calculated for

each of the other locations.

Table 8

Trial 1 y 0 Trial 2 y 0X1 0.26 X1 0.23X2 0.41 X2 0.3X3 0.43 X3 0.31X4 0.47 X4 0.33


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Trial 1 X1 Curve Vs Actual

0

0.2

0.4

0.6

0.8

1

1.2

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2

Y location (mm)

N o n

d i m e n s i o n a

l Q u a n

t i t y

Figure 6


0

0.2

0.4

0.6

0.8

1

1.2

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2

Y location (mm)

N o n

d i m e n s

i o n a

l Q u a n

t i t y

Figure 7


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0

0.2

0.4

0.6

0.8

1

1.2

0 0.5 1 1.5 2 2.5 3

Y location (mm)

N o n

d i m e n s i o n a

l Q u a n

t i t y

Figure 8


0

0.2

0.4

0.6

0.8

1

1.2

0 0.5 1 1.5 2 2.5

Y location (mm)

N o n

d i m e n s

i o n a

l Q u a n

t i t y

Figure 9


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0

0.2

0.4

0.6

0.8

1

1.2

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2

Y location (mm)

N o n

d i m e n s i o n a

l Q u a n

t i t y

Figure 10


0

0.2

0.4

0.6

0.8

1

1.2

0 0.5 1 1.5 2 2.5

Y location (mm)

N o n

d i m e n s i o n a l

Q u a n

t i t y

Figure 11


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0

0.2

0.4

0.6

0.8

1

1.2

0 0.5 1 1.5 2 2.5 3 3.5

Y location (mm)

N o n

d i m e n s i o n a

l Q u a n

t i t y

Figure 12


0

0.2

0.4

0.6

0.8

1

1.2

0 0.5 1 1.5 2 2.5 3 3.5 4

Y location (mm)

N o n

d i m e n s

i o n a

l Q u a n

t i t y

Figure 13

After obtaining the y 0 value for each of the trials the experimental shear stress and boundary layer thickness could be calculated for each of the trials. The boundary layer thickness was calculated using equation eleven. The calculation for the boundary layer thickness for the first x location for the first trial is shown below.

mmm

x y x 001196.1000

)26)(.6.4()(6.4)( 0 ===

The shear stress was then calculated using equation twelve. The calculation for the shear stress first the first x location for the first trial is shown below.


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052752.2

100026.

)/32503.29)(/000182(.)(

)(2

0

===mm

smm Ns x y

V x p s

After obtaining the shear stress and boundary layer thickness for all of the locations using

the experimental results the theoretical equations were applied for a basis of comparison.First the Reynold's number for each of the x locations for each trial was calculated usingV p and the x distance with equation thirteen. The calculation for the Reynold's number for the first x location for the first trial is shown below.

6.203681)/000182(.

)/204.1)(/32503.29)(105(.Re 2

3

===m Ns

mkg smm xV p x

After calculating the Reynold's number the boundary layer thickness could be calculatedusing equation fourteen if the flow was laminar and equation fifteen if the flow is

turbulent. The calculation for the boundary layer thickness for the first x location of trialone is shown below.

mm x

x x

001163.6.203681

)105(.5

Re

5)( ===

After calculating the boundary layer thickness equation sixteen was then used to calculatethe theoretical shear stress. The calculation for the shear stress for the first x location for the first trial is shown below.

)105)(./0000182(.)/204.1)(/32503.29(

)/32503.29)(/0000182(.332.332.)( 23

2

mm Nsmkg sm

smm Ns xV

V x s ==

761672.=

The theoretical and experimental results for the shear stress and boundary layer thicknessare all shown for trial one in table nine and for trial two in table ten.

Table 9

Table 10

Vp=29.32503

Position Distance(mm) ReDelta

ExperimentalTau

ExperimentalDelta

TheoreticalTau

Theoretical

x1 0.105 203681.6 0.001163278 0.761672199 0.001196 2.05275201x2 0.155 300672.9 0.001413366 0.626898029 0.001886 1.30174518x3 0.205 397664.1 0.00162542 0.545112101 0.001978 1.24119889x4 0.255 494655.4 0.001812837 0.488756632 0.002162 1.13556494


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These tables show all of the data calculated for both methods which are the final resultsof the experiment. The Reynold's number column shows that all of the Reynold's number were less than the critical number of 5x10 5 except for the last x location for the secondtrial so the laminar flow calculation could be used for all of the trials except for that one.The boundary layer calculation for the x4 for the second trial required the turbulent flowcalculation and the shear stress could not be determined.

Discussion

As with any experiment this experiment had limitations and sources of error. Oneimportant source of error was the human error introduced when taking the measurements.In the case of the air bench the air flow isn't always maintained at a steady level. Thiscould introduce error because the air isn't always flowing at the exact velocity that itshould be. This also makes the levels of the water in the manometers fluctuate slightly

because the pressure is going up and down. There is definitely error generated when ahuman is trying to read the water level in a manometer when the meniscus is constantlymoving. The percent error between the theoretical boundary layer thickness and thetheoretical boundary layer thickness is shown in table eleven for the first trial and tabletwelve for the second trial.

Table 11

Vp=29.32503

Position Distance(mm)Delta

ExperimentalDelta

TheoreticalPercent

Error Tau

ExperimentalTau

TheoreticalPercent

Error

x1 0.105 0.001163 0.001196 2.812944 0.761672 2.052752 62.89507x2 0.155 0.001413 0.001886 33.44033 0.626898 1.301745 51.84172x3 0.205 0.001625 0.001978 21.69161 0.545112 1.241199 56.08181

Vp=32.64172

PositionDistance

(mm) ReDelta

ExperimentalTau

ExperimentalDelta

TheoreticalTau

Theoreticalx1 0.105 226753.2 0.00110251 0.894478609 0.001058 0.001058x2 0.155 334731 0.001339534 0.736204995 0.00138 0.00138x3 0.205 442708.7 0.001540511 0.640158738 0.001426 0.001426x4 0.255 550686.4 0.006707505 0.283393485 0.001518 N/A


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After calculating the uncertainty for each of the heights the uncertainty for the pressurewas calculated using equation 20 and 21.

( ) ( )

+

=

22

)()( total total total

hair

total P Uhh

P U

h P

U air total

(20)

( )( ) ( )( )( )223223 001528.)/81.9)(/7.995(001414.)/81.9)(/7.995(1, m smmkg m smmkg U s P += Pa3353.20= (21)

This makes the final uncertainty for P total Pa3353.203.102015 . This is a variation of only .019% which is very small so the total pressure can be considered a measurementthat was taken with low uncertainty.

ConclusionAny time that fluid flow is occurring it is important to know the boundary layer

around surfaces that it comes into contact with. This experiment shows both anexperimental and a theoretical way to determine the boundary layer and the shear stresson a flat plate. The experimental way to obtain the shear stress on a plate under turbulentflow is useful because there is no theoretical equation to solve for it. This knowledgecould be important for the design of something like an airplane wing where the shear stress needs to be know but in many cases it will be under turbulent flow. The techniquesused to measure the boundary layer thickness and shear stress in this lab could be avaluable design tool.


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References

1.) Anderson, John (1992). Fundamentals of Aerodynamics (2nd edition ed.). Toronto:S.S.CHAND. pp. 711714.

2.) Munson, Bruce, Donald Young, Theodore Okiishi, and Wade Huebsch. Fundamentals of Fluid Mechanics . 6th. John Wiley & Sons, Inc., 2009.Print.

3.) Zhu, L. 2009. Class notes. Uncertainty. ENME 432L. UMBC. Baltimore, MD

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