THERMODYNAMICS AND FLUID MECHANIC 20

THERMODYNAMICS AND FLUID MECHANIC 1
THERMODYNAMICS AND FLUID MECHANICS
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THERMODYNAMICS AND FLUID MECHANIC 2
TABLE OF CONTENT
TABLE OF CONTENT...............................................................................................................................2
TITLE..........................................................................................................................................................3
INTRODUCTION.......................................................................................................................................3
AIM OF EXPERIMENT.........................................................................................................................5
METHOD....................................................................................................................................................5
EXPERIMENTAL PROCEDURE..........................................................................................................6
RESULTS...................................................................................................................................................7
Presentation of results............................................................................................................................10
Calculation of coefficient of lift.........................................................................................................10
Discussion.................................................................................................................................................20
Conclusion.................................................................................................................................................21
Bibliography..............................................................................................................................................22

THERMODYNAMICS AND FLUID MECHANIC 3
TITLE: LIFT ON AN AEROFOIL
INTRODUCTION
In case a body or a particle is put in a flow, the particle will experience some forces from
its environment fluid (liquid or gas). This force exerted in the same direction of the flow of the
fluid is referred to as a drag. While there is another force that is orthogonal to the direction of the
fluid flow is referred to as downforce or a lift. The lift and the drag forces are generated from the
two effects which are viscosity skin friction and difference in pressure acting of the particle or
the body in a fluid. For the Airfoils which have a streamlined body, the flow will remain attached
over the surfaces of the body. This implies that drag is obtained from skin friction while the lift
is from a difference of pressure between the lower and upper surfaces of the body.
In a bluff object like a chimney or a car, the layer boundary is isolated at the same point
which forms a turbulent wake hence drag force dominates. The airfoil’s lift determined by the
angle between the direction of fluid flow and the angle between the airfoil, this angle is better
referred to as the angle of attack (Weber, 2010). When the angle of attack increases from zero to
maximum it will result in increase of lift also from zero to maximum (critical angle of attack) of
which the lift will abruptly decrease. This critical angle of attack (maximum lift) is referred to as
a stall. The drag, lift and angle of attack in aerofoil is illustrated in the following diagram;

THERMODYNAMICS AND FLUID MECHANIC 4
Figure 1: Showing drag, lift, and angle of attack in aerofoil (Tang, 2010).
From figure 1 above it is possible to relate the drag and the lift to the kinetic of flow ½ ρ μ2 that
has a unit of pressure. Through defining the coefficient of drag and lift CD and CL respectively
such that
L=CL A ρ μ2
2 ……………………………………………………………….........................1
Where A is a measure of the area of the body in fluid, L is the lift force, ρ is the fluid density and
μ the velocity of the fluid.
If the fluid is air then velocity is obtained from the Bernoulli's equation as below;
u= √ 0.9895× 2× ρw
ρa × g × H
1000 …………………………………………………..2
Where
u isthe velocity of air , ρa isthe air density , ρw id the water density , H is the difference ∈ pressure

THERMODYNAMICS AND FLUID MECHANIC 5
and g is the gravitational acceleration. The pressure and of the fluid a affects the density of the
air and this is supported by the following equation
ρatm=mRT ……………………………………………………………………………………..3
Where ρatmatmospheric pressure and T is absolute room temperature and R is the gas constant
(287).
AIM OF EXPERIMENT
This experiment is aimed at measuring the effect of the angle of attack on the airfoil’s lift and to
obtain the angle of stall.
METHOD
There were only three equipment which was employed in conducting this experiment, the first
equipment is a wind tunnel which has an aerofoil section (Cao, 2011). This tunnel has 23 holes
along the aerofoil centerline, 11 holes are along the top of the aerofoil while 12 holes are along
the aerofoil bottom. The second equipment used in conducting the experiment is a manometer
which was employed to measure the pressure at the openings of the holes. The third equipment
is the protractor which is employed to measure the angle of attack (α ¿ as it is adjusted (Kweon,
2010). The wind tunnel is illustrated in the following diagram;

THERMODYNAMICS AND FLUID MECHANIC 6
Figure 2: Showing a wind tunnel
EXPERIMENTAL PROCEDURE
The wind tunnel was made to run at lower than the tunnel´s maximum capacity, this was
very significant so that the velocity can be adjusted bit by bit. The small velocity adjustments
are made to ensure that the air velocity is constant. It is also advisable to tale the readings of the
speed gauge at the maximum speed and then reduce the speed till the manometer records a
reduced speed by about 15 %. The aerofoil was fixed to the required angle of attack, the initial
values of the angle of attack were set to be -50 , 00,50, 100 , 130, 150 and -100. The two further
angles of attack were selected, where one is before the stalls of aerofoil while the other one is
just after the aerofoil´s stall. The wind tunnel was started and then the speed was adjusted to be
equal for all the angle of attack, the speeds were adjusted to about 85% maximum. The pressure
was recorded for every point of the aerofoil.

THERMODYNAMICS AND FLUID MECHANIC 7
RESULTS
The general force equation which acts on a surface is given by F= pA, A is the surface
area while p is the pressure. In this context, F is the magnitude of the force and the direction is
normal to the surface having a positive force. The concern here is only lift force which is
orthogonal to the direction of the airflow. Initially, the angle of attack will be considered such
that the lift force is vertical and the lift is given by L= pAcosθ and θ is the angle which the
surface makes with the horizontal plane as illustrated below;
Figure 3: Showing the representation of angle of attack and the horizontal plane
This is used when there is no pressure change when the surface is flat. At this point, the
change in pressure over the top and bottom aerofoil surface and the surface is also curved which
implies that the force will act in several directions at different points along the surface. At this
point, the lift force can be found by L=∫ pcosθ dAand the p is local pressure over small area dA.
The integral can be performed numerically through Simpson´s rule
L=∑ pn cos θn An , n ist h e numberof the points while pn, An and θn are local pressure, area at
position n and angle of the surface to horizontal. The diagram below illustrates aerofoil having
divisions of length δ Sn where the length begins halfway between the point n and n-1 and this ends

THERMODYNAMICS AND FLUID MECHANIC 8
at halfway between point n and n+a . When the width of the aerofoil is w, and the area An can be
illustrated as An =wδ Sn= wδxn
cos θ ∧δXn ist h e h orizontal projections for
δ Sn. This is illustrated as below;
Figure 4: Showing the movement of air across the top surface of the aerofoil
The total lift can be expressed as below;
L=w cos(α) ( ∑
n=12
n=23
px δX n−∑
1
11
pn δX n ) and the coefficient of the lift is given by the following
equation
CL= 2 L
wsρu2
Width w cancels out and it is not required to find obtain the coefficient. The aerofoil length s1
can be obtained in a good approximation as ¿ ∑
n =1
n=11
δ X n . T h e values of δ X n
have been measured∧given∈the following table;
Table 1: Showing The values of δX_(n )

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Table 2: Showing results for the pressure heads for both bottom and top surfaces

THERMODYNAMICS AND FLUID MECHANIC 10
Presentation of results
Calculation of coefficient of lift
From
CL=2 cos ( α ) ¿ ¿ ¿
While the value of u can be obtained from the following equation;
u= √0.9895× 2× ρW
ρa
× g × H
1000
u= √0.9895× 2× 1000
1214 ×9.81 × 24.4
1000
u= √0.390198
u=0.624658
P= ρw g hn
ρa = Patm
RT = 1018 ×105
287 ×292
ρa =1214

THERMODYNAMICS AND FLUID MECHANIC 11
CALCULATION FOR THE TOP SURFACE
Calculation when angle of attack α=−5
S= cos α . ∑
n=1
n=11
δXn
For angle of attack α =−5
S= cos −5 ׿ ¿
S=0.15172
P= ρw g hn
P= ρw g [ 0.255 ]=1000 × 0.255× 9.81
P= 2500.55
For angle of attack α =0
S= cos 0 × 0.1523
S=0.1523
P= ρw g [ 0.206 ]=1000 × 0.206× 9.81

THERMODYNAMICS AND FLUID MECHANIC 12
P=2020.86
For angle of attack α =5
S= cos 5 ×0.1523=0.15172
s¿ 0.15172
P= ρw g [ 0.122 ] =1000 ×0.122 ×9.81
P= 1196.82
For angle of attack α=10
S= cos 10 ×0.1523=0.15172
s¿ 0.14998
P= ρw g [ 0.052 ]=1000 ×0.052 ×9.81
P= 510.12
For angle of attack α=13
S= cos 13 ×0.1523=0.14839

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s¿ 0.14839
P= ρw g [ 0.022 ] =1000 ×0.022 ×9.81
P=215.82
For angle of attack α=15
S= cos 15 ×0.1523=0.14711
s¿ 0.14711
P= ρw g [ 0.081 ]=1000 ×0.081 ×9.81
P=794.61
For angle of attack α=−10
S= cos −10 ×0.1523=0.1523
s¿ 0.149986
P= ρw g [ 0.293 ] =1000 × 0.081× 9.81
P=2874.33

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CALCULATION FOR THE BOTTOM
Calculation when angle of attack α=−5
P= ρw g [ 0.146 ]=1000 × 0.146× 9.81
P=1432.26
Calculation when angle of attack α=0
P= ρw g [ 0.206 ]=1000 × 0.206× 9.81
P=2020.86
Calculation when angle of attack α =5
P= ρw g [ 0.288 ] =1000 × 0.288× 9.81
P=2825.28
Calculation when angle of attack α =10
P= ρw g [ 0.337 ]=1000 × 0.337 ×9.81
P=3305.97
Calculation when angle of attack α =13
P= ρw g [ 0.351 ] =1000 ×0.351 ×9.81
P=3443.31
Calculation when angle of attack α =15
P= ρw g [ 0.345 ]=1000 × 0.345× 9.81

THERMODYNAMICS AND FLUID MECHANIC 15
P=3384.45
Calculation when angle of attack α=−10
P= ρw g [ 0.068 ] =1000 × 0.068× 9.81
P=667.08
Calculation for δX n for the bottom surface.
δX n= 2.9+4.9+7.6 +9.1+13.1+15.2+15.2+ 15.5+15+15+15.3+23.6
1000 = 152.2
1000 = 0.1524
Calculation for CL of
Calculation when angle of attack α=−5
CL=
2cosα [ ∑
n=12
n=23
pnδXn ]
sp u2
CL=2 cos−5 ¿ ¿ ¿
CL= 324.963
72.144
CL=−4.504
Calculation when angle of attack α=0
CL=2 cos 0 ¿ ¿ ¿

THERMODYNAMICS AND FLUID MECHANIC 16
CL= 0.20286
72.144
CL=0.002811
Calculation when angle of attack α=5
CL=2 cos 5 ¿ ¿ ¿
CL= 494.5225
72.045
CL=6.96
Calculation when angle of attack α =10
CL=2 cos 10 ¿ ¿ ¿
CL= 839.065722
70.292398
CL=11.936
Calculation when angle of attack α =13
CL=2 cos 13 ¿ ¿ ¿
CL= 960.241
70.292
CL=13.66

THERMODYNAMICS AND FLUID MECHANIC 17
Calculation when angle of attack α =15
CL=2 cos 15 ¿ ¿ ¿
CL= 762.302
69.686
CL=10.9391
Calculation when angle of attack α=−10
CL=2 cos−10 ¿ ¿ ¿
CL=−661.978
71.0484
CL=10.9391

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Plot a graph showing how the coefficient of lift changes with the angle of attack
Figure 5: Showing how the coefficient of lift changes with the angle of attack

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Plot graphs showing how the pressure changes across the aerofoil
Figure 6: showing how the pressure changes across the aerofoil

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The blue graph shows the pressure of the top surface while the red line shows the pressure at the
bottom.
Discussion
For the graph of coefficient against the angle of attack, when the angle of attack is low
(say at negative) the coefficient of lift is also low (at negative). When the value of the angle of
attack has increased the coefficient of lift also increases until the lift reaches the maximum
(critical angle of attack). From this, the critical angle of attack is at 13. For the second graph,
the graph illustrating the pressure of the top surface, the increase in the angle of attack results to
decrease in pressure until the angle of attack is 13 which is the critical angle of attack when the
pressure starts to increase (Gandhi Mallela, 2018). While for the pressure for the bottom, the
increase in the angle of attack results in increase in pressure until the critical angle of attack 13
when the pressure starts to reduce.
For the operation of aerofoil which results in a lift, the velocity of air o the top is more
than the velocity of air at the bottom. This results in higher pressure at the bottom and lower
pressure at the top of the aerofoil (Tang, 2010). This principle of operation can also be witnessed
in the second graph where when the velocity increases (increase in the angle of attack) the
pressure reduces for the top surface of the aerofoil. The bottom surface of the aerofoil the
velocity is lower hence the pressure is higher. Some sources of errors in this experiment may
include making some holes bigger which may give inappropriate pressure. This error can be
reduced by ensuring that the hole sizes are equal. Some errors may be due to poor calculations
for the pressure and coefficient of lift. This source of error can be reduced by using the correct
formulae to enable getting the required patterns of the graphs.

THERMODYNAMICS AND FLUID MECHANIC 21
The effects of these errors are very vital for the analysis of the experiment and getting the
required patterns of the graphs which are supported by the theory of the operation of the aerofoil.
Errors in this experiment results in poor values which is propagated into the graphs. And when
this happens, then the pattern of the graphs and theory of the operation of aerofoil cannot be
explained (linked).
Conclusion
In summary, the experiment was perfectly conducted and the values obtained were used
to plot the graphs. The graphs had a perfect pattern which were in accordance with the theory of
operation of aerofoil. When the angle of attack has increased the coefficient of lift also increase
until the critical angle of attack. The velocity of air on top is higher hence the pressure is low
(according to Bernoulli’s effect). These theories were supported by the graphs drawn from the
experimented values. In the experiment, there were some sources of errors which might corrupt
the output of the expected outcome. The effects of these errors can be confirmed from the
graphs plotted, in case there were a lot of errors in the experiment the drawn graphs will not
correspond to the theory of operation of aerofoil. This experiment was perfectly conducted and
the obtained values are confirmed in the critical angle of attack which falls at 130 for the three
graphs.

THERMODYNAMICS AND FLUID MECHANIC 22
Bibliography
Cao, N., Ting, D.S. and Carriveau, R., 2011. The performance of a high-lift airfoil in turbulent
wind. Wind Engineering, 35(2), pp.179-196.
Gandhi Mallela, P.P. and Komaleswarao, M., 2018. Lift and drag performance of NACA0012
airfoil at various angle of attack using CFD. International journals of mechanical and
production engineering research and development, 8(3), pp.89-100.
Kweon, J. and Choi, H., 2010. Sectional lift coefficient of a flapping wing in hovering motion.
Physics of Fluids, 22(7), p.071703.
Tang, D. and Dowell, E.H., 2010. Aeroelastic airfoil with free play at angle of attack with gust
excitation. AIAA journal, 48(2), pp.427-442.
Weber, P.W., Howle, L.E. and Murray, M.M., 2010. Lift, drag, and cavitation onset on rudders
with leading-edge tubercles. Marine technology, 47(1), pp.27-36.