MECH3261- Flow Lab
Table of contents
Section
Page
Aim
1
Introduction
1
Apparatus
1
Methos
2
Observation & Results
3
Discussion
9
Conclusion
9
References
9
Aim
The aim of these experiments is to show how flows around an object and boundary layers
behave. The boundary layer experiment is designed to give a firsthand experience in observing
the development of a boundary layer. The second part of the experiment is aimed at taking
measurements at various points on a wing section to quantitatively study the pressure variations
of the surface of a wing.
Introduction
Fluid flow is a very interesting phenomenon. The way fluid behaves over certain objects and
how it behaves on the surface of an object need to be understood in order to have a detailed
knowledge of this effect. Flow of fluids over a body is not made up of linear regions as one
would expect, rather the profile of a flow depends on several factors, most importantly the
surface in contact. The study of fluid flow allows us to develop more efficient designs in
aerodynamics. This experiment will give us a greater insight of fluid motion.
Apparatus
For performing this experiment we need two main pieces of equipment.

a reservoir with constant water flow over a flat plate with a weir downstream

a wind tunnel with an ellipse shape containing pressure gauges
Method
Boundary Layer Experiment:
1. Setup the apparatus according to the diagram of the previous page.
2. An electrode is inserted into slot A and the machine is turned on that produces
Hydrogen bubbles at the wire and follow the shape of the boundary layer.
3. Take the measurements of the estimated boundary layer thickness and the distance of
the point from the leading edge.
4. The electrode is then moves to position B and the steps are repeated until
measurements have been taken for all four locations.
Wind Tunnel Experiment:
1. Observe the elliptical object inside the wind tunnel; record its size and location of the
pressure taps.
2. Switch the wind tunnel on and observe the manometer readings and determine the
pressure variations inside the ellipse for different angles of attack (0,30,60,90).
Observations & Results
Boundary Layer Experiment:
Flow depths:
Over the downstream weir
Over the leading edge of the plate upstream
y2= 3 mm
y1= 3.5 mm
Observed Boundary Layer thickness at points:
A
xa = 14 mm
B
xb = 15 mm
C
xc = 21 mm
D
xd = 24 mm
1. Flow Velocity:
V1A1 = V2A2
=> V1 = V2A2/A1
Where:
V2 = √𝑔𝑦
= √(9.81) ∗ (0.003)
V2 = 0.171551741 m/s
V1 =
0.171551741∗8.61x10^(−4)
9.3975x10^(−4)
A1 = b1y1
= (0.287-0.0185)*(0.0035)
A1 = 9.3975x10-4 m2
= 0.157175896
V1 = 0.157 m/s
2. Reynolds number at points A,B,C and D:
Rex =
𝐕𝐱
𝓿
Where:


V = V1= 0.157 ms-1
𝓋 = 1x10-6 m2s-1 (Kinematic viscosity of water)
A2 = b2y2
= (0.287)*(0.003)
A2 = 8.61x10-4 m2
Rex = 𝐕𝐱 ⁄ 𝓿
9260
20,100
33,600
47,600
Point
A (x =59 mm)
B (x =128 mm)
C (x =214 mm)
D (x =303 mm)
3. Expected boundary layer thickness at points A,B,C and D if the flow was:
Using Rex from part 2 and putting in the equations below:
Point
Equation =>
Laminar
Turbulent
A (x =59 mm)
B (x =128 mm)
C (x =214 mm)
D (x =303 mm)
2.851015 mm
4.198217 mm
5.428716 mm
6.457912 mm
3.608389504 mm
6.704314128 mm
10.11415289 mm
13.35687417 mm
4. Comparing the theoretical results with the experimental:
Point
A
B
C
D
Laminar
Turbulent
2.851015 mm
4.198217 mm
5.428716 mm
6.457912 mm
3.608389504 mm
6.704314128 mm
10.11415289 mm
13.35687417 mm
Experimental
14 mm
15 mm
21 mm
24 mm
The experimental results seem way off the theoretical results by factor of 2 in most cases.
This may be due to experimental errors such as measurement which was done by a ruler
in this experiment. Since the numbers in turbulent flow compared with the laminar are a
lot closer to the experimental values, we can conclude that the flow was turbulent.
5. Discuss the development of the boundary layer.
In “discussion” section on page 9.
Wind Tunnel Experiment:


Length of major axis of ellipse: 100 mm
Length of minor axis of ellipse: 40 mm
Station Number
TAP 1
TAP 2
Pref
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
Manometer Reading (mm)
Angle of Attack (degrees)
0
30
60
90
96.52
91.44
86.36
81.28
118.11 109.22 93.98
91.44
119.38 119.38 119.38 119.38
130.81 139.7 142.24 142.24
130.81 139.7 143.51 142.24
132.08 140.97 144.78 143.51
137.16 140.97 149.86 144.78
139.7 142.24 147.32 147.32
142.24 138.43 149.86 144.78
144.78 139.7 147.32 146.05
144.78 139.7 142.24 144.78
121.92 106.68 121.92 119.38
116.84 139.7
139.7 142.24
104.14 137.16 139.7 142.24
96.52 137.16 142.24 142.24
95.25 119.38 144.78 139.7
104.14 96.52
127
147.32
114.3
114.3 109.22 134.62
134.62 90.17
86.36
99.06
139.7 105.41 85.09
83.82
127
116.84 83.82 104.14
134.62 132.08 109.22 83.82
127
137.16 101.6 104.14
129.54 137.16
127
132.08
129.54 139.7 142.24 142.24
127
137.16 139.7
139.7
119.38 119.38 119.38 119.38
Coordinates
x
y
49.5
49
44
34
18
0
-18
-34
-44
-49
-49.5
-50
-49.5
-49
-44
-34
-18
0
18
34
44
49
49.5
50
2.82
3.98
9.50
14.66
18.66
20.00
18.66
14.66
9.50
3.98
2.82
0.00
-2.82
-3.98
-9.50
-14.66
-18.66
-20.00
-18.66
-14.66
-9.50
-3.98
-2.82
0.00
Wind Tunnel Dimensions:
Section
Tap 1
0.6
Length (m)
0.36
Area (m^2)
Tap 2
0.3
0.09
1.2 kg/m3
998 kg/m3
1.80x10-5 Pa.s
Density of air (p)
Density of manometer fluid (pm)
Dynamic Viscosity of air
Projected Area In Freestream
Angle (degrees)
0
30
0.012 0.015
Area (m^2)
60
0.025981
90
0.03
1. Velocity of the flow in the wind tunnel:
The velocity can be found by applying Bernoulli’s equations between section 1 and 2 of the wind
tunnel:
𝑃1
𝑝
+
𝑉1
2
+ 𝑔𝑧1 =
𝑃2
𝑝
+
𝑉2
2
+ 𝑔𝑧2
z1 = z2
𝑃1
𝑝
+
𝑉1
2
But
=
𝑃2
𝑝
+
𝑉2
=> 𝑉2 − 𝑉1 =
2
2(𝑃1−𝑃2)
𝑝
P1-P2 = pmg(h2-h1) & V1A1= V2A2
𝑉2 − 𝑉1 =
Therefore
2(pm𝑔(ℎ2−ℎ1))
𝑝
𝑉2 =
=> 𝑉2 −
2𝐴1(pm)𝑔(ℎ2−ℎ1)
𝑝(𝐴1−𝐴2)
𝑉2𝐴2
𝐴1
=
2((pm)𝑔(ℎ2−ℎ1))
=> 𝑉2 =
𝑝
2∗0.36∗998∗9.81∗(0.11811−0.09652)
1.2∗(0.36−0.09)
V2 = 469.7 m/s
2. Reynolds number for each angle of attack:
Re =
𝐕𝐃
𝓿
Where V is the velocity, D is the projected area and 𝓋 is
the dynamic viscosity of air.
Angle (degrees)
Re
0
30
60
5
5
3.13x10 3.91x10 6.78x105
90
7.83x105
= 469.7
3. Normal force due to pressure for each angle of attack
𝐹𝑁 = 𝑑𝑙(𝜌𝑔∆ℎ),
where:





l is the height of the wing section = 0.3 m
d is the distance between 2 manometer points on the section of the wing
∆ℎ = Pref pressure – point pressure
𝑔 = 9.81 m/s2
𝜌 = Density of manometer fluid = 998 kg/m3
0 degrees
0.6
0.4
Normal Force
0.2
0
-0.2
1
3
5
7
9
11
13
15
17
19
21
23
17
19
21
23
-0.4
-0.6
-0.8
-1
Station Number
30 degrees
0.6
0.4
Normal Force
0.2
0
-0.2
1
3
5
7
9
11
13
15
-0.4
-0.6
-0.8
-1
Station Number
60 degrees
0.6
0.4
Normal Force
0.2
0
-0.2
1
3
5
7
9
11
13
15
17
19
21
23
17
19
21
23
-0.4
-0.6
-0.8
-1
Station Number
90 degrees
0.6
0.4
Normal Force
0.2
0
-0.2
1
3
5
7
9
11
13
15
-0.4
-0.6
-0.8
-1
Station Number
4. Total pressure drag and the corresponding drag coefficient:
To find drag force only the x component of the normal force is necessary where:
𝐹𝑥 = 𝐹𝑁 × cos 𝜃
𝐶𝐷 =
𝐹𝐷
0.5𝜌𝑣 2 𝐴
𝐹𝐷 = ∑|𝐹𝑋 |
We obtain the following values for Drag coefficient and Drag force:
0 Deg
2.14
0.91
30 Deg
2.43
1.03
60 Deg
5.19
2.21
90 Deg
5.49
2.33
Discussion
Boundary Layer Experiment:
From our results we can see that the boundary layer is a function of the downstream
length and the Reynolds number. The further downstream the larger the boundary layer
thickness. The only way to minimize the boundary layer thickness without changing the
geometry of the experiment is to increase the velocity. Increasing the velocity increases
the Reynolds number which decreases the boundary layer thickness.
Wind Tunnel Experiment:
It can be seen from the above results that as the angle of attack increases so does the drag
force. Since the drag force is proportional to the drag coefficient then also the drag
coefficient increases with a increase of angle of attack.
Conclusion
From the readings that have been taken and the theoretical results calculated for the hydrogen
bubble experiment it can be seen that our results obtained were off experimental readings by a
factor of 2 at most points This may be due to experimental errors such as measurement which
was done by a ruler in this experiment. Since the numbers in turbulent flow compared with the
laminar are a lot closer to the experimental values, we can conclude that the flow was turbulent.
The wind tunnel has allowed observation and firsthand experience in measuring drag coefficient
and calculating drag force. In general the results obtained are not accurate and this experiment is
more correctly modeled as a qualitative experiment.
References



Experiment handout
“Introduction to Fluid Mechanics” 7th Edition, by Fox and MacDonald
“Fundamentals of Thermal-Fluid Sciences” 3rd Edition, by Cengel and Turner

http://www.aerospaceweb.org/question/aerodynamics/q0184.shtml

http://www.av8n.com/how/htm/aoa.html