Page 2 of 8
Q1 (5 + 5 + 5 + 5 =) 20 marks
Note this question contains word counts, only the number of words specified will be assessed. Within this
word limit you may use equations or figures (each counting for 1 word).
a) The key physical features of air flow over a cylindrical structure can be described by 2 Pi terms:
Reynolds number and Strouhal number. The full-scale structure is 2m in diameter and the free-
stream velocity over it is 1m/s. If the flow is to be modelled in a water channel using a 100mm
diameter cylinder what upstream flow velocity must the water channel generate?
b) Air flows through the circular duct shown in Figure 1. In which section(s) is the flow most likely to
separate? Justify your answer in 30 words or less.
Figure 1
c) Two aerofoil configurations (A & B) are shown in Figure 2, relative flow is horizontal from left to
right.
i. Which configuration is suitable to generate downforce on a vehicle? Justify your answer in
30 words or less.
ii. In 10 words or less describe the main benefit of aerodynamic downforce for vehicle
performance.
Figure 2
d) The water tank as drawn in Figure 3 when stationary begins to accelerates to the right at a constant
acceleration of 3m/s2. The oil in the manometer has a specific gravity of 0.85.
i. What is the slope of the water surface relative to horizontal? Sketch the surface to illustrate
your answer.
ii. What is the gauge pressure at point A?
iii. What is the height, h of the oil surface above the point A?
Figure 3
A B
Oil
1 m
3 m
h
0.5m
A
Page 3 of 8
Q2 25 marks
A shallow jet of water flows over a flat plate as shown in Figure 4. You may assume that the flow is 2D (uniform
into the page). The velocity profiles at two vertical planes 1 and 2 are shown where c, a and b are constants.
The maximum velocity at plane 1 is 0.5m/s and at plane 2 is 0.06 m/s.
Figure 4
a) In your exam booklet draw the flow above showing clearly an appropriate control volume to analyse
the problem
b) What are the mass flow rates through the plate and free-surface respectively?
c) What is the value and units of the constant c in the velocity profile at plane 1?
d) What is the mass flow rate per unit width (into the page) of the jet?
e) Calculations show that for the velocity profile at plane 2 the values of the constants are a = -11.7188
(m-1s-1) and b = 8.4375 (s-1) is this correct? Show calculations to justify your answer.
f) Considering the velocity profile you calculated at plane 1 and the velocity profile given in part e) for
plane 2, which one generates the maximum shear stress and what is the value of this maximum shear
stress?
Page 4 of 8
Q3 25 marks
The 2-pump system shown in Figure 5 moves water between two large tanks from Tank 1 to Tank 2. The water
level of Tank 2 is 20m above that of Tank 1. T-pieces upstream and downstream of the pumps allow the
pumps to be used in parallel. The pumps are identical and fitted with valves to allow isolation, you may
assume that the height difference between the pumps is negligible. The piping between the tanks is all
200mm in diameter, has a surface roughness of 0.4mm and has a total length of 25m outside the pump circuit
(before and after the T-pieces). The length of piping between the two T-pieces is 5m on each path i.e. 10m
in total. Each pump is operating to deliver a head gain of 100m. You may use the following minor loss KL
values in your calculations:
Section KL Section KL
Tank exit 0.3 T-piece (based on higher velocity) 1.2
Bend 0.2 Valve 2.0
Tank entrance 1.0
Figure 5
a) Let the average velocity in the piping outside the pump circuit be Vi, write an equation for the average
velocity of the flow in each pump Vp
b) Write an equation for the major and minor head losses for flow between the tanks in terms of Vi, Vp
and the friction factors outside and inside the pump circuit fi and fp respectively. Simplify the equation
using values given above as much as possible.
c) What is the volume flow rate of water into Tank 2? Hint initially assume the friction factor is for
turbulent flow throughout the system then check your assumption and adjust as necessary.
Page 5 of 8
Q4 30 marks
Water flows through the U-bend pipe of constant diameter (D = 0.2m) shown in Figure 6 which is effectively
3m in length. The average velocity at the inlet is V1 = 1m/s and the mass of the pipe is 10kg. The, minor loss
co-efficient for the bend is KL = 0.6 and p1 = 900Pa gauge. Please use the axis system in the figure where
gravity is aligned with the z-axis.
Figure 6
a) What is the mass flow rate of water through the pipe?
b) What is the pressure difference p = p1 – p2?
c) What force (magnitude and direction) is required to hold the pipe?
d) The pipe is now rotated so that the inlet and outlet flows align with the z-axis and the pipe forms an
upright U shape (i.e. with the inlet and outlets at the top). What force (magnitude and direction) is
required to hold the pipe? Assume that the velocities and pressures are the same as in part c).
END OF EXAM
The following 3 pages contain the Aide Memoire
Page 6 of 8
Aide Memoire
=
1 − 2 = ∫
2
1
= ̅ = ℎ
=
+
=
+
= −
+
= 0 +
22
2
+ 1
2
2 + =
∫ ⃗ . ̂
+
∫
= 0
̅ = ̅
∑ = ∫ ⃗ ⃗ . ̂
∑ = ∑̇⃗ − ∑̇⃗
=
=
=
√
=
=
2
=
∆
1
2
2
=
1
2
2
=
1
2
2
x
lam
x Re
5 2.0Re
37.0
x
turb
x

 34.0* lam 8
*  turb
x
lamDfC Re
33.1
,  2.0, Re
07.0
x
turbDfC 
dy
U
yu 


 −=


0
* )(1
1
+
1
2
2
+ 1 + ℎ =
2
+
2
2
2
+ 2 + ℎ
= ∆ℎ
∆
=
2
2
=
64
ℎ =
2
2
=
22
=
35
=
3
=
√
(ℎ)
3
4
= 1000
−3
= 1.23
−3
= 1.2 × 10
−3 −2
= 1.8 × 10
−5 −2
= 9.8 −2 = 32.2 −2
1 = 0.3048
1 = 0.0254
1 = 0.4536
= /
Ffriction = (coefficient of friction)(Fnormal)
Moment = F X d
Page 7 of 8
Area Moments of Inertia for Common Geometries
Page 8 of 8
Moody Chart for round pipes