CIVL3612/9612 sample exam
Q1
Page 1 of 8
Multiple Multiple choice choice question questionss (15 2 points each = 30 points)
×
Remember to write your answer in the booklet provided. See the sample below.
YOUR EXAM ANSWER BOOKLET
…. and so on
1. In a steady flow, (a) Convecti Convective ve acceleration acceleration equals zero (b) Local acceleration acceleration equals zero zero (c) Total acceleration acceleration equals zero 2. In an incompressible flow (a) The volume and and shape of a fluid element remains unchanged unchanged (b) The volume of a fluid element element remains constant but but the shape can change (c) only the volume volume can change
−V = 0 then the flow is ∇×→
3. If (a) (b) (c) (d)
Incompressible Incompressible Irrotation Irrotational al Invisc Inviscid id Irrespons Irresponsible ible
4. Two distinct potential flows can be combined by superposition superposition because (a) they are irrotational irrotational flows flows (b) they are inviscid inviscid flows flows (c) they are governed governed by linear linear partial differential differential equation 5. The stream function ψ can be defined for a flow only if the flow is (a) steady, steady, incompressible and two-dimensiona two-dimensionall (b) two-dimensional two-dimensional (c) steady and incompressible incompressible 6. Euler’s Euler’s equations for fluid flow governs governs (a) General incompressible incompressible flow flow (b) Inviscid Inviscid flow (c) Two-dimensional wo-dimensional incompressible incompressible flow (d) Irrotation Irrotational al flow flow 7. For steady flow of an incompressible fluid without free surfaces, dynamic and kinematic similarity is achieved (for geometrically similar systems) if (a) the Froude numbers are the same (b) the Euler Euler numbers numbers are the same same (c) the Mach Mach numbers numbers are the same same (d) the Reynolds Reynolds numbers numbers are the same same
CIVL3612/9612 sample exam
Page 2 of 8
8. In a steady flow (a) the velocity does not change with time but can change in space (b) the velocity does not change with time and in space (c) the velocity can change with time and/or space 9. In an incompressible flow V = 0 (a) V = 0 (b) V = 0 (c) (d) All above conditions apply
∇ ×−→−→ ∇−→· ∇
10. Flow over a half-body can be simulated by superposition of (a) uniform flow and a source (b) uniform flow and a vortex (c) uniform flow and a sink (d) uniform flow and a doublet 11. The velocity potential φ can be defined for a flow only if the flow is (a) rotational (b) viscous (c) steady and two-dimensional (d) irrotational 12. The Froude number can be interpreted as (a) ratio of inertia force to external (gravity) force (b) ratio of viscous force to external (gravity) force (c) ratio of external (gravity) force to viscous force (d) ratio of surface tension to inertia force 13. Kinematic similarity between a prototype and its model implies (a) they have same time-scale ratio and force-scale ratio (b) they have same length-scale ratio, time-scale ratio and force-scale ratio (c) they have same length-scale ratio and force-scale ratio (d) they have same length-scale ratio and time-scale ratio 14. In a fully developed viscous flow through a horizontal pipe, the pressure in the direction of flow, (a) remains constant (b) increases linearly (c) decreases linearly (d) increases quadratically 15. Dimples on a golf ball are preferred compared to a smooth ball because (a) a dimpled ball is easier to hold (b) it has reduced friction resistance (c) it looks nicer (d) it has delayed separation and hence reduced pressure drag 16. The lift and drag coefficients ( C L and C D , respectively) for a rigid body typically (a) depend on the Reynolds number (b) depend on the shape of the body (c) vary with the surface roughness (d) All of the above
CIVL3612/9612 sample exam
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17. In a uniform depth flow (a) the change in bottom elevation is compensated by the head loss (b) the change in bottom elevation accelerates the flow downstream (c) head losses are negligible (d) Froude number is always in the subcritical regime 18. For a turbomachine pump, such as a window fan or a propeller, (a) rotation of the fan or propeller results in a movement of fluid (b) rotation of the fan or propeller results in energy being transferred to the fluid (c) rotation of the fan or propeller requires work input to the fan or propeller shaft (d) All of the above 19. A surface wave produced by a disturbance can travel upstream, (a) when the flow is sub-critical (b) when the flow is critical (c) when the flow is super-critical (d) when the flow is laminar 20. Hydraulic jump results in (a) head loss (b) decrease in kinetic energy (c) increase in surface elevation (d) all of the above
Q2
Short answer questions (5 2 points each = 10 points)
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Limit your responses to one to two line sentences only. 1. List two characteristics of a boundary layer 2. State the assumption for potential flow approximation 3. When can one neglect Froude number in analysis of fluid flow? 4. In a circular pipe flow, state why laminar flow is preferred than a turbulent flow? 5. Is acceleration zero in a steady flow? Why?
CIVL3612/9612 sample exam
Q3
Page 4 of 8
Pumps - Similarity relations - 10 points
A centrifugal pump having an impeller diameter of 1 m is to be constructed so that it will supply a head rise of 200 m at a flowrate of 4.1 m 3 /s of water when operating at a speed of 1200 rpm. To study the characteristics of this pump, a 1/5 scale geometrically similar model operated at the same speed is to be tested in the laboratory. Determine the required model discharge and head rise. Assume that both model and prototype operate with the same efficiency (and therefore with same flow coefficient).
Q4
Viscous pipe flow - Major losses - 10 points
Water flows at a rate of 330 litres/min in a 3.5 cm diameter smooth pipe that contains a sudden contraction to a 2.5 cm diameter smooth pipe. 3.5 cm
2.5 cm
?
10 m
Determine L2 if the head loss over the lengths L1 and L2 is the same. Consider kinematic viscosity ν = µ/ρ = 8 10 page 7.
×
Q5
−7
m2 /s for water. Use the Moody chart provided on
Laminar pipe flow - 10 points
Oil flows through a smooth pipe of diameter D = 2 cm between points (1) and (2) that are 2 m apart at a rate Q = 3 10 3 m3 /s.
×
−
1
800 kPa
ℓ 2 m 2 cm 2
45°
Determine the pressure p2 at point (2) if (a) the flow is downwards from (1) to (2) (b) the flow is upwards from (2) to (1) Consider dynamic viscosity µ = 0.40 kg/m s and density ρ = 900 kg/m3 for the oil. Refer to laminar pipe flow equations on page 8.
·
CIVL3612/9612 sample exam
Q6
Page 5 of 8
Laminar boundary layer - 10 points
An approximate velocity distribution for laminar flow is given as 2
y
u y =2 U δ
−
δ
.
The momentum thickness for this profile is given by the expression
θ 2 = . δ 15
(a) Determine an expression for δ (x) using the von K´arm´an integral momentum equation, τ w =
ρU 2
dθ dx
(b) How does this estimate of δ (x) compare with the Blasius/Prandtl solution for laminar flow.
Q7
Flow over immersed body - Drag and body shape - 10 points
A 500 N cube of specific gravity SG = 1.8 falls through water at a constant speed U . Determine U if the cube falls (a) as oriented Figure - A, (b) as oriented in Figure - B. Consider ρH O = 1000 kg/m3 . 2
Figure ‐ A
Shape
D
Figure ‐ B
Reference area
Drag coefficient
A
C D
Reynolds number Re = ρ UD / µ
Cube
A = D2
1.05
Re > 104
Cube
A = D2
0.80
Re > 104
D
CIVL3612/9612 sample exam
Q8
Page 6 of 8
Open Channel Flow - Specific Energy Diagram - 10 points
A smooth transition section connects two rectangular channels as shown in figure. The channel width increases from 1.8 m to 2.1 m, and the water surface elevation remains the same in channel. The upstream depth of the flow is 0.9 m and the head loss during the transition is equivalent to 5% of the upstream dynamic head V 12 /2g .
(a) Determine h, the amount the channel bed needs to be raised across the transition section to maintain the same surface elevation. (b) Sketch the specific energy diagram for the flow indicating its important characteristics.
Q9
Open Channel Flow - Manning Equation - 10 points
For the symmetrical open channel shown in figure the bottom is smooth concrete and the sides are weedy. The bottom slope is S 0 = 0.001. 3.6 m
0.9 m
1.2 m
Determine the flowrate. Refer to the Manning equation provided on page 8 Values for Manning resistance coefficient n Wetted Perimeter
n
A. Natural channels Clean and straight Sluggish with deep pools Major rivers
0.030 0.040 0.035
B. Floodplains Pasture, farmland Light brush Heavy brush Trees
0.035 0.050 0.075 0.15
C. Excavated earth channels Clean Gravelly Weedy Stony, cobbles
0.022 0.025 0.030 0.035
Wetted Perimeter
D. Artificially lined channels Glass Brass Steel, smooth Steel, painted Steel, riveted Cast iron Concrete, finished Concrete, unfinished Planed wood Clay tile Brickwork Asphalt Corrugated metal Rubble masonry
n 0.010 0.011 0.012 0.014 0.015 0.013 0.012 0.014 0.012 0.014 0.015 0.016 0.022 0.025
CIVL3612/9612 sample exam
Page 7 of 8 _ D _
∋
5 4 0 . 0 . 0 0
3 0 . 0
5 2 1 0 . 0 . 0 0
8 6 1 0 0 0 . 0 . 0 . 0 0 0
4 0 0 . 0
2 0 0 . 0
8 6 4 1 0 0 0 0 0 0 0 0 . 0 . 0 . 0 . 0 0 0 0
2 0 0 0 . 0
1 0 0 0 . 0
5 0 0 0 0 . 0
1 0 0 0 0 . 0 8 6 4 ) 0 1 ( 2
7
7
8
0 1
6 4 ) 0 1 ( 2
6
6
8
0 1
6 4
_ D _ _ µ V _
) 0 1 ( 2
ρ _
5
w o l f t n e l u b r u t y l l o h W
h t o o m S
= e R 5
8
0 1
6 4 ) 0 1 ( 2
4
4
8
r a n w i o l m a f L 1 . 9 8 0 0 . 0 . 0 0
7 0 . 0
6 0 . 0
5 0 . 0
4 0 . 0
3 0 . 0
5 2 0 . 0
2 0 . 0
5 1 0 . 0
e g n a r n o i t i s n a r T
0 1
6 4 ) 0 1 ( 2
3
3
0 1
1 9 8 0 . 0 0 0 0 . 0 . 0 0
f
The Moody Chart - Friction factor as a function of Reynolds number and relative roughness.
CIVL3612/9612 sample exam
Page 8 of 8
Other definitions
hLminor Minor loss coefficient: K L = (V 2 /2g) V 2 Major head loss: h Lmajor = f D 2g 2 p V + z Total head: + γ 2g
∂u τ w = µ ∂y
y =0
Drag coefficient: C D =
D 1 ρV 2 A 2
Skin friction coefficient: c f =
τ w 1 ρV 2 2
Laminar Pipe Flow Solution (for a pipe inclined at angle θ from the horizontal)
V =
(∆ p
− γ sin θ)D
2
,
32µ
Q =
π(∆ p
− γ sin θ)D
4
128µ
∆ p
,
− γ sin θ = 2τ
r
Laminar Boundary Layer (Blasius/Prandtl Solution)
δ = x
δ 1.721 = , x Rex
5 , Rex
θ 0.664 = x Rex
∗
√
√
3/2
τ w = 0.332U
ρµ x
√
0.664 cf = , Rex
,
√
1 C Df =
cf dx
0
Relations for Open Channel Flows
√ V gy z − z Bottom slope S = Froude number: F r = 1
0
Hydraulic radius Rh =
2
Area wetted perimeter
Shear stress in uniform flow: τ w = γRh S 0
hL Friction slope: S f = V 2 q 2 = y + Specific energy: E = y + 2g 2gy 2
Rh2/3 S 01/2 Manning equation: V = n dy S f S 0 = Gradually varying flow: dx 1 F r2
− −
For hydraulic jump:
y2 1 = y1 2
− 1 + 1 + 8F r 2
1
hL =1 y1
−
y 2 F r12 + 1 y1 2
2
y −
1
y2
Relations for Pumps
V 2 + U 2 W 2 U V θ = 2 W shaft wshaft = = U 2 V θ2 ˙ m
−
− U V θ 1
1
Power supplied to the fluid, P f = γQha
ps V s2 p v + NPSHR = γ 2g γ patm pv z 1 NPSHA = γ γ
− − − − ΣhL
gh a Q Head rise coefficient: C H = 2 2 = φ 1 ω D ωD 3 W shaft Q = φ Power coefficient: C P = 2 ρω 3D 5 ωD 3 Q Flow coefficient: C Q = ωD 3 C Q C H η= C P ω Q ω Q N S = , S = S (gh a )3/4 (g NPSHR )3/4
√
√
