Fluid Mechanics Sheet 23

1) Question.
Consider the following statements.
1. Run-of-river plants can be located on any river.
2. Runaway speed of a turbine is generally 180% of normal speed.
3. Underground power stations are suited to areas susceptible to land slides.
4. Higher the specific speed, higher will be the discharge and head.
Which of these statements are correct ?
Answer.
- 1
  
  1 and 2
- 2
  
  2 and 3
- 3
  
  1 and 4
- 4
  
  2 and 4
Answer: 2

Explanation:
2) Question.

To generate 10,000 hp under a head of 81 m while working at a speed of 500 rpm, the turbine of choice would be
Answer.
- 1
  
  Pelton
- 2
  
  Kaplan
- 3
  
  Bulb
- 4
  
  Francis
Answer: 4

Explanation:
3) Question.

The height of a hydraulic jump in a stilling pool was found to be 10 cm in a model with $l_{p} / l_{m} = 36$ . The prototype jump height would be
Answer.
- 1
  
  0.6 m
- 2
  
  3.6 m
- 3
  
  21.6 m
- 4
  
  indeterminable for want of adequate data
Answer: 2

Explanation:
4) Question.

Which one of the following can be a set of velocity components of a two-dimensional flow ?
Answer.
- 1
  
  $u = x + y a n d v = x^{2} + y^{2}$
- 2
  
  u= x+y and v= x-y
- 3
  
  u= xy and v= x/y
- 4
  
  $u = x^{2} + y^{2} a n d v = x^{2} - y^{2}$
Answer: 2

Explanation:
5) Question.
Consider the following statements :
1. Pumps in series operation allow the head to increase.
2. Pumps in series operation increase the flow rate.
3. Pumps in parallel operation increase the flow rate.
4. Pumps in parallel operation allow the head to increase.
Which of these statements are correct ?
Answer.
- 1
  
  1 and 3
- 2
  
  1 and 4
- 3
  
  2 and 4
- 4
  
  3 and 4
Answer: 1

Explanation:
6) Question.
Which of the following statements are true in relation to water hammer phenomenon ?
1. It causes surface erosion in pipes.
2. The pressure rise is given by $ρ C U$ for sudden closure of valve.
3. It is accompanied by serious cavitation.
4. The volume modulus of fluid is the relevant fluid property.
5. It is governed by the Reynolds number of the flow.
Select the correct answer using the codes given below.

Codes :
Answer.
- 1
  
  3 and 5
- 2
  
  2 and 4
- 3
  
  2 and 5
- 4
  
  1,2,3 and 4
Answer: 2

Explanation:
7) Question.

A pipe network consists of a pipe of 60 cm diameter and branches out at a point F into two branches, one of 30 cm diameter and the other of 45 cm diameter. These branch pipes rejoin at a point B. The velocity in the first branch ( of 45 cm diameter) is 1.5 m/sec. Which one of the following statements is true ?
Answer.
- 1
  
  The velocity in the second branch is 1.0 m/sec.
- 2
  
  The velocity in the second branch is 2.25 m/sec.
- 3
  
  The velocity in the second branch is 2/3 (=0.667) m/sec.
- 4
  
  The potential drop between F and B in both branches is the same.
Answer: 4

Explanation:
8) Question.

The loss of head at various pipe fittings is given by the expression $\frac{K v^{2}}{2 g}$ . If values of K were 0.40, 0.90, 1.5 and 2.2, then these would correspond respectively to
Answer.
- 1
  
  foot valve of pump, $45^{0}$ elbow, $90^{0}$ elbow and close return bend
- 2
  
  $45^{0}$ elbow, $90^{0}$ elbow, foot value of pump and close return bend
- 3
  
  $90^{0}$ elbow, foot value of pump, close return bend and $45^{0}$ elbow
- 4
  
  foot value of pump, close return bend, $45^{0}$ elbow and $90^{0}$ elbow
Answer: 2

Explanation:
9) Question.

$\bar{A}$ ping-pong ball, having a diameter of 3.6 cm and weighing 2.4 g, is served with a horizontal velocity of 10 m/sec and a spin that gives rise to a coefficient of lift of 0.2. Assuming the density of air to be 0.00129 gf/cc, the lift experienced by the ball is nearly
Answer.
- 1
  
  13 gf
- 2
  
  1.3 gf
- 3
  
  0.13 gf
- 4
  
  0.013 gf
Answer: 3

Explanation:
10) Question.

In the stokes experiment of falling sphere, it is found that a sphere of 5 mm diameter falls in a liquid with terminal velocity 20 mm/s giving a drag coefficient of 240. The ratio of specific gravities is 2.85. Which one of the following is the kinematic viscosity of the liquid in stokes ?
Answer.
- 1
  
  3.5
- 2
  
  10.0
- 3
  
  225.0
- 4
  
  1000.0
Answer: 2

Explanation:
11) Question.

In the model of a highway bridge constructed to a scale of 1:25, the force of water on the pier was measured to be 0.5 kg. The force on the prototype pier will be
Answer.
- 1
  
  7501.5 kg
- 2
  
  7622.5 kg
- 3
  
  7812.5 kg
- 4
  
  7916.5 kg
Answer: 3

Explanation:
12) Question.

Water having kinematic viscosity of 0.01 stoke flows at a velocity of 2m/sec in a pipe of 15 cm diameter. For dynamic similarity, the velocity of oil of kinematic viscosity 0.03 stoke in a pipe of same diameter will be
Answer.
- 1
  
  0.33 m/sec
- 2
  
  0.66 m/sec
- 3
  
  2 m/sec
- 4
  
  6 m/sec
Answer: 4

Explanation:
13) Question.

A cylindrical vessel of radius 42.31 cm and height 1 m is open at the top. It holds water to half its depth. Which one of the following values approximates the speed at which the cylinder is to be rotated about the vertical axis, so as to make the apex of the paraboloid just reach the centre of the bottom of the vessel ?
Answer.
- 1
  
  100 rpm
- 2
  
  150 rpm
- 3
  
  250 rpm
- 4
  
  300 rpm
Answer: 1

Explanation:
14) Question.

The velocity potential $ϕ$ at any point for a two-dimensional steady, irrotational flow in polar coordinates, is given by (with usual notations) $ϕ = m \frac{\cos θ}{r}$

This equation represents a
Answer.
- 1
  
  vortex
- 2
  
  sink
- 3
  
  source
- 4
  
  doublet
Answer: 4

Explanation:
15) Question.

In steady flow of a compressible fluid through a pipe, the density, area and velocity at a particular section are $1.5 k g / m^{3}$ , $0.5 m^{2}$ and $3 m / s$ respectively. At another section the density and area are $0.75 k g / m^{3}$
Answer.
- 1
  
  1.5 m/s
- 2
  
  3.0 m/s
- 3
  
  4.5 m/s
- 4
  
  6.0 m/s
Answer: 2

Explanation:
16) Question.

A rectangular open channel carries a discharge of $15 m^{3} / s$ when the depth of flow is 1.5 m and the bed slope is 1:1440. What will be the discharge through the channel at the same depth if the slope would have been 1:1000 ?
Answer.
- 1
  
  $21.6 m^{3} / s$
- 2
  
  $18 m^{3} / s$
- 3
  
  $14.4 m^{3} / s$
- 4
  
  $12.5 m^{3} / s$
Answer: 2

Explanation:
17) Question.

A symmetrical right circular cone of wood floats in fresh water with axis vertical and the apex downmost. The axial height of the cone is l. The submerged portion has a height h, measured upwards from the apex. What would be the height of the centre of buoyancy from the apex ?
Answer.
- 1
  
  h/2
- 2
  
  5/8 h
- 3
  
  2/3 h
- 4
  
  3/4 h
Answer: 4

Explanation:
18) Question.

The surface tension of water at $20^{0}$ C is $75 \times 10^{- 3} N / m .$ The difference in the water surfaces within and outside an open ended capillary tube of 1 mm internal bore, inserted at the water surface, would nearly be
Answer.
- 1
  
  5 mm
- 2
  
  10 mm
- 3
  
  15 mm
- 4
  
  20 mm
Answer: 3

Explanation:
19) Question.

Two small orifices A and B of diameters 1 cm and 2 cm, respectively, are placed on the sides of a tank at depths of $h_{1}$ and $h_{2}$ below the open liquid surface. If the discharges through A and B are equal, then the ratio of $h_{1}$ and $h_{2}$ (assuming equal $C_{d}$ values) will be
Answer.
- 1
  
  16:1
- 2
  
  8:1
- 3
  
  4:1
- 4
  
  2:1
Answer: 1

Explanation:
20) Question.

The displacement thickness of a boundary layer is
Answer.
- 1
  
  the distance to the point where (v/V)= 0.99
- 2
  
  the distance where the velocity 'v' is equal to the shear velocity V*, that is, where v=V*
- 3
  
  the distance by which the main flow is to be shifted from the boundary to maintain the continuity equation
- 4
  
  one half the actual thickness of the boundary layer
Answer: 3

Explanation:

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