Fluid Mechanics Sheet 25

1) Question.

A hydraulic model of a spillway is constructed with a scale 1:16. If the prototype discharge is 2048 cumec, then the corresponding discharge for which the model should be tested is
Answer.
- 1
  
  1 cumec
- 2
  
  2 cumec
- 3
  
  4 cumec
- 4
  
  8 cumec
Answer: 2

Explanation:
2) Question.

With 'n' variables and 'm' fundamental dimensions in a system, which one of the following statements relating to the application of the buckingham's pi Theorem is incorrect ?
Answer.
- 1
  
  With experience, pi terms can be written simply by inspection of variables in a flow system.
- 2
  
  Buckingham's pi theorem is not directly applicable in compressible flow problem.
- 3
  
  Buckingham's pi theorem yields dimensionless pi terms given by the difference between the number of variables and the number of fundamental dimensions.
- 4
  
  Buckingham's pi theorem reduces the number of variables by the number of fundamental dimensions involved.
Answer: 3

Explanation:
3) Question.
Consider the following statements relating to fluid dynamics :
1. Momentum equation contains only vector quantities.
2. Energy equation involves scaler quantities only.
3. Irrotational flow occurs in real fluid.
4. In uniform flow, there is no variation of velocity, at a given time, with respect to distance.
Of these statements
Answer.
- 1
  
  1,2 and 3 are correct
- 2
  
  2,3 and 4 are correct
- 3
  
  1,2 and 4 are correct
- 4
  
  1,3 and 4 are correct
Answer: 3

Explanation:
4) Question.
Consider the following statements relating to the stability of floating as well as submerged bodies :
1. A submerged body is stable when the centre of gravity is below the centre of buoyancy.
2. A floating body is stable when the centre of gravity is above the centre of buoyancy.
3. A floating body is stable when the centre of gravity is below the metacentre.
4. A submerged body is in stable equilubrium when the centre of gravity conincides with the centre of buoyancy.
Of these statements
Answer.
- 1
  
  1,2 and 3 are correct
- 2
  
  2,3 and 4 are correct
- 3
  
  1,2 and 4 are correct
- 4
  
  1,3 and 4 are correct
Answer: 4

Explanation:
5) Question.

The discharge per metre width at the foot of a spillway is $10 m^{3} / s$ at a velocity of 20 m/s. A perfect free hydraulic jump will occur at the foot of the spillway when the tail water depth is approximately equal to
Answer.
- 1
  
  4.50 m
- 2
  
  5.00 m
- 3
  
  5.50 m
- 4
  
  6.50 m
Answer: 4

Explanation:
6) Question.

The head loss in a pipe of diameter d, carrying oil at a flow rate Q over a distance 1 is h. The pipe is replaced by another with half the diameter, all other things remaining the same. The head loss in this case will be
Answer.
- 1
  
  0.5 h
- 2
  
  2.0 h
- 3
  
  8.0 h
- 4
  
  32.0 h
Answer: 4

Explanation:
7) Question.
Which of the following assumptions are made in the analysis of jet impinging normally on a moving plate ?
1. Friction between jet and plate is neglected.
2. flow is steady.
3. Momentum of jet is unchanged.
4. Plate moves at a constant velocity.
Choose the correct answer using the codes given below.

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

Explanation:
8) Question.

A wooden plank (sp.gr. 0.5) 1 m x 1 m x 0.5 m floats in water with 1.5 kN load on it with 1 m x 1 m surface horizontal. The depth of plank lying below water surface shall be
Answer.
- 1
  
  0.178 m
- 2
  
  0.250 m
- 3
  
  0.403 m
- 4
  
  0.500 m
Answer: 3

Explanation:
9) Question.

The ratio of pressures between two points A and B located respectively at depths 0.5 m and 2 m below a constant level of water in a tank is
Answer.
- 1
  
  $1 : \sqrt{2}$
- 2
  
  1:2
- 3
  
  1:4
- 4
  
  1:16
Answer: 3

Explanation:
10) Question.

A jet of water issues from a 5 cm diameter nozzle, held vertically upwards, at a velocity of 20 m/sec. If air resistance consumes 10% of the initial energy of the jet, then it would reach a height; above the nozzle, of
Answer.
- 1
  
  18.35 m
- 2
  
  19.14 m
- 3
  
  19.92 m
- 4
  
  20.00 m
Answer: 1

Explanation:
11) Question.

Given the x-component of the velocity $u = 6 x y - 2 x^{2}$ , the y-component of the flow v is given by
Answer.
- 1
  
  $6 y^{2} - 4 x y$
- 2
  
  $- 6 x y + 2 x^{2}$
- 3
  
  $6 x^{2} - 2 x y$
- 4
  
  $4 x y - 3 y^{2}$
Answer: 4

Explanation:
12) Question.

A circular surface area $200 c m^{2}$ is inclined to the x and y axes such that the unit vector normal to the surface is given by $n = 0.4 i + 0.3 j$ . If a force of 2000 kg acts on the x-axis, then the normal stress on the surface will be
Answer.
- 1
  
  $10 k g / c m^{2}$
- 2
  
  $5 k g / c m^{2}$
- 3
  
  $4 k g / c m^{2}$
- 4
  
  $3 k g / c m^{2}$
Answer: 2

Explanation:
13) Question.

In a two-dimensional incompressible flow, if the fluid velocity components are given by

$u = x - 4 y, v = - y - 4 x$

then the stream function $ψ$ is given by
Answer.
- 1
  
  $x^{2} - x y + 2 y^{2}$
- 2
  
  $2 x^{2} + 2 x y + y^{2}$
- 3
  
  $2 x^{2} + x y - 2 y^{2}$
- 4
  
  $2 x^{2} - x y + 2 y^{2}$
Answer: 3

Explanation:
14) Question.

A three-dimensional state of stress can be split into the two components, the hydrostatic state and the deviatoric component. Then magnitude of the hydrostatic state pressure is given by
Answer.
- 1
  
  $(σ_{x} + σ_{y} + σ_{z}) / 3$
- 2
  
  $(σ_{x} + σ_{y} + σ_{z}) / 4$
- 3
  
  $(σ_{x} + σ_{y} + σ_{z}) / 6$
- 4
  
  $(σ_{x} + σ_{y} + σ_{z})$
Answer: 1

Explanation:
15) Question.

The following statements relate to water surface profiles in gradually varied flow of an open channel.

1. $M_{1}$ and $S_{1}$ curves meet $y_{0}$ line asymptotically and tend to be horizontal as $y \to \infty$ .

2. $M_{2}$ and $S_{2}$
Answer.
- 1
  1 and 3 are correct
- 2
  1 and 4 are correct
- 3
  2 and 4 are correct
- 4
  3 and 4 are correct
Answer: 2

Explanation:
16) Question.
The standard step method of gradually varied flow computations involves the application of
Answer.
- 1
  differential equation of gradually varied flow
- 2
  continuity and energy equations
- 3
  continuity and momentum equations
- 4
  continuity equation and equation of motion
Answer: 2

Explanation:
17) Question.
The sequent depth ratio in a hydraulic jump formed in a horizontal rectangular channel is 16.48. The Froude number of the super-critical stream is
Answer.
- 1
  4.0
- 2
  8.0
- 3
  12.0
- 4
  120
Answer: 3

Explanation:
18) Question.
Water flows uniformly down a $30^{0}$ slope in a very rough channel at a normal depth of 8 cm. The intensity of bed shear in $k g f / m^{2}$ will be about
Answer.
- 1
  
  400
- 2
  
  40
- 3
  
  20
- 4
  
  6.3
Answer: 2

Explanation:
19) Question.

A penstock is 3000 metres long. Pressure wave travels in it with a velocity of 1500 m/s. If the turbine gates are closed uniformly and completely in a period of 4.5 seconds, then it is called
Answer.
- 1
  
  rapid closure
- 2
  
  slow closure
- 3
  
  sudden closure
- 4
  
  uniform closure
Answer: 2

Explanation:
20) Question.
Consider the following statements.

In a pipe network
1. at any junction of a loop, the total inflow is equal to the total outflow
2. at any junction, loss of head in clockwise branch is equal to the loss of head in anti-clockwise branch
3. at any junction, head is same
4. head loss in each loop is the same
Of these statements
Answer.
- 1
  
  1 and 2 are correct
- 2
  
  3 and 4 are correct
- 3
  
  2 alone is correct
- 4
  
  4 alone is correct
Answer: 1

Explanation:

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