Fluid Mechanics Sheet 28

1) Question.

Assertion A: Water hammer occurs when the quick-acting valve at the end of a long pipeline is suddenly closed.

Reason R: Surge tanks are provided in penstocks to relieve the penstock of high water hammer pressure when the flow into a turbine is stopped due to low power demand.
Answer.
- 1
  
  Both A and R are true and R is the correct explanation of A
- 2
  
  Both A and R are true but R is not a correct explanation of A
- 3
  
  A is true but R is false
- 4
  
  A is false but R is true
Answer: 1

Explanation:
2) Question.

Assertion A: Continuity equation must hold good in a pipe network system.

Reason R: In a pipe network analysis, the flow into any junction must be equal to the flow out of the junction.
Answer.
- 1
  
  Both A and R are true and R is the correct explanation of A
- 2
  
  Both A and R are true but R is not a correct explanation of A
- 3
  
  A is true but R is false
- 4
  
  A is false but R is true
Answer: 1

Explanation:
3) Question.

Assertion A: There is no flow in the direction perpendicular to a stream line at any point on it

Reason R: Stream line consists of a number of infinitesimally small segments such that all of them lie along the directions of velocity vectors of fluid particles at those segments
Answer.
- 1
  
  Both A and R are true and R is the correct explanation of A
- 2
  
  Both A and R are true but R is not a correct explanation of A
- 3
  
  A is true but R is false
- 4
  
  A is false but R is true
Answer: 1

Explanation:
4) Question.

Assertion A: The movement of two blocks of wood wetted with hot glue requires greater and greater effort as the glue is drying up.

Reason R: Viscosity of liquids varies inversely with temperature.
Answer.
- 1
  
  Both A and R are true and R is the correct explanation of A
- 2
  
  Both A and R are true but R is not a correct explanation of A
- 3
  
  A is true but R is false
- 4
  
  A is false but R is true
Answer: 1

Explanation:
5) Question.

Assertion A: A minor change in specific energy at or close to critical state will cause a major change in depth.

Reason R: A critical state of flow is characterized by its Froude number being equal to unity.
Answer.
- 1
  
  Both A and R are true and R is the correct explanation of A
- 2
  
  Both A and R are true but R is not a correct explanation of A
- 3
  
  A is true but R is false
- 4
  
  A is false but R is true
Answer: 2

Explanation:
6) Question.

Assertion A: The inlet velocity triangle for a Pelton turbine is a straight line

Reason R: For a Pelton turbine, the vane angle at inlet is $180^{0}$
Answer.
- 1
  
  Both A and R are true and R is the correct explanation of A
- 2
  
  Both A and R are true but R is not a correct explanation of A
- 3
  
  A is true but R is false
- 4
  
  A is false but R is true
Answer: 1

Explanation:
7) Question.

Assertion A: Irrotational flow exists when the net rotation of the fluid about its mass centre is zero.

Reason R: There is always a possibility of rotation in ideal fluid and therefore, ideal fluids cannot have irrotational flow.
Answer.
- 1
  
  Both A and R are true and R is the correct explanation of A
- 2
  
  Both A and R are true but R is not a correct explanation of A
- 3
  
  A is true but R is false
- 4
  
  A is false but R is true
Answer: 3

Explanation:
8) Question.
Assertion A: In the equation $h_{f} = f \frac{1}{d} \frac{v^{2}}{2 g}$ , for laminar flow through the pipe, the term v (mean velocity of flow) is given by $v = \frac{(p_{1} - p_{2}) r^{2}}{8 μ l}$
Reason R: The term 'f' (friction factor) in the above equation equals
64
Answer.

1
Both A and R are true and R is the correct explanation of A

2
Both A and R are true but R is not a correct explanation of A

3
A is true but R is false

4
A is false but R is true

Answer: 1

Explanation:

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9) Question.
Assertion A: Water flows through a pipe connecting two reservoirs. The line joining the water surface levels in the reservoirs is the hydraulic gradient. Reason R: There will be no negative gauge pressure anywhere in the pipeline, as long as the pipeline lies below the hydraulic gradient.
Answer.
- 1
  Both A and R are true and R is the correct explanation of A
- 2
  Both A and R are true but R is not a correct explanation of A
- 3
  A is true but R is false
- 4
  A is false but R is true
Answer: 2

Explanation:
10) Question.
Assertion A: If laminar flow of oil between two points of a given pipeline is doubled, then the power consumption is increased to four times the original power. Reason R: In laminar flow through circular pipes, head loss varies directly as the discharge.
Answer.
- 1
  Both A and R are true and R is the correct explanation of A
- 2
  Both A and R are true but R is not a correct explanation of A
- 3
  A is true but R is false
- 4
  A is false but R is true
Answer: 1

Explanation:
11) Question.
Assertion A: In Rayleigh's method of dimensional analysis, the dependent variable is written as the function of exponential terms of independent variables. Reason R: In Rayleigh's method, when the number of independent variable exceeds three, the exponents of non-repeating variables are expressed as the exponents of repeating variables.
Answer.
- 1
  Both A and R are true and R is the correct explanation of A
- 2
  Both A and R are true but R is not a correct explanation of A
- 3
  A is true but R is false
- 4
  A is false but R is true
Answer: 2

Explanation:
12) Question.
Assertion A: The following potential function in two-dimensional flow field represents rotational flow $φ = 2 x^{2} - 3 y^{2}$

Reason R: For the given function $\frac{δ u}{δ x} + \frac{δ v}{δ y} \neq 0$
Answer.
- 1
  
  Both A and R are true and R is the correct explanation of A
- 2
  
  Both A and R are true but R is not a correct explanation of A
- 3
  
  A is true but R is false
- 4
  
  A is false but R is true
Answer: 4

Explanation:
13) Question.

Assertion A: Pressure intensity in a liquid flow is a form of energy.

Reason R: The pressure gradient is a measure of the rate of energy dissipation in steady uniform flow.
Answer.
- 1
  
  Both A and R are true and R is the correct explanation of A
- 2
  
  Both A and R are true but R is not a correct explanation of A
- 3
  
  A is true but R is false
- 4
  
  A is false but R is true
Answer: 2

Explanation:
14) Question.

Assertion A: The specific speed of a Pelton wheel is generally much less than that of a reaction turbine.

Reason R: Pelton wheels generally use more than one nozzle and the specific speed is defined for power developed per nozzle.
Answer.
- 1
  
  Both A and R are true and R is the correct explanation of A
- 2
  
  Both A and R are true but R is not a correct explanation of A
- 3
  
  A is true but R is false
- 4
  
  A is false but R is true
Answer: 2

Explanation:
15) Question.

Assertion A: At the critical state of flow, the specific force is a minimum for the given discharge.

Reason R: For a minimum value of the specific force, the first derivative of force with respect to depth should be unity.
Answer.
- 1
  
  Both A and R are true and R is the correct explanation of A
- 2
  
  Both A and R are true but R is not a correct explanation of A
- 3
  
  A is true but R is false
- 4
  
  A is false but R is true
Answer: 3

Explanation:
16) Question.

Assertion A: Gravity influences the pipe flow.

Reason R: Gravity term (g) appears explicitly in Darcy-Weisbach formula for pipe flow resistance.
Answer.
- 1
  
  Both A and R are true and R is the correct explanation of A
- 2
  
  Both A and R are true but R is not a correct explanation of A
- 3
  
  A is true but R is false
- 4
  
  A is false but R is true
Answer: 4

Explanation:
17) Question.

Assertion A: Flow in the boundary layer is always laminar.

Reason R: In turbulent flow on a smooth boundary, a laminar sub-layer still exists within the boundary layer.
Answer.
- 1
  
  Both A and R are true and R is the correct explanation of A
- 2
  
  Both A and R are true but R is not a correct explanation of A
- 3
  
  A is true but R is false
- 4
  
  A is false but R is true
Answer: 4

Explanation:
18) Question.

The ratio of volume flow rates in two dynamical similar systems governed by Froude modelling is equal to (assume $g_{r} = 1$ )

( $L_{r}$ is length scale ratio)
Answer.
- 1
  
  ${L_{r}}^{1 / 2}$
- 2
  
  ${L_{r}}^{3 / 2}$
- 3
  
  ${L_{r}}^{5 / 2}$
- 4
  
  ${L_{r}}^{7 / 2}$
Answer: 3

Explanation:
19) Question.

Which of the following quantities is dimensionless ?

[F= force, $ρ$ = density, $μ$ = dynamic viscosity, $M^{1} L^{- 1} T^{- 1}$ = dimensions of dynamic viscosity]
Answer.
- 1
  
  $\frac{ρ F}{μ}$
- 2
  
  $\frac{μ^{2} ρ}{F}$
- 3
  
  $\frac{ρ F}{μ^{2}}$
- 4
  
  $\frac{μ}{ρ^{2} F}$
Answer: 3

Explanation:
20) Question.

The dimensions of pressure gradient dp/dx in a fluid are
Answer.
- 1
  
  $M^{1} L^{- 1} T^{- 2}$
- 2
  
  $M^{- 1} L^{- 3} T^{- 2}$
- 3
  
  $M^{1} L^{- 2} T^{- 2}$
- 4
  
  $M^{1} L^{- 3} T^{- 2}$
Answer: 3

Explanation:

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