Fluid Mechanics Sheet 29

1) Question.

The shear stress in a fluid may be expresssed as $τ = μ {(\frac{d v}{d y})}^{n}$ where $μ$ is the viscosity, dv/dy is the velocity gradient and n is constant. The n-values for Newtonian and non-Newtonian fluids will be respectively
Answer.
- 1
  
  n=1 and n> 1
- 2
  
  n<1 and n<1
- 3
  
  n=1 and n<1
- 4
  
  n=1 and n $\neq$ 1
Answer: 4

Explanation:
2) Question.

The differential equation for energy for a reversible adiabatic flow may take the form
Answer.
- 1
  
  $d p + d (ρ V^{2}) = 0$
- 2
  
  $V d V + e^{2} \frac{d ρ}{ρ} = 0$
- 3
  
  $2 V d V + \frac{d ρ}{ρ} = 0$
- 4
  
  $V d V + \frac{d ρ}{ρ} = 0$
Answer: 4

Explanation:
3) Question.

The friction factor (f), in terms of boundary shear stress ( $τ_{0}$ ), is given by ( $ρ$ = mass density, v= mean velocity)
Answer.
- 1
  
  $\frac{2 ρ v^{2}}{τ_{0}}$
- 2
  
  $\frac{τ_{0}}{2 ρ v^{2}}$
- 3
  
  $\frac{2 τ_{0}}{ρ v^{2}}$
- 4
  
  $\frac{ρ v^{2}}{2 τ_{0}}$
Answer: 3

Explanation:
4) Question.
Which of the following equations will be satisfied by irrotational flow of an incompressible fluid ?

1. $\frac{δ u}{δ x} + \frac{δ v}{δ y} + \frac{δ w}{δ z} = 0$
2.
δuδy+δvδx=δ<
Answer.

1
3 and

2
1 and 2

3
1 and 3

4
1 and 4

Answer: 4

Explanation:

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5) Question.
Assuming that the thrust T of a propeller depends on the diameter D, speed of advance V, angular velocity $ω$ , dynamic viscosity $μ$ and mass density $ρ$ , which of the following non-dimensional parameters can be derived by Dimensional Analysis.

1. $\frac{T}{ρ D^{2} V^{2}}$

2. $\frac{V D}{μ}$
Answer.
- 1
  
  1,2 and 3
- 2
  
  2,3 and 4
- 3
  
  1,3 and 4
- 4
  
  1,2 and 4
Answer: 3

Explanation:
6) Question.

In a gradually varied flow, if $\frac{d y}{d x}$ is positive, then $\frac{d E}{d x}$ will be
Answer.
- 1
  
  always zero
- 2
  
  positive if $y < y_{c}$
- 3
  
  negative if $y > y_{c}$
- 4
  
  always negative
Answer: 2

Explanation:
7) Question.

Which one of the following is the correct representation of the sequence of surface profiles if the channel slope changes from mild to steep ?
Answer.
- 1
  
  $M_{1,} S_{1}$
- 2
  
  $M_{3} S_{2}$
- 3
  
  $M_{2} S_{3}$
- 4
  
  $M_{2} S_{2}$
Answer: 4

Explanation:
8) Question.

In the distored model of a river, the horizontal and vertical scale ratios are $L_{H}$ and $L_{V}$ respectively. The discharge ratio will be
Answer.
- 1
  
  ${L_{H}}^{1 / 2} {L_{V}}^{2}$
- 2
  
  $L_{H} {L_{V}}^{3 / 2}$
- 3
  
  ${L_{H}}^{2} {L_{V}}^{1 / 2}$
- 4
  
  ${L_{H}}^{3} {L_{V}}^{- 1 / 2}$
Answer: 2

Explanation:
9) Question.

If two geometrically similar models having a scale ratio $L_{r}$ are operated in a given laboratory at the same Froude number, then all the corresponding accelerations will be in the ratio of
Answer.
- 1
  
  ${L_{r}}^{1.5}$
- 2
  
  ${L_{r}}^{}$
- 3
  
  ${L_{r}}^{0.5}$
- 4
  
  l
Answer: 4

Explanation:
10) Question.

The overall drag coefficient of an aircraft of weight W and wing area S is given by $C_{D} = a + b {C_{L}}^{2}$ where a and b are constants. The maximum drag in horizontal flight will be
Answer.
- 1
  
  $W \sqrt{a b}$
- 2
  
  $2 W \sqrt{a b}$
- 3
  
  $4 W \sqrt{a b}$
- 4
  
  $6 W \sqrt{a b}$
Answer: 2

Explanation:
11) Question.

The ratio of the coefficient of friction drag in laminar boundary layer compared to that in turbulent boundary layer is proportional to
Answer.
- 1
  
  ${R_{L}}^{1 / 2}$
- 2
  
  ${R_{L}}^{1 / 5}$
- 3
  
  ${R_{L}}^{3 / 10}$
- 4
  
  ${R_{L}}^{- 3 / 10}$
Answer: 4

Explanation:
12) Question.

Given $φ = \frac{3}{2} (y^{2} - x^{2})$ , the discharge passing between the streamlines through the points (1,3) and (3,3) is
Answer.
- 1
  
  2 units
- 2
  
  4 units
- 3
  
  8 units
- 4
  
  12 units
Answer: 4

Explanation:
13) Question.

Vorticity in the z-direction is given by
Answer.
- 1
  
  $(\frac{δ u}{δ x} + \frac{δ v}{δ γ})$
- 2
  
  $(\frac{δ u}{δ x} - \frac{δ v}{δ γ})$
- 3
  
  $(\frac{δ v}{δ x} + \frac{δ u}{δ γ})$
- 4
  
  $(\frac{δ v}{δ x} - \frac{δ u}{δ γ})$
Answer: 4

Explanation:
14) Question.

Assertion A: The discharge (Q) through a triangular weir is given by $Q = \frac{8}{15} C_{d} \sqrt{2 g} h^{5 / 2} \tan (\frac{θ}{2})$ where $C_{d}$ is the coefficient of discharge, h is the head of flow, $θ$ is the apex angle of the weir and g is the acceleration due to gravity.

Reason R: The cross-secti
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:
15) Question.

Assertion A: Any discharge will flow as critical in a wide rectangular channel whose bed slope is 1 in $C^{2} / g$

Reason R: The critical depth of flow through a wide rectangular channel is ${(q^{2} / g)}^{1 / 3}$
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:
16) Question.

Assertion A: Loss of head at a sudden expansion in a pipe is greater than that at a sudden contraction.

Reason R: Flow in a sudden expansion tends to be irrotational.
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:
17) Question.

Assertion A: When both gravitational and viscous forces are predominant in a flow scale ratio can be chosen at will.

Reason R: With both gravitational and viscous forces being predominant, scale ratio depends upon kinematic viscosity of the fluids.
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.

Assertion A: Energy is lost in sudden contraction in a pipeline

Reason R: If the flow is now reversed, energy can be gained at the transition which acts as an expansion
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:
19) Question.

Assertion A: The kinematic viscosity of both air and water decreases as the temperature increases.

Reason R: The kinematic viscosity of liquids and gases at a given pressure is a function of 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: 4

Explanation:
20) Question.

Assertion A: In the standing-wave flume, flow occurs in a super-critical state so that discharge can be related to a depth upstream of flow.

Reason R: A standing wave flume is a venturi flume operating under one condition in which a hydraulic jump is formed.
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:

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