Fluid Mechanics Sheet 27

1) Question.

If $F_{r}$ is the Froude number for a flow in a triangular channel, then the Froude number for same velocity and same depth of flow in rectangular channel will be
Answer.
- 1
  
  $F_{r}$
- 2
  
  $\frac{F_{r}}{\sqrt{2}}$
- 3
  
  $\sqrt{2 F_{r}}$
- 4
  
  $\frac{F_{r}}{\sqrt{3}}$
Answer: 2

Explanation:
2) Question.

The critical velocity for a flow of $q m^{3} / s e c / m e t r e$ width of a wide rectangular channel is given by
Answer.
- 1
  
  ${(\frac{q^{2}}{g})}^{\frac{1}{3}}$
- 2
  
  ${(q g)}^{1 / 3}$
- 3
  
  $\sqrt{q g}$
- 4
  
  none of the above
Answer: 2

Explanation:
3) Question.

For a trapezoidal channel section to be most economical, its hydraulic radius must be equal to

[y= the depth of flow]
Answer.
- 1
  
  $\frac{y}{4}$
- 2
  
  $\frac{y}{2}$
- 3
  
  $\frac{y}{2 \sqrt{2}}$
- 4
  
  $\frac{y}{3 \sqrt{2}}$
Answer: 2

Explanation:
4) Question.

The relationship between Manning's coefficient n and Chezy's coefficient c is given by

[R= the hydraulic mean depth]
Answer.
- 1
  
  $c = \frac{R^{2 / 3}}{n}$
- 2
  
  $c = \frac{R^{1 / 6}}{n}$
- 3
  
  $c = \frac{R^{1 / 3}}{n}$
- 4
  
  $c = \frac{R^{1 / 4}}{n}$
Answer: 2

Explanation:
5) Question.

If 'f' is the friction factor, then the Chezy's coefficient is proportional to
Answer.
- 1
  
  f
- 2
  
  $\sqrt{f}$
- 3
  
  $\frac{1}{f}$
- 4
  
  $\frac{1}{\sqrt{f}}$
Answer: 4

Explanation:
6) Question.

The Froude number is defined as $F = \frac{v}{\sqrt{g D}}$ where v is the mean velocity of flow, g is acceleration due to gravity and D is
Answer.
- 1
  
  depth of flow
- 2
  
  hydraulic depth
- 3
  
  hydraulic mean depth
- 4
  
  all of the above
Answer: 2

Explanation:
7) Question.

For laminar flow in circular pipes, the Darcy's friction factor F is equal to

[ $R_{e}$ = Reynolds number]
Answer.
- 1
  
  $16 / R_{e}$
- 2
  
  $32 / R_{e}$
- 3
  
  $64 / R_{e}$
- 4
  
  none of the above
Answer: 3

Explanation:
8) Question.

The equation $τ = - \frac{d p}{d l} \frac{r}{2}$ for flow through circular tubes, where $τ$ is shear stress at distance r from centre, is applicable for
Answer.
- 1
  
  laminar flow only
- 2
  
  turbulent flow only
- 3
  
  critical flow
- 4
  
  both laminar and turbulent flows
Answer: 4

Explanation:
9) Question.

The discharge through a Cipolletti weir is given by

[symbols have their usual meanings]
Answer.
- 1
  
  $\frac{2}{3} C_{d} \sqrt{2 g} L H^{3 / 2}$
- 2
  
  $\frac{8}{15} C_{d} \sqrt{2 g} \tan \frac{θ}{2} H^{5}$
- 3
  
  $\frac{2}{3} C_{d} \sqrt{2 g} (L - 0.2 H) H^{3 / 2}$
- 4
  
  $\frac{2}{3} C_{d} \sqrt{2 g} L H^{5 / 2}$
Answer: 1

Explanation:
10) Question.

The energy loss in orifice flow is given by

[ w= coefficient of velocity, H= head on orifice ]
Answer.
- 1
  
  $H (1 - w^{2})$
- 2
  
  $H (w^{2} - 1)$
- 3
  
  $H (1 - \frac{1}{w^{2}})$
- 4
  
  $H (\frac{1}{w^{2}} - 1)$
Answer: 1

Explanation:
11) Question.

The continuity equation

$ρ_{1} V_{1} A_{1} = ρ_{2} V_{2} A_{2}$

is based on the following assumption regarding flow of fluid

[ $ρ_{1}, ρ_{2}$ = mass densities ]
Answer.
- 1
  
  steady flow
- 2
  
  uniform flow
- 3
  
  incompressible flow
- 4
  
  frictionless flow
Answer: 1

Explanation:
12) Question.

The total pressure on a plane surface inclined at an angle $θ$ with the horizontal is equal to

[ p= pressure intensity at centroid of area, A= area of plane surface ]
Answer.
- 1
  
  pA
- 2
  
  pA sin $θ$
- 3
  
  pA cos $θ$
- 4
  
  pA tan $θ$
Answer: 1

Explanation:
13) Question.

The rise of liquid of specific weight $γ$ in a capillary tube of radius r is given by

[ $σ$ = surface tension of the liquid ]
Answer.
- 1
  
  $\frac{σ}{2 r γ}$
- 2
  
  $\frac{2 σ}{r}$
- 3
  
  $\frac{2 σ}{r γ}$
- 4
  
  $\frac{γ σ}{2 r}$
Answer: 3

Explanation:
14) Question.

Separation of boundary layer takes place under
Answer.
- 1
  
  positive pressure gradient in the direction of flow
- 2
  
  negative pressure gradient in the direction of flow
- 3
  
  zero pressure gradient in the direction of flow
- 4
  
  very rough surface
Answer: 1

Explanation:
15) Question.
Consider the following statements in relation to dimensionless numbers:
1. Inertia force is always involved in the expression of any dimensionless number.
2. Weber number is significant in a flow system where viscous force dominates.
3. Mach number is significant in a flow system where the flow is of compressible fluid.
4. Reynolds number is significant where both gravity force and viscous force predominates.
Of these statements
Answer.
- 1
  
  1 and 2 are correct
- 2
  
  1 and 3 are correct
- 3
  
  2 and 4 are correct
- 4
  
  3 and 4 are correct
Answer: 2

Explanation:
16) Question.

A pitot tube (coefficient= 1.0) is used to measure the velocity of air of mass density $1.2 k g / m^{3}$ . If the head difference in a vertical U-tube filled with water is 12mm, then the velocity of air (in m/s) will be
Answer.
- 1
  
  10
- 2
  
  14
- 3
  
  17
- 4
  
  20
Answer: 2

Explanation:
17) Question.

Which one of the following pairs is correctly matched ?
Answer.
- 1
  
  Prandtl : Flow through channels
- 2
  
  Continuity equation: Law of conservation of energy
- 3
  
  Mixing length: Laminar flow
- 4
  
  Karman vortex street: Flow past a cylinder
Answer: 4

Explanation:
18) Question.

Which one of the following statements on similitude is correct ?
Answer.
- 1
  
  To achieve dynamic similarity between the model and the prototype, there need not be any geometric similarity.
- 2
  
  For kinematic similarity between the model and the prototype, the ratios of forces between the model and the prototype should be the same.
- 3
  
  For dynamic similarity between model and prototype in a compressible flow system, the Weber numbers must be the same.
- 4
  
  For dynamic similarity between the model and the prototype, the ratio of forces must be the same.
Answer: 4

Explanation:
19) Question.

The velocity components in a 2-D flow for an incompressible fluid are given by the equations

u= 2xy; $v = a^{2} + x^{2} + y^{2}$

The flow
Answer.
- 1
  
  satisfies irrotationality condition and the continuity equation
- 2
  
  satisfies irrotationality condition but not the continuity equation
- 3
  
  does not satisfy the irrotationality condition but satisfies the continuity equation
- 4
  
  does not satisfy either the irrotationality condition or the continuity equation
Answer: 2

Explanation:
20) Question.

When a ship moving on seawater enters a river and moves inland, it is expected to
Answer.
- 1
  
  rise a little
- 2
  
  sink a little
- 3
  
  maintain the same level of draft
- 4
  
  rise or fall depending on whether it is made of wood or steel
Answer: 2

Explanation:

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