## Fluid Mechanics - May 2014

### Civil Engineering (Semester 3)

TOTAL MARKS:

TOTAL TIME: HOURS

**1 (a)** Define and explain following fluid properties.

(1) Surface tension

(2) Dynamic viscosity

(3) Capillarity(7 marks)
**1 (b)** What is the use of manometer? Prove that intensity of pressure at any point in a
fluid at rest has same magnitude in all directions.(7 marks)
**2 (a)** State Bernoulli's equation for compressible flow. Derive Bernoulli's equation
for adiabatic process.(7 marks)
**2 (b)** A circular plate 3.5 m diameter is immersed in water in such a way that its
greatest and least depth below free surface is 4 m and 1.5 m respectively.
Determine the total pressure on one face of the plate and position of the center
of pressure(7 marks)
**2 (c)** Define force of buoyancy and meta-centre. Discuss the conditions of equilibrium
for floating and sub-merged bodies with neat sketches.(7 marks)
**3 (a) i)** A stream function in a two dimensional flow is ψ = 4xy. Calculate the
velocity at the point (4, 3). Find the corresponding velocity potential ϕ.(4 marks)
**3 (a) ii)** State Bernoulli's equation for steady incompressible fluid flow. What
assumptions are made in its derivation?(3 marks)
**3 (b)** What is venturimeter? Derive an expression for discharge through a
Venturimeter.(7 marks)
**3 (c) i)** Define the terms : Stream line , Equipotential line , Flownet(3 marks)
**3 (c) ii)** What is pitot tube? How velocity at any point is determined by pitot tube?(4 marks)
**3 (d)** A horizontal venturimeter with inlet diameter 30 cm and throat diameter 10 cm
is used to measure the flow of oil of specific gravity 0.8. The discharge of oil
through venturimeter is 50 liters/s. Find the reading of the oil-mercury
differential manometer. Take C_{d} = 0.98.(7 marks)
**4 (a)** A horizontal pipe of diameter 450 mm is suddenly contracted to a diameter of
250 mm. The pressure intensities in larger and smaller pipe are given as
14.5 N/cm^{2} and 12.5 N/cm^{2} respectively. If C_{c} = 0.62. Find loss of head due to contraction and discharge of water.(7 marks)
**4 (b) i)** What do you understand by pipes in series and pipes in parallel?(4 marks)
**4 (b) ii)** Define: Co-efficient of velocity, Co-efficient of discharge, Vena-contracta.(3 marks)
**5 (a)** Derive an expression for discharge through fully submerged and partially
submerged orifice.(7 marks)
**5 (b)** Water is flowing in a rectangular channel of 1.5 m wide and 0.75 m deep. Find
discharge over a rectangular weir of crest length 65 cm, if head of water over
the crest of weir is 25 cm and water flow over the weir. Take C_{d} = 0.62. Take approach velocity into consideration.(7 marks)
**5 (c) i)** What is orifice and mouthpiece? What is its use?(2 marks)
**5 (c) ii)** A circular tank of diameter 3 m contains water up to height of 4 m. The tank
is provided with an orifice of diameter 0.4 m at the bottom. Find time taken by
water to fall from 4.0 m to 1.0 m and for completely emptying the tank.
Take C_{d} = 0.98.(5 marks)
**5 (d)** Prove that the discharge through a triangular notch or weir is

$$Q=\dfrac{8}{15}\times C_{d}\times \dfrac{\theta}{2}\times \sqrt{2g}H^{5}/2$$(7 marks)