## Fluid Mechanics - Jun 2015

### Mechanical Engg. (Semester 3)

TOTAL MARKS: 100

TOTAL TIME: 3 HOURS
(1) Question 1 is compulsory.

(2) Attempt any **four** from the remaining questions.

(3) Assume data wherever required.

(4) Figures to the right indicate full marks.
**1 (a)** Differentiate the following:

i) Liquids & gasses

ii) Pseudoplastic and Dilatant fluids.(4 marks)
**1 (b)** Derive the expression for surface of hollow bubble and liquid jet.(6 marks)
**1 (c)** Vertical gap 2.2cm wide of infinite extent contains a fluid of viscosity 2.0NS/m^{2} and specific gravity 0.9. A thin metallic plate 1.2m×1.2m×0.2cm is to be lifted up with a velocity of 0.15 m/sec through the gap. If the plate is in the middle of the gap, find the force required to lift the plate. Weight of the plate is 40N.(10 marks)
**2 (a)** Convert 1 kg/cm^{2} pressure in terms of:

i) meters of water

ii) mm of mercury.(4 marks)
**2 (b)** With neat sketch, explain working of single column manometer.(6 marks)
**2 (c)** A circular plate 3.0m diameter having concentric circular hole of diameter 1.5m is immersed in water such a way that its greatest and least depths from free surface are 4m and 1.5m respectively. Determine total pressure on one face of the plate and the position of centre of pressure.(10 marks)
**3 (a)** Explain briefly:

i) Steady and Unsteady flow

ii) Uniform and Non uniform flow.(4 marks)
**3 (b)** If for a two dimensional potential flow, the velocity potential is given by ϕ=x(2y-1), determine value of stream function ψ at that point.(6 marks)
**3 (c)** Derive expression for metacentric height for a floating body in liquid.(10 marks)
**4 (a)** Derive Euler's equation of motion. Obtain Bernoulli's equation from Euler's equation of motion. State the assumptions made.(10 marks)
**4 (b)** A pump has a tapering pipe running full of water. The pipe is placed vertically with the diameter at the base and top being 1.2m and 0.6m respectively. The pressure at the upper end is 240mm of mercury (vacuum). The pressure at the upper end is 15kN/m^{2}. Assume loss of head to be 20% difference in velocity head. Calculate the discharge when flow is vertically upwards and difference in elevation is 3.9m.(10 marks)
**5 (a)** Derive expression for actual discharge through orifice meter. Explain how orifice meter is different from venturimeter.(10 marks)
**5 (b)** In a fuel injection system, small droplets are formed by break up of liquid jet. Assume the droplet diameter 'd' is function of liquid density ρ, viscosity μ, surface tension σ, nozzle diameter D and jet velocity V. Show using Buckingham's π-theorem $$ d/D = \phi \left [ \dfrac {\rho VD}{\mu} , \ \dfrac {\sigma}{\mu V} \right ] $$ Considering (D, V, μ) are repeating variables.(10 marks)
**6 (a)** Derive expression for loss of head due to sudden enlargement during fluid flow.(8 marks)
**6 (b)** Horizontal pipe of diameter 500mm is suddenly contracted due to a diameter of 250mm. The pressure intensities in the large and smaller pipe is given as 13.734 N/cm^{2} and 11.772 N/cm^{2} respectively. Find the loss of head due to contraction if C_{e}=0.62. Also determine rate of flow.(8 marks)
**6 (c)** Find the diameter of a pipe of length 2000m when the rate of flow of water through the pipe is 200 litres/sec and head loss due to friction is 4m. Take value C=50 in Chezy's equation. Given hydraulic mean depth m=d/4.(4 marks)
**7 (a)** For flow between two parallel stationary plates show that maximum velocity is 1.5 times average velocity.(8 marks)
**7 (b)** A crude oil of viscosity 0.97 and relative density 0.9 is flowing through a horizontal circular pipe of diameter 100 mm and length 10m. Calculate the difference of pressure at two ends if 100kg of oil of collected in a tank in 30 seconds. Assume laminar flow.(8 marks)
**7 (c)** Explain how laminar and turbulent flows are different.(4 marks)
**8 (a)** Derive expression for velocity of sound.(8 marks)
**8 (b)** Find displacement thickness, momentum thickness for the velocity distribution in boundary layer given by $$ \dfrac {u}{U} = 2 \left ( y/\delta \right ) - \left ( y/\delta \right )^2 $$(8 marks)
**8 (c)** Write short notes on:

i) Drag & lift forces

ii) Subsonic and Supersonic flows.(4 marks)