## Fluid Mechanics - Dec 2015

### Mechanical Engineering (Semester 4)

TOTAL MARKS: 80

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

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

(3) Assume data if required.

(4) Figures to the right indicate full marks.
**1 (a)** Define a fluid and distinguish between ideal and real fluids.(5 marks)
**1 (b)** A stone weights 2KN in air and 168N in water. Calculate the volume and specific gravity.(5 marks)
**1 (c)** Explain Hydrostatic law.(5 marks)
**1 (d)** Define steam lines, path lines and streak lines.(5 marks)
**1 (e)** Define Mach number, stagnation density and stagnation temperature.(5 marks)
**2 (a)** The velocity components in two dimensional flow fields are as follows

u=y^{3}/3+2x-x^{2}y, v=xy^{2}-2y-x^{3}/3.

i) whether the flow is possible

ii) obtain an expression for steam function

iii) obtain an expression for potential function.(10 marks)
**2 (b)** A sliding gate 3m and 1.5m high situated in a vertical plane has a coefficient of friction between itself and guide of 0.18. If the gate weight is 19n and its upper edge is at a depth of 9m, what vertical force is required to raise it? Neglect buoyancy force on gate.(10 marks)
**3 (a)** Starting from the Navier Stokes equation for an incompressible Newtonian fluid derive Bernoulli's equation starting the assumptions.(10 marks)
**3 (b)** Derive the expression for stagnation density and stagnation temperature.(10 marks)
**4 (a)** A pipeline of length 2400m is used for power transmission. If 115KW power is to be transmitted through the pipe in which water having a pressure of 500 N/cm^{2} at inlet is flowing? Find the diameter of the pipe and efficiency of transmission if the pressure drop over the length of pipe is 100 N/cm^{2}. Take f=0.026 also find diameter if pipe corresponding to maximum efficiency of transmission.(10 marks)

### Write short note on.

**4 (b) (i)** Moody's diagram(5 marks)
**4 (b) (ii)** Major and minor losses.(5 marks)
**5 (a)** A normal shock wave occurs in a duct in which air is flowing at a Mach number of 1.5. The static pressure and temperature upstream of the shock wave is 1.5 bar and 270°C. Determine pressure, temperature and mach number downstream of the shock. Also calculate strength of shock.(10 marks)
**5 (b)** Explain Prandtl's mixing length theory.(10 marks)
**6 (a)** The velocity profile within a laminar boundary layer over a flat plate is given by the equation.

u/U =2(y/δ) - (y/δ)^{2}

Where U is the mean stream velocity and δ is the boundary layer thickness. Determine the displacement thickness and momentum thickness.(10 marks)

### Explain

**6 (b) (i)** Aerofoil theory(5 marks)
**6 (b) (ii)** Reynolds Transportation theorem.(5 marks)