## Fluid Mechanics - Jun 2015

### Mechanical Engineering (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.

### Answer any one question from Q1 and Q2

**1 (a)** State and prove Hydrostatic Law.(6 marks)
**1 (b)** Discuss various types of flows.(6 marks)
**2 (a)** A body with gravity force of 500 N with a flat surface area
of 0.2 m^{2} slides down a lubricated inclined plane making a 30° angle with the horizontal. For viscosity of 0.1 kg.m/s and body speed of 1 m/s. Determine the lubricant film thickness.(6 marks)
**2 (b)** Prove that streamlines and equipotential lines are orthogonal to each other.(6 marks)

### Answer any one question from Q3 and Q4

**3 (a)** Derive an expression for Euler's equation along stream-Line(6 marks)
**3 (b)** Write short notes on:

(i) Hydrodynamically smooth and rough boundaries.

(ii) Velocity profile of Turbulent flow.(6 marks)
**4 (a)** What is Pitot tube? Derive expression for velocity. Draw with all labels Pitot static tube.(6 marks)
**4 (b)** Derive expression for velocity distribution for flow in fixed parallel plates.(6 marks)

### Answer any one question from Q5 and Q6

**5 (a)** Derive an expression for Darcy-Weisbach equation.(6 marks)
**5 (b)** Discharge Q of a centrifugal pump can be assumed to be dependent on density of liquid ρ, viscosity of liquid μ, pressure p, impeller diameter D, and speed N in RPM. Using Buckingham theorem, show that : $$ Q=ND^3 \phi \left [ \dfrac{gH}{N^2D^2}, \dfrac {v}{ND^2} \right ] $$(7 marks)
**6 (a)** What are repeating variables? What points are important while selecting repeating variables?(6 marks)
**6 (b)** A siphon of dia. 200 mm connects two reservoirs having a
a difference of elevation of 20 m. The total length of siphon
is 800m and the summit is 5 m above the water level in
the upper reservoir. If separation takes place at 30 kPa (absolute). Find maximum length of siphon from upper reservoir to summit. Take friction factor = 0.016, P atm. = 10.3 m of water.(7 marks)

### Answer any one question from Q7 and Q8

**7 (a)** Derive an expression for displacement, momentum and energy thicknesses.(9 marks)
**7 (b)** A car of frontal area 1.4 m^{2} travels in still air with speed 72 kmph. If drag coefficient is 0.350, calculate power required to drive the car at this speed. Density of air is 1.2 kg/m^{3}.(4 marks)
**8 (a)** Discuss boundary layer development over flat plate.(7 marks)
**8 (b)** Write a short note on 'Flow around cylinder and aerofoil'.(6 marks)