## Fluid Mechanics - May 2014

### 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)** What is viscosity? State and explain Newtons Law of viscosity.(6 marks)
**1 (b)** Discuss various type of flows with examples.(6 marks)
**2 (a)** A circular plate of diameter 1.2 m placed vertically in water in such a way that the centre of the plate is 2.5 m below the free surface of water. i) determine total pressure on the plate ii) position of centre of pressure.(6 marks)
**2 (b)** Explain i) surface tension ii) Vapour pressure iii) compressibility(6 marks)

### Answer any one question from Q3 and Q4

**3 (a)** Derive an expression for velocity profile for laminar flow through pipe.(6 marks)
**3 (b)** A liquid of viscosity of 24.5 poise is flowing between two horizontal plates 100 mm apart with a maximum velocity of 1.5 m/s. Calculate

i) The discharge per meter width

ii) shear stress at the plates

iii) The difference in pressure between two plates.(6 marks)
**4 (a)** A 200 mm x 100 mm venturimeter is provided in a vertical pipe carrying water flowing in a upward direction. A differential mercury manometer connected to the inlet and throat gives a reading of 220 mm. Find the rate of flow.(6 marks)
**4 (b)** Derive an expression for continuity equation for 3-D flow.(6 marks)

### Answer any one question from Q5 and Q6

**5 (a)** Derive an expression for Darcy-Weisbach equation.(6 marks)
**5 (b)** Using Buckingham's ?- theorem, show that the velocity through a circular orifice is given by $$ V = \sqrt{2gH}\phi \left [\dfrac {D}{H}, \dfrac {\mu}{\rho VH} \right ] $$ All terms carry usual meaning.(7 marks)
**6 (a)** Explain i) Mach Number ii) Froude Number iii) Euler Number(6 marks)
**6 (b)** A 2500m long pipeline is used for transmission of power. 120kW power is to be transmitted through the pipe in which water having a pressure of 4000kN/m^{2} at inlet is flowing. If the pressure drop over the length of pipe is 800 kN/m^{2} and f=0.006. Find

i) Diameter of the pipe

ii) Efficiency of transmission.(7 marks)

### Answer any one question from Q7 and Q8

**7 (a)** If velocity distribution in laminar boundary layer over a flat plate is assumed to be given by equation u = a + by +cy^{2}, determine its form using the necessary boundary conditions.(6 marks)
**7 (b)** Assuming the cross-selection area of a car to be 2.7 m^{2 with a drag coefficient of 0.6 estimate the energy requirement at a speed of 60 km/h. Assuming the weight of a car to be 30 kN and coefficient of friction 0.012. Assume density to be 1.208 kg/m3.}(7 marks)
**8 (a)** Draw profile of symmetrical and unsymmetrical aerofoil and define following terms of an aerofoil i) Chord line ii) Angle of attack iii) stall iv) Camber(6 marks)
**8 (b)** Write a short note on 'Seperation of Boundary Layer its Control'.(7 marks)