## Fluid Mechanics - Jun 2013

### Mechanical Engineering (Semester 4)

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)** Define the following properties of fluid:

Specific weight

specific gravity

Vapour pressure

Capability

Surface tension(10 marks)
**1 (b)** A shaft of 250mm diameter rotates inside a sleeve of 120mm long at 200rpm.If the thickness of oil film between shaft and sleeve is 1.5mm,find the power lost in friction.the dynamic viscosity of oil used is 8 poise(10 marks)
**2 (a)** obtained the total pressure and the centre of pressure on an inclined plain surface immersed in fluid(10 marks)
**2 (b)** A differential U -Tube mercury manometer is used to measure pressure between two water pipes A and B .Find the pressure at A if the level difference in mercury in the manometer is 150mm as shown fig.the pressure at B is 300 kPa

(10 marks)
**3 (a)** Explain the method to find metacentric height experimentally(8 marks)
**3 (b)** The stream function for a two-dimensional flow is given by?=2xy.Find the velocity at the point p(4,2). Also find the velocity potential function(12 marks)
**4 (b)** A 10km long water pipe is laid a slope of 3 in 4.The diameter of the lower end and upper end are 120mm and 180mm respectively pressure gauges fixed at the lower end upper end reads 0.2MPa and respectively.Determine the flow rate of water through the pipe(10 marks)
**4 (a)** Obtain the Euler\'s equation of motion along a stream line and hence derive Bernaulis equation for a steady incompressible fluid flow(10 marks)
**5 (a)** Derive an expression for discharge through a rectangular notch(10 marks)
**5(b)** Using Buckingham's π-theorem prove that the frictional torque T of a disc of diameter D rotating at a speed N in fluid of viscosity μ and density ρ in a turbulent flow is given by $$T=D^{5}N^{2}\rho \phi \left [ \frac{M}{D^{2}N\rho } \right ]$$(10 marks)
**6 (a)** Derive Darcy \'s equation for the loss of head due to friction in a circular pipe (10 marks)
**6 (b)** Water is supplied to a town having a population of 1 lakh from a reservoir 6km away from the town and is stipulated that half of the daily supply of 8-litres per head should be delivered in 8hrs .What should b e the diameter of the supplier pipe?The loss of head due to friction in the line is 2m.Take f=0.002(10 marks)
**7 (a)** Derive Hagen-Poiseuille\'s equation for viscous flow through a circular pipe (10 marks)
**7 (b)** A pipe of diameter 240mm and length is laid at a slope of 1 in 250 .An oil of specification gravity 0.85 and viscosity 180cp is pumped up at a rate of 10liters /sec. find the head lost due to friction and the power required to pump the oil(10 marks)
**8 (a)** Explain the following:

Drag

Lift

Momentum thickness

Mach number

Mach cone (10 marks)
**8 (b)** A flat plate 2m × 2m moves at 40km/hour in the stationary air density 1.2kg/m^{3If the coefficient of drag and lift are 0.75 respectively, determinethe lift force the drag forcethe resultant forceThe power required to keep the plate in motion}(10 marks)