## Fluid Mechanics - Jan 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)** Differentiate between the following and mention their units:

Specific weight and mass density.

Surfaces tension and capillarity.

Dynamic viscosity and kinematic viscosity(9 marks)
**1 (b)** Obtain an expression for capillarity rise(3 marks)
**1 (c)** In a 50mm long journal bearing arrangement, the clearance between the two at concentric condition is 0.1mm. The shaft is 2.0mm in diameter and rotates at 300rpm. The dynamic viscosity of the lubricant used 0.01 pas and the velocity variation in the lubricant is linear considering the lubricant to be Newtonian, calculate the frictional torque the journal has to overcome and the corresponding power loss.(8 marks)
**2 (a)** Obtain an expression for the force exerted and centre of pressure for a completely submerged inclined plane surface.(10 marks)
**2 (b)** A cylindrical roller gate 3m in diameter is placed on the dam is such a way that water is just going to spill. If the gate is 6m, calculate the magnitude and direction of the resultant force due to water acting on it(10 marks)
**3 (a)** Define the terms:

Centre of buoyancy

Metacentre

Metacentric height(4 marks)
**3 (b)** A solid cylinder of diameter 4m has a height of 3m.find the metacentric height of the cylinder when it is floating in water with its axis vertical.Take specific gravity of the cylinder as 0.6(8 marks)
**3 (c)** Explain the different types of fluid flows.(8 marks)
**4 (a)** Obtain an expression for Bernauli equation from Euler\'s equation of motion and also mention the assumption made(10 marks)
**4 (b)** A pipe 300m long has a slope of 1 in 100 and tapers from 1m diameter at the high end 0.5m at the low end. Quantity of water flowing is 5400 litre per minute. If the pressure at the high end is 70kPa,find the pressure at low end.(10 marks)
**5 (a)** Derive an expression for discharge through venturimeter.(10 marks)
**5 (b)** The resisting force \'F\' of a supersonic plane dunning flight can be considered as dependent upon the length of aircraft \'l\', velocity \'v\' air viscosity ?, air density \'&partial;\' and bulk modulus of air \'K\', Express the functional relationship between these variables and the resisting force.(10 marks)
**6 (a)** Derive Darcy-Weisbach equation for loss of head in pipe due to friction(10 marks)
**6 (b)** A 5cm diameter pipe takes off abruptly from a large tank and rum abruptly to 10cm diameter and runs 45m, and next discharge directly in velocity of 1.5 m/s.compute the necessary height of water surface discharge.Take t = 0.0065 in the Darcy equation(10 marks)
**7 (a)** prove that the maximum velocity in a circular pipe for viscous is equal average velocity of the flow(10 marks)
**7 (b)** An oil of viscosity 10 poise flow between two parallel fixed plates which are kept at a distance of 50mm apart.Find the rate of flow of oil between the plates if the drop of pressure in a length of 1.2m be 0.3 N/cm^{2}. The Width of the plates Is 200mm(10 marks)
**8 (a)** Define

lift and drag

Displacement, momentum and energy thickness

Mach number, Mach cone and Mach angle.(10 marks)
**8 (b)** A man descends to the ground from an aeroplane with the help of a parachute while hemispherical having a diameter of 4m against the resistance of air with uniform velocity of 25m/s.find the weight of the man if the weight of the parachute is 9.81 N.Take C_{D} =0.6 and density of air = 1.25 kg/m^{3}(10 marks)