 VTU Mechanical Engineering (Semester 3)
Fluid Mechanics
January 2013
Total marks: --
Total time: --
INSTRUCTIONS
(1) Assume appropriate data and state your reasons
(2) Marks are given to the right of every question
(3) Draw neat diagrams wherever necessary

1 (a) Differentiate between the following and mention their units:
specific weight and mass density.
surfaces tension and capillarity.
Dyanamic viscosity and kinematic viscosity
9 M
1 (b) Obtain an expression for capillarity rise
3 M
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 Considerning the lubricant to be newtonian, calculate the frictional torque the journal has to overcome and the corressponding power loss.
8 M

2 (a) Obtain an expression for the force exerted and centre of pressur efor a completely submerged inclined plane surface.
10 M
2 (b) A cylindrical roller gate 3m in diameter is placed on the dam is such a way that water is just going to spil. If the gate is 6m, calculate the magnitude and direction of the resultant force due to water acting on it
10 M

3 (a) Define the terms:
Centre of buoyancy
Metacentre
Metacentric height
4 M
3 (b) A solid cylinder of diameter 4m has a height of 3m.find the metacenteic height of the cylinder when it is floating in water with its axis vertical.Take specific gravity of the cylinder as 0.6
8 M
3 (c) Explain the different types of fluid flows.
8 M

4 (a) Obtain an expression for bernoulli equation from Euler's equation of motion and also mention the assumption made
10 M
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. Qunatity of water flowing is 5400 litres per miniute. If the pressure at the high end is 70kPa,find the pressure at low end.
10 M

5 (a) Derive an expression for discharge through venturimeter.
10 M
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 μ, air density '&partial;' and bulk modulus of air 'K', Express the functional relationship between these variables and the resisting force.
10 M

6 (a) Derive Darcy-Weisbach equation for loss of head in pipe due to friction
10 M
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 M

7 (a) prove that the maximum velocity in a circular pipe for viscous is equal average velocity of the flow
10 M
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 paltes Is 200mm
10 M

8 (a) Define
lift and drag
Displacement, momentum and energy thickness
Mach number, Mach cone and mach angle.
10 M
8 (b) A man descends to the ground from an aeroplane with the help of a parachute while homispherical 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 parature is 9.81 N.Take C_{D} =0.6 and density of air = 1.25 kg/m^{3}
10 M

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