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VTU Civil Engineering (Semester 3)
Mechanics of Fluids
June 2014
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) Define the following fluid properties with units:
i) Mass density
ii) Specific gravity
iii) Dynamic viscosity
iv) Vapour pressure
v) Capillarity.
10 M
1 (b) A 150mm diameter vertical cylinder rotates concentrically inside another cylinder of diameter 151.0mm. Both cylinder are 250mm high. The space between the cylinders is filled with a liquid whose viscosity is unknown. If a torque of 12 N-m is required to rotate the inner cylinder at 100rpm. Determine the viscosity of the fluid.
10 M

2 (a) State and prove Pascal's law.
6 M
2 (b) With neat sketch, explain Bourdon's pressure gauge.
6 M
2 (c) An open tank contains water up to a depth of 2m and above it an oil of specific gravity 0.9 for a depth of 1m. Find the pressure intensity.
i) At the interface of the pressure intensity
ii) At the bottom of the tank.
8 M

3 (a) Define: i) Total Pressure;
ii) Centre of pressure
4 M
3 (b) Obtain an expression for total pressure and centres of pressure for inclined surface submerged in liquid.
8 M
3 (c) A trapezoidal channel 2m wide at the bottom and 1m deep has sides slopes 1:1. Determine: i) Total pressure; ii) Centre of pressure, when it is full of water.
8 M

4 (a) Distinguish between:
i) Laminar and turbulent flow
ii) Uniform and non uniform flow.
4 M
4 (b) Obtain an expression for continuity equation for three dimensional flows.
8 M
4 (c) If for a two dimensional potential flow, the velocity potential is given by ϕ=x(2y-1). Determine the velocity at the point P(4,5). Determine also the value of stream function ψ at the point P.
8 M

5 (a) Derive Bernoulli's equation from Euler's equation with assumptions made.
8 M
5 (b) Derive the equation from the discharge through venturimeter.
6 M
5 (c) Water is flowing through a pipe having diameter 300mm and 200mm at the bottom and upper end respectively. The intensity of pressure at the bottom end is 24.52 N/cm2 and the pressure at the upper end is 9.81 N/cm2. Determine the difference in datum head if the flow through pipe is 40/ps.
6 M

6 (a) Define:
4 M
6 (b) Distinguish between compound pipe and equivalent pipe.
6 M
6 (c) A1 a sudden enlargement of water main from 240mm to 480mm diameter, the hydraulic gradient rises by 10mm. Estimate the rate of flow.
10 M

7 (a) Define hydraulic co-efficient and Determine the hydraulic co-efficient experimentally.
10 M
7 (b) A 25mm diameter nozzle discharges 0.76 m3 of water/minute, when the head is 60m. The diameter of the jet is 22.5mm. Determine the values of Cc, Cv, Cd and loss of head due to fluid resistance.
10 M

8 (a) Distinguish between:
i) Sharp crested and broad crested weirs.
ii) Orifice and mouth piece.
iii) Broad crested weir and submerged weir.
6 M
8 (b) Derive an expression for discharge over a triangular notch.
6 M
8 (c) Water flows over a rectangular weir 1m wide at a depth of 15 cm and afterwards passes through a triangular right angled weir. Taking Cd for rectangular weir 0.62 and for triangular 0.59. Find the depth over the triangular weir.
8 M

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