 VTU Mechanical Engineering (Semester 4)
Fluid Mechanics
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 find properties and state their units:

i) Specific weight
ii) Viscosity
iii) Surface tension
iv) Specific volume.
6 M
1 (b) Classify the various types of fluids with the help of a diagram and briefly explain them.
5 M
1 (c) An oil film of thickness 1.5 mm is used for lubrication between a square plate of size 0.9×0.9 m and an inclined plane having an angle of inclination 20° with the horizontal. The weight of the square plate is 392.4 N and it slides down the plane with a uniform velocity of 0.2 m/s. Find the dynamics viscosity of oil.
9 M

2 (a) State and prove hydrostatic law.
6 M
2 (b) The measurements of pressure at the base and top of a mountain are 74 cm and 60 cm of mercury respectively. Calculate the height of the mountain if air has a mass density of 1.22 kg/m3.
6 M
2 (c) Derive expression for total pressure and centre of pressure for a plane surface immersed vertically in a static mass of fluid.
8 M

3 (a) Define the terms buoyancy, center of buoyancy, meta-centre and meta-centric height.
6 M
3 (b) A block of wood of specific gravity 0.8 floats in water. Determine the meta-centric height of block if its size is 3 m long. 2 m wide and 1 m height. State whether equilibrium is stable or unstable.
8 M
3 (c) Derive continuity equation in Cartesian coordinates.
6 M

4 (a) Derive Euler's equation of motion for ideal fluids and hence deduce Bernoulli's equation of motion. State the assumption made.
10 M
4 (b) A pipe line carrying oil of specific gravity 0.8 changes in diameter from 300 mm at position (1) to 600 mm in diameter at position (2), which is 5 m at a higher level. If the pressure at position (1) and (2) are 100 kN/m2 respectively and discharge is 300 lps. Determine (i) loss of head and (ii) directions of flow.
10 M

5 (a) Derive an expression for discharge through a venturi-meter.
8 M
5 (b) State Buckingham's theorem.
4 M
5 (c) The frictional torque 'T' of a disc of diameter 'D" rotating at a speed of 'N' in a fluid of velocity '°' and density '?' in a turbulent flow is given by $T=D^2N^2 \rho \phi \left [ \dfrac {M}{D^2 n \rho} \right ]$ . Prove this relation using Buckingham's ? theorem.
8 M

6 (a) Derive Darcy's relation for a turbulent flow through a circle pipe.
10 M
6 (b) Find the diameter of a pipe of length 2000 m when the rate of flow of water through the pipe is 200 lps and head lost due to friction is 4,. Take the value of 'C'=50 in Chezy's formula.
10 M

7 (a) Prove that the ratio of maximum velocity a verage in a viscous flow of fluid through a circular pipe is 2.0.
10 M
7 (b) Lubricating oil of specific gravity 0.85 and dynamic viscosity 0.1 N-s/m2 is pumped through a 3cm diameter pipe. If the pressure drop per meter length of the pipe is 15 kPa. Determine

i) The mass flow rate of oil in kg/min
ii) The shear stress at the pipe wall.
iii) Reynolds number of the flow and
iv) The power required per 40m length of the pipe to maintain the flow.
10 M

8 (a) The experiments were conducted in a wind tunnel with a wind speed of 50 km/hr on a flat plate of size 2m long and 1m wide. The density of air is 1.15 kg/m3. The coefficients of lift and drag are 0.75 and 0.15 respectively. Determine:

i) Lift force
ii) Drag force
iii) The resultant force
iv) Direction of resultant force
v) Power exerted by air on plate.
10 M
8 (b) Briefly explain, what is meant by boundary layer and hence define,

i) Displacement thickness
ii) Momentum thickness
6 M
8 (c) Define Mach number and derive an expression for the same.
4 M

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