1(a) Mention any 4 properties of
a fluid. (04 Marks)

(b) With a neat sketch, explain
the working of differential U-tube manometer. (06 Marks)

(c) A square lamina of side 0.6 m
is immersed in water with one of its diagonal horizontal to the surface of
water and the top corner point is 0.6 m below the free surface of water.
Calculate the force on one side of the lamina and the location of centre of
pressure. (06 Marks)

(d) Two circular discs of
diameter of 200 mm are mounted coaxially and the gap of 0.13 mm between the
plates is filled a viscous liquid (viscosity 0.14 Pa.s). Calculate the torque
necessary to rotate one disc relative to other at a uniform speed of 7 rev/s.
(04 Marks)

2(a) What are streamline,
pathline and streak line? Write equations. (06 Marks)

(b) A stream function for a two
dimensional flow field is expressed by an equation ψ = 3x + 4y + 2x

^{2}– 2y^{2}. Determine the corresponding velocity potential function. (04 Marks)
(c) Explain briefly the principle
of superposition and show how it can be used to analyze the flow over arbitrary
shaped bodies. (06 Marks)

(d) A 5 cm × 3 cm venturimeter
placed at an angle of 30

^{0}with the horizontal carries a liquid of specific gravity of 0.80. The deflection of a differential mercury manometer shows deflection of 10 cm for a particular flow rate. Estimate the flow rate. Take coefficient of discharge of the venturimeter as 0.96. (04 Marks)
3(a) Explain Reynolds transport
theorem. (06 Marks)

(b) A small hydropower plant
operates under 100 m of head and using 30 m

^{3}/s of water to produce electric power. Head loss due to friction from inlet to exit is 20 m. Estimate the power extracted by the turbine if it discharges water at 2 m/s into the atmosphere at its exit. (04 Marks)
(c) Explain the properties of
stress tensor. ( 06 Marks)

(d) Explain the terms vorticity
and circulation. (04 Marks)

4(a) Write continuity equation,
equations of motion and energy equation in spherical coordinates. (05 Marks)

(b) Prove that in an annulus
pipe, stresses are positive at the walls. (07 Marks)

(c) Derive Hagen-Poiesuille
equation for the flow through a circular pipe. (08 Marks)

5(a) Explain Ossen approximation.
(06 Marks)

(b) Explain the properties of
boundary layer equation. (06 Maerks)

(c) Show that in a two
dimensional creeping flow, the stream function obeys the biharmonic equation.
(04 Marks)

(d) What is the head loss in
meters of water in a 300 m long smooth 10 cm diameter pipe carrying 0.1 m

^{3}/s of water at 20^{0}C. Use Blausius formula for calculating friction factor. (04 Marks)
6(a) Write a short note on flow
over bluff bodies. (04 Marks)

(b) Distinguish between
Boussinesq hypothesis and Prandtl’s mixing length hypothesis. (08 Marks)

(c) Define Mach number. What are
zone of action and zone of silence? (04 Marks)

(d) Estimate the velocity and
Mach number of a projectile which reflects a shock wave of angle 30

^{0}in air at pressure of 0.95 kg/cm^{2}at a temperature of 3^{0}C. (04 Marks)
7(a) Explain Buckingham π-theorem.
(04 Marks)

(b) As per Stoke’s law, the
terminal velocity V of a small sphere of density ρ

_{s }and diameter D depends on the density of the liquid ρ_{f}, dynamic viscosity µ and acceleration due to gravity g. Express the functional relationship between the variables in a dimensionless form. (06 Marks)
(c) What are the assumptions made
during the internal estimate of the error? (04 Marks)

(d) A 1:50 scale model of a boat
has a wave resistance of 0.02 N when operating in water at 1 m/s. Find the
corresponding prototype resistance. Find also the horsepower required for the
prototype. What velocity does this test represent in the prototype? (06 Marks)

8(a) Using a neat sketch, explain
the working of Laser Doppler Anemometer. (08 Marks)

(b) Reynolds stress model is a
seven-equation model and is well suited for fluid flow analysis through complex
geometries. Explain. (04 Marks)

(c) What purpose Nacelle and
gearbox serves in a wind turbine? (04 Marks)

(d) Mention some disadvantages of
hydropower. (04 Marks)

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