Cochin University of Science and Techology (CUST) 2007 B.Tech Mechanical Engineering first term fluid mechanics and heat engines - Question Paper

BTECH 1st SERIES exam SEPTEMBER 2007

FLUID MECHANICS AND HEAT ENGINES Max marks:50

Time:2 Hrs
PART A

1. describe the subsequent fluid properties with their units of measurements.
1) Mass density 2) Weight density 3) Specific quantity 4) Specific gravity
5) Dynamic & kinematic viscosity.

2. explain the various kinds of fluid flow.

3. Derive Darcy-Weishbach formula for calculating loss of head due to friction.

4. define the Rayleigh’s method for dimensional analysis.

PART B

5. a) The velocity potential function for a 2 dimensional flow is x(2y-1). At a point
P(4,5), determine 1) the velocity 2) the value of stream function.

b) State Bernoulli’s theorem. elaborate the assumptions & limitations of the theorem?

c) A 300*150mm venturimeter is given in a vertical pipe line carrying coil of
specific gravity 0.90, the flow being upwards. The difference in elevations of the
throat part & entrance part of the venturimeter indicates a gauge deflection of
250mm. compute 1) discharge of the coil 2) pressure difference b/w the entrance &
throat part.
OR

6. a) State and prove Bernoulli’s theorem.

b) obtain the discharge through a trapezoidal notch which is 1m wide at the top & 0.40m
at the bottom & is 30cm in height. The head of water on the notch is 20cm. presume
Cd for rectangular portion as 0.62 while for triangular portion as 0.60.

c) The water is flowing through a taper pipe of length 100m having diameter 600mm at
the upper end & 300mm at the lower end. The pipe has slope of one in 30. obtain the
pressure at the lower end if the pressure at the higher level is 19.62N/sq.cm.

7. a) A horizontal pipe 150mm diameter is joined by sudden enlargement to a 225mm
diameter pipe. Water is flowing through it at the rate of 0/05meter cube/sec. obtain 1)
Loss of head due to abrupt expansion 2) Pressure difference in the 2 pipes 3)
change in pressure if the change of part is gradual without any loss.

b) discuss geometric, kinematic & dynamic similarities

c) discuss the various model laws which are being used to attain dynamic likeness
in model testing.

d) The ratio of lengths of a submarine & its model is 30:1. The speed of
submarine(prototype) is 10m/s. The model is to be tested in a wind tunnel. obtain the
speed of air in the tunnel. Also, determine the ratio of the drag b/w the model & its
prototype. Kinematic viscosities in sea water & air are 0.012 Stokes & 0.016 Stokes
respectively. The density for sea water & air is 1030kg/meter cube & 1.24kg/metre
cube respectively.
OR

8. a) discuss dimensional homogeneity.

b) The pressure drop in a pipe depends upon the mean velocity of flow v, length of
pipe l, diameter of pipe d, viscosity of fluid, avg. height of roughness projections
on inside pipe surface k and mass density. By using Buckingham’s theorem, find a
dimensionless expression for pressure drop. Also, show that hf = 4flvsq./2dg where
hf is the head loss due to friction, w is the specific weight of fluid & f is the
coefficient of friction.

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Earning:   Approval pending.