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Derive Euler’s equation of motion. Obtain Bernoulli’s equation from Euler’s
equation of motion.
State the assumptions made in the derivation of Bernoulli’s equation.
Write the expressions for shear stress and velocity distribution in a pipe and
sketch a figure to show its distribution along the diameter of a pipe.
Describe the Reynolds experiment to classify laminar and turbulent flows with a
neat figure.
Explain the difference between major and minor losses in pipes. List any two
minor losses.
A crude oil of viscosity 0.97 poise and relative density 0.9 is flowing through a
horizontal circular pipe of diameter 100 mm and of length 10 m. Calculate the
difference of pressure at the two ends of the pipe, if 100 kg of the oil is
collected in a tank in 30 seconds.
PART C

Answer any four full questions, each carries 10 marks.

Define displacement thickness and momentum thickness. Derive an expression

for the displacement thickness and momentum thickness.

Explain the following terms : i) Laminar boundary layer 11) Turbulent layer

iii) boundary layer thickness.

Write the Von-Karman momentum integral equation and state the terms in it.
Describe the development of boundary layer over a horizontal flat plate which is
kept in a flow field with a neat sketch.

The pressure difference Ap in a pipe of diameter D and length L due to a
turbulent flow depends on the velocity ५, viscosity ||, density 0 and roughness
k. Using Buckingham’s pi theorem, obtain an expression for Ap.

List the three types of similarities and explain them.

A ship 300 m long moves in sea-water, whose density is 1030 kg/m’, a 1:100
model of this ship is to be tested in a wind tunnel. The velocity of air in the
wind tunnel around the model is 30 m/s and the resistance of the model is 60 N.
Determine the velocity of ship in sea-water and also the resistance of the ship in
sea- water. The density of air is given as 1.24 kg/m? . Take kinematic viscosity

of sea-water and air as 0.012 stokes and 0.018 stokes respectively.

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