MU Mechanical Engineering (Semester 4)
Fluid Mechanics
May 2016
Total marks: --
Total time: --
(1) Assume appropriate data and state your reasons
(2) Marks are given to the right of every question
(3) Draw neat diagrams wherever necessary

Solve any FOUR
1(a) Define a fluid and explain Newton's law of viscosity
5 M
1(b) Explain boundary layer separation and methods to control it
5 M
1(c) A two dimensional flow is described in the Lagrangian system as
x = x0e-kt + y0 (1-e-2kt) and y = y0e-kt.
Find the equation of a fluid particlein the flow field
5 M
1(d) Explain Induced drag
5 M
1(e) Draw a sketch of an Orifice meter
5 M

2(a) Find the magnitude and direction of resultant pressure acting on a curved face of a dam which is shaped according to the relation y = x2/9 as shown in the figure. The height of the water retain by the dam is 10m. Consider the width of the dam as unity.

10 M
2(b) The stream lines is represented by Ψ = x2+y2
(i) Find its corresponding velocity potential
(ii) Determine the velocity and its direction at (2,2)
(iii) Sketch the streamlines and also show the direction of flow.
10 M

3(a) Starting from Navier stoke equation for incompressible laminar flow; derive an equation for velocity profile for Couette flow. State the assumptions made.
10 M
3(b) 360 lit/sec of water is flowing in a pipe. The pipe is sent by 120°. The pipe bend measure 360 mm × 240 mm and volume at the bend is 0.14m3. The pressure at the entrance is 73 KN/m2 and exit is 2.4m above the entrance section. Find the resultant force and the direction on the bend
10 M

4(a) If velocity distribution, u in laminar boundary layer over a flat plate is assumed to be given by second order polynomial
                    u = a + by + cy2
where y is the perpendicular distance measured from the surface of the flat plate, and a, b and c are constant. Determine the expression of velocity distribution in dimensionless form as, U is main stream velocity at boundary layer thickness δ. Further also find boundary layer thickness in terms of Reynolds number.
10 M
4(b) A pipe 60 mm diameter and 450 m long slopes upwards at 1 in 50 an oil of viscosity 0.9 Ns / m2 and sp. gr. 0.9 is required to be pumped at the rate of 5 liters/s
(1) Is the flow laminar?
(2) What pressure difference is required to attain this condition?
(3) What is the power of the pump required assuming overall efficiency 65%?
(4) What is the centre line velocity and the velocity gradient at pipe wall?
10 M

5(a) Foe a normal shock wave in air Mach number is 3. If the atmospheric pressure and air density are 26.5 KN/m2 and 0.413 kg/m3 respectively, determine the flow conditions before and after the shock wave. Tank γ = 1.4
10 M
5(b) Derive an expression of 'critical pressure ratio' for compressible fluid flow
10 M

6(a) A pipe pf diameter 0.4 m and of length 2000 m is connected to a reservoir at one end. The other end of the pipe is connected to a junction from which two pipes of length 1000m and diameter 30 cm runs parallel. These parallel pipes are connected to another reservoir which is having a level of water 10m below the water level of the above reservoir. Determine the total discharge, if coefficient of friction f=0.015.neglect the minor losses.
10 M
6(b) Explain
(i) Moodys Diagram
(ii) Major and Minor losses in pipes.
10 M

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