Fluid Mechanics - May 2016
Mechanical Engineering (Semester 4)
TOTAL MARKS: 80
TOTAL TIME: 3 HOURS (1) Question 1 is compulsory.
(2) Attempt any three from the remaining questions.
(3) Assume data if required.
(4) Figures to the right indicate full marks.
Solve any FOUR
1(a) Define a fluid and explain Newton's law of viscosity(5 marks)
1(b) Explain boundary layer separation and methods to control it(5 marks)
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 marks) 1(d) Explain Induced drag(5 marks) 1(e) Draw a sketch of an Orifice meter(5 marks) 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.
(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 marks) 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 marks) 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 marks) 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 marks) 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 marks) 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 marks) 5(b) Derive an expression of 'critical pressure ratio' for compressible fluid flow(10 marks) 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 marks) 6(b) Explain
(i) Moodys Diagram
(ii) Major and Minor losses in pipes.(10 marks)