LOYOLA COLLEGE (AUTONOMOUS), CHENNAI – 600 034

B.Sc. DEGREE EXAMINATION –MATHEMATICS
FIFTH SEMESTER – APRIL 2007
MT 5401 – FLUID DYNAMICS
Date & Time: 03/05/2007 / 9:00 – 12:00 Dept. No. Max. : 100 Marks
SECTION A
Answer ALL Questions. (10 x 2 = 20)
 Define Lagrangian method of fluid motion.
 State the components of acceleration in Cartesian coordinates?
 What is the equation of continuity for (i) a homogeneous steady flow of fluid, (ii) a nonhomogeneous incompressible flow of fluid.
 Show that u = a+ by – cz, v = d – bx + ez, w = f + cx – ey are the velocity components of a possible liquid motion.
 Write down the boundary condition when a liquid is in contact with a rigid surface.
 Write down the stream function in terms of fluid velocity.
 If = A(x^{2} – y^{2}) represents a possible flow phenomena, determine the stream function.
 State the Bernoulli’s equation for a steady irrotational flow?
 What is the complex potential of sources at a_{1}, a_{2}, ….,a_{n} with strengths m_{1}, m_{2},…,m_{n} respectively?
 Describe the shape of an aerofoil.
SECTION B
Answer ANY FIVE Questions. (5 x 8 = 40)
 (a) Define a streamline. Derive the differential equation of streamline.
(b) Determine the equation of streamline for the flow given by . (4 + 4)
 Explain local, convective and material derivatives.
 The velocity field at a point is . Obtain pathlines and streaklines.
 Show that the velocity potential satisfies the Laplace equation. Also find the streamlines.
 Derive Euler’s equation of motion for onedimensional flow.
 Explain how to measure the flow rate of a fluid using a Venture tube.
 Derive the complex potential of a doublet.
 Explain the image system of a source with regard to a plane.
SECTION C
Answer ANY TWO Questions. (2 x 20 = 40)
 The velocity components of a twodimensional flow system can be given in Eulerian system by . Find the displacement of the fluid particle in the Lagrangian system.
 (a) Show that is a possible form of a bounding surface of a liquid.
(8 + 12 marks)
 (a) Derive Bernoulli’s equation.
(b) Explain the functions of a pitot tube with a neat diagram. (10 + 10 marks)
 State and prove the theorem of Kutta and Joukowski.
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