LOYOLA COLLEGE (AUTONOMOUS), CHENNAI – 600 034

B.Sc. DEGREE EXAMINATION – MATHEMATICS
FIFTH SEMESTER – November 2008
MT 5405 – FLUID DYNAMICS
Date : 121108 Dept. No. Max. : 100 Marks
Time : 9:00 – 12:00
SECTION A
Answer ALL questions: (10 ´ 2 = 20)
 Define a steady flow.
 Define pathlines.
 What is the condition if the rigid surface in contact with the fluid motion is at rest?
 Determine pressure, if the velocity field q_{r} = 0, , q_{z} = 0 satisfies the equation of motion where A, B are constants.
 Find the stream function y, if j = A(x^{2} – y^{2}) represents a possible fluid motion.
 What is the complex potential of sinks a_{1}, a_{2} …… a_{n} with strength m_{1}, m_{2} …… m_{n} situated at the points z_{1}, z_{2} …… z_{n} respectively?
 Define a twodimensional doublet.
 Define vortex tube.
 Find the vorticity components of a fluid motion, if the velocity components are
u = Ay^{2} + By + C, v = 0, w = 0.
 Define the term camber.
SECTION B
Answer any FIVE questions: (5 ´ 8 = 40)
 The velocity in a 3dimensional flow field for an incompressible fluid is . Determine the equation of streamlines passing through the point (1, 1, 1).
 Derive the equation of continuity.
 Draw and explain the working of a Venturi tube.
 Prove that for the complex potential the streamlines and equipotentials are circles.
 Obtain the complex potential due to the image of a doublet with respect to a plane.
 Show that the velocity vector is everywhere tangent to the lines in the XYplane along which y(x, y) = a constant.
 Let , (A, B, C are constants) be the velocity vector of a fluid motion. Find the equation of vortex lines.
 Discuss the structure of an aerofoil.
SECTION C
Answer any TWO questions: (2 ´ 20 = 40)
 a) For a twodimensional flow the velocities at a point in a fluid may be expressed in the Eulerian coordinates by u = x + y + 2t and v = 2y + t. Determine the Lagrange coordinates as functions of the initial positions , and the time t.
 b) If the velocity of an incompressible fluid at the point (x, y, z) is given by where . Prove that the fluid motion is possible and the velocity potential is . (10 + 10)
 Derive the Euler’s equation of motion and deduce the Bernoulli’s equation of motion.
 a) Obtain the complex potential due to the image of a source with respect to a circle.
 b) The particle velocity for a fluid motion referred to rectangular axes is given by the components, where A is a constant. Find the pressure associated with this velocity field. (12 + 8)
 a) Show the motion specified by , (k being a constant) is an irrotational flow.
 b) State and prove the theorem of KuttaJoukowski. (5 + 15)
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