# Loyola College B.Sc. Mathematics Nov 2008 Fluid Dynamics Question Paper PDF Download

LOYOLA COLLEGE (AUTONOMOUS), CHENNAI – 600 034

# AB 14

B.Sc. DEGREE EXAMINATION – MATHEMATICS

FIFTH SEMESTER – November 2008

# MT 5405 – FLUID DYNAMICS

Date : 12-11-08                     Dept. No.                                        Max. : 100 Marks

Time : 9:00 – 12:00

SECTION A

Answer ALL questions:                                                                                 (10 ´ 2 = 20)

2. Define pathlines.
3. What is the condition if the rigid surface in contact with the fluid motion is at rest?
4. Determine pressure, if the velocity field qr = 0, , qz = 0 satisfies the equation of motion where A, B are constants.
5. Find the stream function y, if j = A(x2y2) represents a possible fluid motion.
6. What is the complex potential of sinks a1, a2 …… an with strength m1, m2 …… mn situated at the points z1, z2 …… zn respectively?
7. Define a two-dimensional doublet.
8. Define vortex tube.
9. Find the vorticity components of a fluid motion, if the velocity components are

u = Ay2 + By + C, v = 0, w = 0.

1. Define the term camber.

SECTION B

Answer any FIVE questions:                                                                         (5 ´ 8 = 40)

1. The velocity in a 3-dimensional flow field for an incompressible fluid is . Determine the equation of streamlines passing through the point (1, 1, 1).
2. Derive the equation of continuity.
3. Draw and explain the working of a Venturi tube.
4. Prove that for the complex potential the streamlines and equipotentials are circles.
5. Obtain the complex potential due to the image of a doublet with respect to a plane.
6. Show that the velocity vector is everywhere tangent to the lines in the XY-plane along which y(x, y) = a constant.
7. Let , (A, B, C are constants) be the velocity vector of a fluid motion. Find the equation of vortex lines.
8. Discuss the structure of an aerofoil.

SECTION C

Answer any TWO questions:                                                                         (2 ´ 20 = 40)

1. a) For a two-dimensional 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.
2. 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)

1. Derive the Euler’s equation of motion and deduce the Bernoulli’s equation of motion.

1. a) Obtain the complex potential due to the image of a source with respect to a circle.
2. 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)

1. a) Show the motion specified by , (k being a constant) is an irrotational flow.
2. b) State and prove the theorem of Kutta-Joukowski.                             (5 + 15)

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