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)

 

1. Define a steady flow.
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 q_r = 0, , q_z = 0 satisfies the equation of motion where A, B are constants.
5. Find the stream function y, if j = A(x² – y²) represents a possible fluid motion.
6. What is the complex potential of sinks a₁, a₂ …… a_n with strength m₁, m₂ …… m_n situated at the points z₁, z₂ …… z_n 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.

10. Define the term camber.

 

SECTION B

 

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

 

11. 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).
12. Derive the equation of continuity.
13. Draw and explain the working of a Venturi tube.
14. Prove that for the complex potential the streamlines and equipotentials are circles.
15. Obtain the complex potential due to the image of a doublet with respect to a plane.
16. Show that the velocity vector is everywhere tangent to the lines in the XY-plane along which y(x, y) = a constant.
17. Let , (A, B, C are constants) be the velocity vector of a fluid motion. Find the equation of vortex lines.
18. Discuss the structure of an aerofoil.

 

 

 

 

 

SECTION C

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

 

19. 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.
20. 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)

 

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

 

21. a) Obtain the complex potential due to the image of a source with respect to a circle.
22. 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)

 

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

 

 

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