LOYOLA COLLEGE (AUTONOMOUS), CHENNAI – 600 034

CV 18

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)

1. Define Lagrangian method of fluid motion.
2. State the components of acceleration in Cartesian coordinates?
3. What is the equation of continuity for (i) a homogeneous steady flow of fluid, (ii) a non-homogeneous incompressible flow of fluid.
4. Show that u = a+ by – cz, v = d – bx + ez, w = f + cx – ey are the velocity components of a possible liquid motion.
5. Write down the boundary condition when a liquid is in contact with a rigid surface.
6. Write down the stream function in terms of fluid velocity.
7. If = A(x² – y²) represents a possible flow phenomena, determine the stream function.
8. State the Bernoulli’s equation for a steady irrotational flow?
9. What is the complex potential of sources at a₁, a₂, ….,a_n with strengths m₁, m₂,…,m_n respectively?
10. Describe the shape of an aerofoil.

SECTION B

Answer ANY FIVE Questions.         (5 x 8 = 40)

11. (a) Define a streamline. Derive the differential equation of streamline.

(b) Determine the equation of streamline for the flow given by .         (4 + 4)

12. Explain local, convective and material derivatives.
13. The velocity field at a point is . Obtain pathlines and streaklines.
14. Show that the velocity potential satisfies the Laplace equation. Also find the streamlines.
15. Derive Euler’s equation of motion for one-dimensional flow.
16. Explain how to measure the flow rate of a fluid using a Venture tube.
17. Derive the complex potential of a doublet.
18. Explain the image system of a source with regard to a plane.

 

 

SECTION C

Answer ANY TWO Questions.          (2 x 20 = 40)

19. The velocity components of a two-dimensional flow system can be given in Eulerian system by . Find the displacement of the fluid particle in the Lagrangian system.
20. (a) Show that is a possible form of a bounding surface of a liquid.

(8 + 12 marks)

21. (a) Derive Bernoulli’s equation.

(b) Explain the functions of a pitot tube with a neat diagram.                             (10 + 10 marks)

22. State and prove the theorem of Kutta and Joukowski.

 

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