LOYOLA COLLEGE (AUTONOMOUS), CHENNAI – 600 034
B.Sc. DEGREE EXAMINATION – MATHEMATICS
FIFTH SEMESTER – November 2008
MT 5401 - FLUID DYNAMICS
Date : 12-11-08
Time : 9:00 - 12:00
Dept. No.
CC 14
Max. : 100 Marks
PART - A
(10  2 = 20 marks)
Answer ALL questions:
1. Define a steady flow.
2. What is an incompressible fluid?
3. If the velocity distribution is q  xyi  yz j  zx k , then find the velocity components.
4. What is the application of a Venturi tube?
5. When is a flow irrotational?
6. What is the complex potential of a source with strength m situated at the points z = z1?
7. Define a two-dimensional sink.
8. Define a vortex tube.
9. Define a vorticity vector.
10. Explain the magnitude and components of lift.
PART - B
(5  8 = 40 marks)
Answer any FIVE questions:
11. Write a note on Lagrangian method of describing a fluid motion.
12. Show that the fluid motion specified by q  3 y 4 z 2 i  4 x 3 z 2 j  3x 2 y 2 k is a possible motion for an
incompressible fluid.
x
y
z
,v 
,w
13. Define pathlines and determine the equation of pathlines if u 
.
1 t
1 t
1 t
14. Draw and explain the working of a Pitot tube
15. Draw and explain the working of a Venturi tube.
16. Obtain the complex potential due to the image of a doublet with respect to a plane.
17. Let q  xyzi  3x 2 y j  ( xz 2  y 2 z)k be the velocity vector of a fluid motion. Find the voriticity
components.
18. Discuss the structure of an aerofoil.
PART - C
Answer any TWO questions:
(2  20 = 40 marks)
19. a) Derive the equation of continuity.
A( x j  yi)
(A being a constant), find whether q satisfies the
x2  y2
equation of continuity. Find the equation of streamlines.
(10 + 10)
b) For the motion specified by q 
1
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.
b) Test whether the motion specified by q  [ Ay, Ax,0] is an irrotational flow and if so determine
the velocity potential.
(12 + 8)
22. a) State and prove the theorem of Kutta-Joukowski.
b) Derive Joukowski transformation.
(10 + 10)
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