LOYOLA COLLEGE (AUTONOMOUS), CHENNAI – 600 034 M.Sc. DEGREE EXAMINATION – MATHEMATICS

THIRD SEMESTER – NOV 2006
MT 3953 – FLUID DYNAMICS
Date & Time : 01112006/9.0012.00 Dept. No. Max. : 100 Marks
Answer ALL Questions.
I a) (i) Derive the equation of continuity in the form
[OR]
(ii)State and prove Euler’s equation of motion. (8)
 b) (i) The velocity of an incompressible fluid is given by .
Prove that the liquid motion possible and that the velocity potential is .
Also find the stream lines.
[OR]
(ii)State and prove Holemn Hortz vorticity theorem (17)
II a) (i)Show that the two dimensional flow described by the equation
is irrotational. Find the stream lines and equaipotentials.
[OR]
(ii)State and prove Milne Thomson circle theorem. (8)
 b) (i) In a two dimensional fluid motion the stream lines are
given by .Then show that where A and B are constants. Also find the velocity.
[OR]
(ii) State and prove Blasius theorem. (17)
P.T.O.
III a)(i)Write a note on Joukowskis transformation.
[OR]
(ii) State and prove Kutta and Joukowskis theorem. (8)
b)(i) Discuss the geometrical construction of an aerofoil.
[OR]
(ii) Discuss the liquid motion past a sphere. (17)
IV a) (i) Find the exact solution of a liquid past a pipe of elliptical cross section.
[OR]
(ii) Discuss the flow between two parallel plates. (8)
 b) (i) Prove that .
[OR} (ii) Derive the NavierStokes equation of motion for viscous fluid. (17)