LOYOLA COLLEGE (AUTONOMOUS), CHENNAI – 600 034
M.Sc. DEGREE EXAMINATION – MATHEMATICS
THIRD SEMESTER – NOV 2006
AA 29
MT 3953 - FLUID DYNAMICS
Date & Time : 01-11-2006/9.00-12.00
Dept. No.
Max. : 100 Marks
Answer ALL Questions.
I a) (i) Derive the equation of continuity in the form
d
 .q  0
dt
[OR]
(ii)State and prove Euler’s equation of motion.
(8)
 3xy 3 yz 3z 2 
b) (i) The velocity of an incompressible fluid is given by  5 , 5 , 5  .
r
r 
 r
Prove that the liquid motion possible and that the velocity potential is
cos 
.
r2
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
  x  2 x 2  2 y 2 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
  log
x2
y2

 1 .Then
a 2   b2  
by

show
that

a 2    b 2    B 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.
b) (i) Prove that
(8)
d
    q   2  .
dt


[OR}
(ii) Derive the Navier-Stokes equation of motion for viscous fluid.
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(17)