Loyola College M.Sc. Mathematics Nov 2006 Fluid Dynamics Question Paper PDF Download

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

AA 29

THIRD SEMESTER – NOV 2006

         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

[OR]

(ii)State and prove Euler’s equation of motion.                               (8)

 

  1. 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)

 

  1. 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)

 

  1. b) (i) Prove that .

[OR}                                                                                                                                                  (ii) Derive the Navier-Stokes equation of motion for viscous fluid.      (17)

 

 

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