LOYOLA COLLEGE (AUTONOMOUS), CHENNAI – 600 034
B.Sc. DEGREE EXAMINATION – MATHEMATICS
FIFTH SEMESTER – APRIL 2012
MT 5405 – FLUID DYNAMICS
Date : 27-04-2012 Dept. No. Max. : 100 Marks
Time : 1:00 – 4:00
Answer ALL questions: 10 ´ 2 = 20
- Define Stream tube.
- Show that the velocity field the stream lines are circular.
- Write down the boundary condition for the flow when it is in moving.
- Prove that the fluid motion is possible if .
- What is the complex potential of source with strength m situated at the origin?
- Find the stream function y, if j = A(x2 – y2) represents a possible fluid motion
- Define velocity potential.
- Define vortex lines.
- Find the vorticity components of a fluid motion, if the velocity components are
u = c(x + y), v = – c(x + y).
- Define camber.
Answer any FIVE questions: 5 ´ 8 = 40
- Find the equation of streamlines and path lines of a flow given by .
- Explain pitot tube.
- Derive the equation of continuity.
- Derive the Bernoulli’s equation of motion for the fluid.
- Prove that for the complex potential the streamlines and equipotentials are circles.
- Obtain the complex potential due to the image of a doublet with respect to the circle.
- Let , (A, B, C are constants) be the velocity vector of a fluid motion. Find the equation of vortex lines.
- State and prove the theorem of Kutta-Joukowski.
Answer any TWO questions: 2 ´ 20 = 40
- (a)The velocity components for a two dimensional fluid system can be given in the Eulerian system by . Find the displacement of a fluid particle in the Lagrangian system
(b)If the velocity of an incompressible fluid at the point (x, y, z) is given by where . Prove that the fluid motion is possible and the velocity potential is . (10 + 10)
- (a)Derive the Euler’s equation of motion.
(b)Draw and explain the working of a Venturi tube. (12 + 8)
21.(a)What arrangement of sources and sinks will give rise to the function?
(b)Obtain the complex potential due to the image of a source with respect to a circle. (12 + 8)
- (a)Discuss the structure of an aerofoil.
(b) Derive Joukowski transformation. ( 8+12)