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

__Section A__

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*(*x*^{2}–*y*^{2}) 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.

__Section B__

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.

__Section C__

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)