LOYOLA COLLEGE (AUTONOMOUS), CHENNAI – 600 034
B.Sc. DEGREE EXAMINATION – MATHEMATICS
FIFTH SEMESTER – November 2008
MT 5405 – FLUID DYNAMICS
Date : 12-11-08 Dept. No. Max. : 100 Marks
Time : 9:00 – 12:00
Answer ALL questions: (10 ´ 2 = 20)
- Define a steady flow.
- Define pathlines.
- What is the condition if the rigid surface in contact with the fluid motion is at rest?
- Determine pressure, if the velocity field qr = 0, , qz = 0 satisfies the equation of motion where A, B are constants.
- Find the stream function y, if j = A(x2 – y2) represents a possible fluid motion.
- What is the complex potential of sinks a1, a2 …… an with strength m1, m2 …… mn situated at the points z1, z2 …… zn respectively?
- Define a two-dimensional doublet.
- Define vortex tube.
- Find the vorticity components of a fluid motion, if the velocity components are
u = Ay2 + By + C, v = 0, w = 0.
- Define the term camber.
Answer any FIVE questions: (5 ´ 8 = 40)
- The velocity in a 3-dimensional flow field for an incompressible fluid is . Determine the equation of streamlines passing through the point (1, 1, 1).
- Derive the equation of continuity.
- Draw and explain the working of a Venturi tube.
- 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 a plane.
- Show that the velocity vector is everywhere tangent to the lines in the XY-plane along which y(x, y) = a constant.
- Let , (A, B, C are constants) be the velocity vector of a fluid motion. Find the equation of vortex lines.
- Discuss the structure of an aerofoil.
Answer any TWO questions: (2 ´ 20 = 40)
- a) For a two-dimensional flow the velocities at a point in a fluid may be expressed in the Eulerian coordinates by u = x + y + 2t and v = 2y + t. Determine the Lagrange coordinates as functions of the initial positions , and the time t.
- 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)
- Derive the Euler’s equation of motion and deduce the Bernoulli’s equation of motion.
- a) Obtain the complex potential due to the image of a source with respect to a circle.
- b) The particle velocity for a fluid motion referred to rectangular axes is given by the components, where A is a constant. Find the pressure associated with this velocity field. (12 + 8)
- a) Show the motion specified by , (k being a constant) is an irrotational flow.
- b) State and prove the theorem of Kutta-Joukowski. (5 + 15)
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