## 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

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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## Loyola College B.Sc. Mathematics April 2007 Fluid Dynamics Question Paper PDF Download

LOYOLA COLLEGE (AUTONOMOUS), CHENNAI – 600 034

 CV 18

B.Sc.  DEGREE EXAMINATION –MATHEMATICS

FIFTH SEMESTER – APRIL 2007

MT 5401FLUID DYNAMICS

Date & Time: 03/05/2007 / 9:00 – 12:00        Dept. No.                                                     Max. : 100 Marks

SECTION A

Answer ALL Questions.                     (10 x 2 = 20)

1. Define Lagrangian method of fluid motion.
2. State the components of acceleration in Cartesian coordinates?
3. What is the equation of continuity for (i) a homogeneous steady flow of fluid, (ii) a non-homogeneous incompressible flow of fluid.
4. Show that u = a+ by – cz, v = d – bx + ez, w = f + cx – ey are the velocity components of a possible liquid motion.
5. Write down the boundary condition when a liquid is in contact with a rigid surface.
6. Write down the stream function in terms of fluid velocity.
7. If = A(x2 – y2) represents a possible flow phenomena, determine the stream function.
8. State the Bernoulli’s equation for a steady irrotational flow?
9. What is the complex potential of sources at a1, a2, ….,an with strengths m1, m2,…,mn respectively?
10. Describe the shape of an aerofoil.

SECTION B

Answer ANY FIVE Questions.         (5 x 8 = 40)

1. (a) Define a streamline. Derive the differential equation of streamline.

(b) Determine the equation of streamline for the flow given by .         (4 + 4)

1. Explain local, convective and material derivatives.
2. The velocity field at a point is . Obtain pathlines and streaklines.
3. Show that the velocity potential satisfies the Laplace equation. Also find the streamlines.
4. Derive Euler’s equation of motion for one-dimensional flow.
5. Explain how to measure the flow rate of a fluid using a Venture tube.
6. Derive the complex potential of a doublet.
7. Explain the image system of a source with regard to a plane.

SECTION C

Answer ANY TWO Questions.          (2 x 20 = 40)

1. The velocity components of a two-dimensional flow system can be given in Eulerian system by . Find the displacement of the fluid particle in the Lagrangian system.
2. (a) Show that is a possible form of a bounding surface of a liquid.

(8 + 12 marks)

1. (a) Derive Bernoulli’s equation.

(b) Explain the functions of a pitot tube with a neat diagram.                             (10 + 10 marks)

1. State and prove the theorem of Kutta and Joukowski.

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## Loyola College B.Sc. Mathematics April 2008 Fluid Dynamics Question Paper PDF Download

LOYOLA COLLEGE (AUTONOMOUS), CHENNAI – 600 034

B.Sc. DEGREE EXAMINATION – MATHEMATICS

# XZ 15

FIFTH SEMESTER – APRIL 2008

# MT 5401 – FLUID DYNAMICS

Date : 05/05/2008                Dept. No.                                        Max. : 100 Marks

Time : 9:00 – 12:00

PART – A

Answer all:                                                                                 10 x 2 = 20

2.Write the Euler’s equation of motion in terms of spherical polar co ordinates.

3.What are stagnation points?

4.What are the applications of Pitot tube?

5.Explain the term complex potential.

6 Define Source and Sink.

7.State a fundamental property of vortex.

8.Define a vorticity vector.

9.Prove that flow is irrotational for

10.What is  lift of an Aerofoil ?

PART – B

Answer any five:                                                                               5 x 8 = 40

1. The velocity in a three dimensional flow field for an incompressible fluid is

given  by . Determine the equation of streamlines passing

through the point (1,1,1).

1. Derive the relationship between Eulerian and Lagrangian points in space.
2. Show that the velocity potential satisfies the Laplace

equation. Also determine the stream lines.

1. Derive the Euler’s equation of motion.

1. Briefly explain Pitot tube.

1. Stream is rushing from a boiler through a conical pipe, the diameters of the ends of which are D and d. If V and v be the corresponding velocities of the stream and if the motion be supposed to be that of divergence from the vertex of the cone prove that      where k is the pressure divided by density.

(P.T.O)

1. Find the vorticity of the fluid motion in spherical polar coordinates

, and .

1. Define aerofoil and discuss about its structure.

# PART –C

Answer any two:                                                                               2 x 20 = 40

19a) A mass of fluid is in motion so that the lines of motion lie on the surface of

coaxial cylinders. Show that the equation of continuity is

.

1. b) For a 2-D flow the velocities at a point in a fluid may be expressed in the

Eulerian co ordinate by u= 2x+2y+3t    and v = x+ y+ , determine them in

Lagrangian.

20 a) If the velocity of an incompressible fluid at the point (x ,y, z) is given by

, prove that the liquid motion is possible and that the

velocity potential is . Also determine the stream lines.

1. Draw and explain Venturi tube.

21  a) What arrangements of source and sinks will give rise to the function

? Draw a rough sketch of the stream lines.

1. b) The particle velocity for a fluid motion referred to rectangular axes is given by the components , where A is a constant. Show that this is a possible motion of an incompressible fluid  under nobody force in an infinite fixed rigid tube. Also determine the pressure associated  with this velocity field where .

• a) Derive Joukowski transformation.
1. b) State and prove Kutta Jowkowski theorem.

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## Loyola College B.Sc. Mathematics Nov 2008 Fluid Dynamics Question Paper PDF Download

LOYOLA COLLEGE (AUTONOMOUS), CHENNAI – 600 034

# AB 14

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

SECTION A

Answer ALL questions:                                                                                 (10 ´ 2 = 20)

2. Define pathlines.
3. What is the condition if the rigid surface in contact with the fluid motion is at rest?
4. Determine pressure, if the velocity field qr = 0, , qz = 0 satisfies the equation of motion where A, B are constants.
5. Find the stream function y, if j = A(x2y2) represents a possible fluid motion.
6. What is the complex potential of sinks a1, a2 …… an with strength m1, m2 …… mn situated at the points z1, z2 …… zn respectively?
7. Define a two-dimensional doublet.
8. Define vortex tube.
9. Find the vorticity components of a fluid motion, if the velocity components are

u = Ay2 + By + C, v = 0, w = 0.

1. Define the term camber.

SECTION B

Answer any FIVE questions:                                                                         (5 ´ 8 = 40)

1. 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).
2. Derive the equation of continuity.
3. Draw and explain the working of a Venturi tube.
4. Prove that for the complex potential the streamlines and equipotentials are circles.
5. Obtain the complex potential due to the image of a doublet with respect to a plane.
6. Show that the velocity vector is everywhere tangent to the lines in the XY-plane along which y(x, y) = a constant.
7. Let , (A, B, C are constants) be the velocity vector of a fluid motion. Find the equation of vortex lines.
8. Discuss the structure of an aerofoil.

SECTION C

Answer any TWO questions:                                                                         (2 ´ 20 = 40)

1. 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.
2. 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)

1. Derive the Euler’s equation of motion and deduce the Bernoulli’s equation of motion.

1. a) Obtain the complex potential due to the image of a source with respect to a circle.
2. 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)

1. a) Show the motion specified by , (k being a constant) is an irrotational flow.
2. b) State and prove the theorem of Kutta-Joukowski.                             (5 + 15)

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## Loyola College B.Sc. Mathematics April 2012 Fluid Dynamics Question Paper PDF Download

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

1. Define Stream tube.
2. Show that the velocity field the stream lines are circular.
1. Write down the boundary condition for the flow when it is in moving.
2. Prove that the fluid motion is possible if .
3. What is the complex potential of source with strength m situated at the origin?
4. Find the stream function y, if j = A(x2y2) represents a possible fluid motion
5. Define velocity potential.
6. Define vortex lines.
7. Find the vorticity components of a fluid motion, if the velocity components are

u = c(x + y), v = – c(x + y).

1. Define camber.

Section B

Answer any FIVE questions:                                                                               5 ´ 8 = 40

1. Find the equation of streamlines and path lines of a flow given by .
2. Explain pitot tube.
3. Derive the equation of continuity.
4. Derive the Bernoulli’s equation of motion for the fluid.
1. Prove that for the complex potential the streamlines and equipotentials are circles.
2. Obtain the complex potential due to the image of a doublet with respect to the circle.
3. Let , (A, B, C are constants) be the velocity vector of a fluid motion. Find the equation of vortex lines.
4. State and prove the theorem of Kutta-Joukowski.

Section C

Answer any TWO questions:                                                                         2 ´ 20 = 40

1. (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)

1. (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)

1. (a)Discuss the structure of an aerofoil.

(b) Derive Joukowski transformation.                                                                         ( 8+12)

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## Loyola College B.Sc. Mathematics Nov 2012 Fluid Dynamics Question Paper PDF Download

LOYOLA COLLEGE (AUTONOMOUS), CHENNAI – 600 034

B.Sc. DEGREE EXAMINATION – MATHEMATICS

FIFTH SEMESTER – NOVEMBER 2012

# MT 5405 – FLUID DYNAMICS

Date : 10/11/2012             Dept. No.                                        Max. : 100 Marks

Time : 9:00 – 12:00

Section A

Answer ALL questions:                                                                                                                         10 ´ 2 = 20

1. Define stream tube.
2. Show that is a possible motion.
3. The velocity vector q is given by determine the equation of stream line.
4. Write down the boundary condition for the flow when it is moving.
5. What is the complex potential of a source with strength m situated at the points z=z1
6. Find the stream function y, if j = A(x2y2) represents a possible fluid motion
7. Find the vorticity vector for the velocity
8. Define vortex tube and vortex filament.
9. What is lift of an aerofoil?
10. Define camber.

Section B

Answer any FIVE questions:                                                                                        5 ´ 8 = 40

1. Explain Material, Local and Convective derivative fluid motion.
1. Find the equation of streamlines and path lines of a flow given by
1. Explain the construction of a Venturi tube.
2. Prove that for the complex potential the streamlines and equipotentials are circles.
3. For an incompressible fluid. Find the vorticity vector and equations of stream line.
4. Derive the equation of continuity.
5. Find the stream function y(x, y, t) for a given velocity field u = 2Axy, v = A(a2 + x2 y2).
6. State and prove the theorem of Kutta-Joukowski.

Section C

Answer any TWO questions:                                                                                                      2 ´ 20 = 40

1. (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 + t and v = 2x+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)

1. Derive the Euler’s equation of motion and deduce the Bernoulli’s equation of motion.

1. (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)

1. (a)Discuss the structure of an aerofoil.

(b)Derive Joukowski transformation.                                                                   (8+12 )

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