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Sunday, December 30, 2018

Dibrugarh University Arts Question Papers:MATHEMATICS (Major) (Fluid Mechanics)' November-2015

Course: 503
(Fluid Mechanics)
Full Marks: 80
Pass Marks: 32
Time: 3 hours
The figures in the margin indicate full marks for the questions
(A) Hydrodynamics
(Marks: 35)

1. (a) Write the equation of path line. 1
(b) In a motion velocity potential is single valued, then write the nature of the motion. 1
(c) If vorticity vector of every fluid particle is zero, then write the nature of the motion. 1
(d) Define vorticity vector. 2
(e) Write the differences between streamlines and path lines. 3
(f) Derive the equation of continuity of fluid flow by Euler’s method. 7
Find the equation of streamlines for the flow at the point. 7
2. (a) State True or False: 1
Impulsive pressure at any point in a fluid is the same in every direction.
(b) State Kelvin’s circulation theorem. 1
(c) Derive Bernoulli’s equation of motion of fluid. 7
Derive Euler’s equation of motion. 7
(d) A velocity field is given by
Find the stream function at . 3
3. (a) Using Green’s theorem, find the expression for kinetic energy T of a liquid. 4
(b) A velocity field is given by
Determine whether the flow is irrotational or not. 4
Show that in irrotational motion the velocity cannot be a maximum in the interior of the fluid. 4

(B) Hydrostatics
(Marks: 45)
4. (a) Define density of a homogeneous substance. 1
(b) Write the entity to which the pressure at any point in a homogeneous liquid is proportional below the effective surface. 1
(c) Find the specific gravity of a mixture of number of substances whose volumes and specific gravities are given.    5
(d) Prove that at rest under gravity, the pressure is same at all points in the same horizontal plane.
(e) Show that at rest under gravity horizontal planes are surfaces of equal density. 5
The pressures at two points and in a homogeneous liquid are and. Prove that the pressure at the point which divides in the ratio is
5. (a) Define whole pressure. 2
(b) Describe force of buoyancy. 2
(c) Find the centre of pressure of a triangle immersed in a liquid with vertex in the surface and base horizontal.        6
(d) Show that the thrust of a heavy homogeneous liquid on a plane area is the product of the area and the pressure of its centre of gravity, when atmospheric pressure is neglected. 6
A cone full of water is placed on its side on a horizontal table. Show that the thrust on the base is , where is the weight of the contained fluid and is the vertical angle of the cone.                                                                                                                                                      6
6. (a) Write the conditions of equilibrium for a body floating freely in a homogeneous liquid. 3
(b) Write the forces acting on a body immersed in a liquid and supported by a string. 3
(c) Describe stable, unstable and neutral equilibria of a body immersed in liquid. 6
A thin metallic circular cylinder contains water to a depth and floats in water with its axis vertical, immersed to a depth. Show that the vertical position is stable if the height of the centre of gravity of the cylinder above its base is less than. 6


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