Fluid Mechanics-I

(i) Surface tension is a phenomenon due to:

1. Viscous forces
2. Cohesion between the liquid molecules
3. Adhesion between liquid and solid molecules
4. Adhesion and cohesion both

(ii) The centre of buoyancy is:

1. Centre of gravity of the body
2. Centre of the displaced fluid volume
3. Point of intersection of the buoyant force and the centre line of the body
4. Point of intersection of the buoyant force and the gravitational force

(iii) There is no geometrical distinction between the streamline, pathline and streakline in case of:

1. Steady flow
2. Uniform flow
3. Laminar flow
4. Irrotational flow

(iv) The Bernoulli's equation refers to the conservation of:

1. Mass
2. Momentum
3. Force
4. Energy

(a) Explain the phenomenon of capillarity. Write an expres-sion for capillary rise of a liquid.

(b) A plate, 0.025 mm distant from a fixed plate, moves at 60 cm/s and requires a force 2 N/m² to maintain this speed. Determine the viscosity of the fluid kept between the plates.

(a) How does viscosity of a fluid vary with temperature?

(b) The pressure re outside the droplet of water of diameter 0.04 mm i. 10.32 N/cm². Calculate the pressure within the droplet if surface tension is given as 0.0725 N/m of water.

(a) Define and explain the followings with examples:

1. Stream line
2. Path line

(b) The stream function for a two dimensional flow is given by Ψ=2xy. Determine the velocity at the point P(2,3). Find the velocity potential function.

(a) Define and explain the followings:

1. Velocity potential function
2. Stream tube

(b) The velocity vector in a fluid flow is given by V = 4 x³ i - 10 x² y j + 2 t k. Find the velocity and acceleration of a fluid particle at (2,1,3) at time t = 1 unit.

(a) State Bernoulli's theorem. Also state the assumptions made in the derivation of Bernoulli's theorem.

(b) The water is flaving through a pipe having diameters 20 cm and 10 cm at sections 1 and 2 respectively. The rate of flow through pipe is 35 litres/s. The section 1 is 6m above datum and section 2 is 4m above datum. If the pressures at section 1 is 39.24 N/cm², find the intensity of pressure at section 2.

(a) Discuss the conditions of equilibrium for a sub merged body.

(b) Determine the total pressure force on a circular plate of diameter 1.5 m. which is placed vertically in water in such a way that the centre of the plate is 3m below the free surface of water. Find the position of centre of pressure also.

(a) State and explain the Pascal's law.

(b) The right limb of a simple U-tube manometer containing mercury is open to the atmosphere, while the left limb is connected to a pipe in which a fluid of specific gravity 0.9 is flowing. The centre of the pipe is 12 cm below the level of mercury in the right limb. Find the pressure of fluid in the pipe if the difference fo mercury level in the two limbs is 20 cm.