FLUID MECHANICS (ME-404) - Important Questions

Explain the stability of a floating body in terms of centre of gravity, centre of buoyancy and metacentre, and explain why the relative position of CG vs CB alone is insufficient to decide stability.

A vertical rectangular plate 3 m x 2 m is immersed in water with its top edge 1 m below the free surface. Determine the total hydrostatic pressure force and the location of centre of pressure on the plate.

Determine the average bulk modulus of elasticity of a liquid if the pressure is increased from 70 N/cm2 to 130 N/cm2 and the volume decreases by 0.15%.

State Newton's law of viscosity and explain viscosity, dynamic and kinematic viscosity with units. Distinguish between Newtonian and non-Newtonian fluid behaviour.

Describe the different types of fluid flow and distinguish between steady vs unsteady, uniform vs non-uniform, compressible vs incompressible, rotational vs irrotational, and laminar vs turbulent flow.

A stream function in two-dimensional incompressible flow is given by psi = 2xy. Determine the corresponding velocity potential Phi and the velocity components.

A 30 cm diameter pipe conveying water branches into two pipes of diameters 20 cm and 15 cm. The average velocity in the 30 cm pipe is 2.5 m/s. Apply the continuity equation to find the discharge and velocities in the branched sections.

Define and explain path line, streamline, streak line and stream tube. State the differences between them with examples.

State and prove Bernoulli's theorem for flow along a streamline. List all assumptions made and explain how it is modified for real viscous flows.

A horizontal venturimeter with inlet diameter 200 mm and throat diameter 100 mm is used to measure flow of oil of specific gravity 0.8. The differential mercury manometer shows a deflection. Determine the discharge using continuity and Bernoulli's equation with Cd.

A hemispherical parachute is designed to decelerate a payload of mass 120 kg falling vertically at terminal velocity 8 m/s in air of density 1.2 kg/m3. Determine the required diameter of the parachute from vertical equilibrium W = CD*(1/2)rhoA*V^2.

Laminar flow is taking place in a pipe of diameter 200 mm with maximum velocity 1.5 m/s. Find the mean velocity, the radius at which mean velocity occurs, and the velocity at 4 cm from the wall of the pipe.

Three pipes of lengths 800 m, 500 m and 400 m and diameters 400 mm, 300 mm and 200 mm respectively are connected in series. For a given difference in reservoir levels and friction factor, determine the discharge through the compound system and the equivalent diameter of a single pipe replacing it.

What is boundary layer separation? Explain the physical mechanism of separation on a curved surface and the effect of favourable and adverse pressure gradient on it.

For the boundary-layer velocity profile u/U = 2(y/delta) - (y/delta)^2, compute the displacement thickness, momentum thickness and energy thickness in terms of delta.

Define stagnation temperature, stagnation pressure and stagnation density. Derive the expression T0/T = 1 + [(gamma-1)/2]M^2 for isentropic compressible flow and write a short note on stagnation properties.