ISRO Scientist or Engineer Mechanical 2014

The velocity potential function $$\varnothing$$ satisfy the Laplace equation :
$$\frac{\delta^2 \varnothing}{\delta x^2} + \frac{\delta^2 \varnothing}{\delta y^2} + \frac{\delta^2 \varnothing}{\delta z^2} = 0$$. Then the flow is

For a two dimensional potential flow, the velocity potential is given by:
$$\varnothing = 4x(3y - 4)$$ The numerical value of stream function at the point(2, 3) is

The velocity distribution in a turbulent boundary layeris given by $$\frac{u}{v} = \left(\frac{y}{\delta}\right)^{\frac{1}{7}}$$. What is the displacement thickness $$\delta^*$$

The specific weight W of ocean water changes according to the equation $$W = W_o + C \surd h. W_o = $$Specific weight of ocean water at free surface and C is a constant. The pressure as a function of depth h is given by

The model of a propeller, 3 m diameter, cruising at 10 m/sec in air, is tested in a wind tunnel on a 1:10 scale model. If thrust of 50 N is measured on the model at 5 m/sec wind speed, then thrust on prototype will be

As shown in Fig. below, an ideal gas is confined to a cylinder by a piston. The piston is pushed down slowly so that the gas temperature remains at $$27^\circ C$$. During the compression, 900 J of work is done on the gas. Find the entropy change of the gas.

Determine the number of degrees of freedom used in the analysis of the mechanical system of below mentioned Figure.

The difference in the Potential energies between two arbitrary positions downward displacements X1 and X2. (X2 > X1)

Water having kinematic viscosity of 0.01 stoke flows at a velocity of 2 m/sec in a pipe of 15 cm diameter. For dynamic similarity, the velocity of oil of kinematic viscosity of 0.03 stoke in a pipe of same diameter will be

An inclined plate 2 m long and 1 m widelies with its length inclined at $$45^\circ$$ to the surface of water and its nearest edge is 1 m below it. If specific weight of water is 1000kg/m$$^3$$, then total pressure force on the plate (in kg) is approximately