Fluid Mechanics...

A two- dimensional flow field is defined as \(\vec V = \vec ix - \vec jy\) the equation of the streamline passing through the point (1, 2) is 

Find the value of ‘a’ for fluid flow given by V = (axy² + 2y)î + (3xy + x²y)ĵ.

Find the flow rate across two points P (4, 2) an Q (1, 1), given that stream function Ψ = 3x(y² + 1) + 2x³ _______

The circulation ‘Γ’ around a circle of radius 2 units for the velocity field u = 2x + 3y and v = - 2y is

In a two-dimensional incompressible steady flow, the velocity component u = Ae^x is obtained. What is the other component ‘v’ of velocity?

A leaf is caught in a whirlpool. At a given instant, the leaf is at a distance of 120 m from the centre of the whirlpool. The whirlpool can be described by the following velocity distribution:

\({V_r} = - \left( {\frac{{60 \times {{10}^3}}}{{2\pi r}}} \right)\frac{m}{s}\;and\;{V_\theta } = \frac{{300 \times {{10}^3}}}{{2\pi r}}m/s\;\)where r (in meters) is the distance from the centre of the whirlpool. What will be the distance of the leaf from the centre when it has moved through half a revolution?

Water is directed vertically upwards from a nozzle of 20 m diameter with a velocity of 10 m/s. What will be the diameter of water jet at a point 3 m above the nozzle? Assume the jet remains circular and neglected only loss of energy.

Find convective acceleration at point P(2, 1) for the given stream function