In a two-dimensional steady flow field, in a certain region of the x-y plane, the velocity component in the x-direction is given by v_{x} = x^{2} and the density varies as $\rho =\frac{1}{x}$ . Which of the following is a valid expression for the velocity component in the y-direction, v_{y} ?

A nozzle is so shaped that the average flow velocity changes linearly from 1.5 m/s at the beginning to 15 m/s at its end in a distance of 0.375 m. The magnitude of the convective acceleration (in m/s^{2}) at the end of the nozzle is _________

The velocity components of a two dimensional plane motion of a fluid are : $u=\frac{{y}^{3}}{3}+2x-{x}^{2}y\mathrm{and}v=x{y}^{2}-2y-\frac{{x}^{3}}{3}$

The correct statement is:

(A)
Fluid is incompressible and flow is irrotational

(B)
Fluid is incompressible and flow is rotational

For a two dimensional flow field, the stream function $\Psi $ is given as $\Psi =\frac{3}{2}({y}^{2}-{x}^{2})$.The magnitude of discharge occurring between the stream lines passing through points (0,3) and (3,4) is: