For a continuity equation given $$\nabla .\overrightarrow V = 0$$ to be valid, $$\overrightarrow V $$ where is the velocity vector, which one of the folllowing is a necessary condition ?

In a steady flow through a nozzle, the flow velocity on the nozzle axis is given by $$u = {u_0}\left( {1 + 3x/L} \right),\,\,$$ where $$x$$ is the distance along the axis of the nozzle from its inlet plane and $$L$$ is the length of the nozzle. The time required for a fluid particle on the axis to travel from the inlet to the exit plane of the nozzle is .

A two-dimensional flow field has velocities along the $$x$$ and $$y$$ directions given by $$u = {x^2}t$$ and $$v = - 2xyt$$ respectively, where $$t$$ is time. The equation of streamline is

In a two-dimensional velocity field with velocities $$u$$ and $$v$$ along $$x$$ and $$y$$ directions respectively, the convective acceleration along the $$x$$-direction is given by