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

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

The velocity components in the $$x$$ and $$y$$ directions of a two dimensional potential flow are $$u$$ and $$v$$, respectively. Then $${{\partial u} \over {\partial y}}$$ is equal to

A fluid flow is represented by the velocity field $$\overrightarrow V = ax\,\overrightarrow i + ay\,\overrightarrow j ,$$ where a constant . The equation of stream line passing through a point $$(1, 2)$$ is