List of top Fluid Mechanics and Thermal Sciences Questions on Differential equations of continuity and momentum

A two dimensional flow has velocities in \( x \) and \( y \) directions given by \( u = 2xyt \) and \( v = -y^2 t \), where \( t \) denotes time. The equation for the streamline passing through \( x = 1, y = 1 \) is
For a two-dimensional, incompressible flow having velocity components \(u\) and \(v\) in the x and y directions, respectively, the expression \[ \frac{\partial(u^2)}{\partial x} + \frac{\partial(uv)}{\partial y} \] can be simplified to: