List of top Fluid Mechanics and Mechanical Operations Questions on Equation of continuity asked in GATE CH

The velocity field in an incompressible flow is $ \mathbf{v} = axy\hat{i} + v_y\hat{j} + \beta\hat{k} $, where $ \hat{i} $, $ \hat{j} $, and $ \hat{k} $ are unit vectors in the $ (x, y, z) $ Cartesian coordinate system. Given that $ a $ and $ \beta $ are constants, and $ v_y = 0 $ at $ y = 0 $, the correct expression for $ v_y $ is:

A three-dimensional velocity field is given by $V = 5x^2y\,\mathbf{i} + Cy\,\mathbf{j} - 10xyz\,\mathbf{k}$, where $\mathbf{i},\mathbf{j},\mathbf{k}$ are unit vectors in $x,y,z$ directions. If $V$ describes an incompressible fluid flow, the value of $C$ is