SSC JE Civil Engineering 29-Oct-2020 Shift 1 Paper

Given:
$\overrightarrow{\mathit{U}}=\left(\mathit{g}{\mathit{x}}^3\right)\mathit{i}+\left(6{\mathit{x}}^2\mathit{y}\right)\mathit{j}$
Since given has component in x and y direction and no component in ‘z’ direction, so it is a 2D velocity field.
Further $\overrightarrow{\mathit{u}}=2{\mathit{x}}^3$ & $\mathit{U}=\left(6{\mathit{x}}^2\mathit{y}\right)$
$\frac{\partial \mathit{u}}{\partial \mathit{x}}=6{\mathit{x}}^2;\frac{\partial \mathit{u}}{\partial \mathit{y}}=6{\mathit{x}}^2$
Since, $\frac{\partial \mathit{u}}{\partial \mathit{x}}+\frac{\partial \mathit{v}}{\partial \mathit{y}}=6{\mathit{x}}^2+6{\mathit{x}}^2\ne 0$ ⇒ not a flow.
Since, the given velocity vector did not satisfied the continuity equation, so it did not represent the flow or flow is not possible.
Also, is there is no flow, hence is no sense of saying whether the flow is rotational or irrotational flow.