Given that
U = velocity in the x-direction
V = velocity in the y-direction
A two-dimensional flow in x-y plane is irrotational if1
\(\frac{{\partial u}}{{\partial x}} = \frac{{\partial v}}{{\partial y}}\)
2
\(\frac{{\partial u}}{{\partial x}} = \frac{{\partial u}}{{\partial y}}\)
3
\(\frac{{\partial v}}{{\partial x}} = \frac{{\partial u}}{{\partial y}}\)
4
\(\frac{{\partial v}}{{\partial x}} = \frac{{\partial v}}{{\partial y}}\)