Let be $"$u$"$ a scalar $($NOT A VECTOR$).$ The vector u will take the

name of "flow potential". Demonstrate that:

grad$(gradu)=0$

Hint: Note that:

$\frac{de{l}^{2}u}{\text{d}\text{e}\text{l}\text{x}\text{y}}=\frac{de{l}^{2}u}{\text{d}\text{e}\text{l}\text{y}\text{x}}=\frac{\text{d}\text{e}\text{l}\frac{\text{d}\text{e}\text{l}\text{u}}{\text{d}\text{e}\text{l}\text{y}}}{\text{d}\text{e}\text{l}\text{x}}$

The flow potential is commonly used in advanced fluid mechanics to

solve some complex problems $($e$.$g$.$ we use it in Coastal Engineering$).$

All potential functions are irrotational as you saw in this exercise.