Assume ideal fluid and irrotational flow.

We assume the fluid ideal and the flow irrotational. Under such assumptions, the velocity field $\vec{v}$ satisfies the equation

$$\nabla\times\vec{v} = 0, \notag$$

which implies that the velocity field $\vec{v}$ can be written as the gradient of a function $\phi(x,y,z)$, denoted as the potential function.

$$\vec{v} = \nabla\phi \notag$$