Laplace's irrotational motion

(fluid mechanics) Irrotational flow of an inviscid, incompressible fluid.

Laplace's equation for irrotational motion of an inviscid, incompressible fluid is partial differential equation (1), where x₁, x₂, x₃ are rectangular caresian coordinates in an inertial reference frame, and Eq. (2)
1.

2.
gives the velocity potential. The fluid velocity components, u₁, u₂, u₃ in the three respective rectangular coordinate directions are given by u_i = ∂φ/∂x_i, i = 1, 2, 3. More generally, in any inertial coordinate system, the equation is div (grad φ) = 0 and the velocity vector is v = grad φ. Irrotational motion implies that the fluid particles translate without rotation (like the cars on a ferris wheel). See also Fluid flow.