Laplace's irrotational motion

Laplace's irrotational motion

Laplace's equation for irrotational motion of an inviscid, incompressible fluid is partial differential equation (1), where x₁, x₂, x₃ are rectangular cartesian 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 = ∂&phgr;/∂x_i, i = 1, 2, 3. More generally, in any inertial coordinate system, the equation is div (grad &phgr;) = 0 and the velocity vector is v = grad &phgr;. Irrotational motion implies that the fluid particles translate without rotation (like the cars on a ferris wheel). See Fluid flow