Using navier-stokes equation and the above result show that

Question

Vorticity Equation

For an incompressible fluid with const viscosity, show that

∇.[( ∇^→. ∇)V^→] = 1/2 ∇²(V^→.V^→) - V^→.(∇²V^→) - ω^→.ω^→

Using Navier-Stokes equation and the above result, show that the pressure distribution can be related to the velocity and vorticity by

∇²(P/δ) ω^→.ω^→ + V^→.(∇²V^→) - 1/2∇²(v^→.v^→)