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Show pressure distribution related to velocity and vorticity

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Reference no: EM13939038

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→)

Reference no: EM13939038

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