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 qunwuhe@hotmail.com October 13, 2007 01:18

How to get Pressure field from velocity field

Once I got a flow field which is divergence free, how can I calculate the coresponding pressure field then I can get the pressure drop.

Thx

 Jonas Holdeman October 13, 2007 09:04

Re: How to get Pressure field from velocity field

Given a divergence-free flow field, the "pressure Poisson" equation can be used to calculate the pressure from the velocity.

 gocarts October 13, 2007 21:23

Re: How to get Pressure field from velocity field

Could apply Bernoulli's Theorem whereby:

Cp = (P - Pref) / (rho.Vref^2 / 2)

Cp = 1 - q^2 / Vref^2

where Cp = Pressure Coefficient, P = Static Pressure at x, Pref = Reference Static Pressure, rho = density, Vref = Reference Velocity Magnitude, q = Velocity Magnitude at x

 Adrin Gharakhani October 14, 2007 02:03

Re: How to get Pressure field from velocity field-

This implies you know Cp. It also applies to particular physics (check basic fluid dynamics books). The pressure Poisson equation suggested By Jonas is the answer. Apply the divergence operator to the Navier-Stokes equation and use "continuity" for incompressible flow to get the source term for the Poisson equation

 gocarts October 14, 2007 07:38

Re: How to get Pressure field from velocity field-

Of course you are both right on the Poisson equation being the most general solution for an incompressible flow.

However, for an invisid flow Bernoulli's is valid without knowing Cp - rearranging the original formula to eliminate Cp - gives static pressure directly as:

P = Pref + (rho / 2).(Vref^2 - q^2)

Given the original poster only specified they had a divergence free velocity field I presumed they may have obtained it from an inviscid methodology such as a panel method.

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