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October 13, 2007, 01:18 
How to get Pressure field from velocity field

#1 
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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 

October 13, 2007, 09:04 
Re: How to get Pressure field from velocity field

#2 
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Given a divergencefree flow field, the "pressure Poisson" equation can be used to calculate the pressure from the velocity.


October 13, 2007, 21:23 
Re: How to get Pressure field from velocity field

#3 
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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 

October 14, 2007, 02:03 
Re: How to get Pressure field from velocity field

#4 
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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 NavierStokes equation and use "continuity" for incompressible flow to get the source term for the Poisson equation
adrin 

October 14, 2007, 07:38 
Re: How to get Pressure field from velocity field

#5 
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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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