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

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

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

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

adrin

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.