Dear Hamid,

I suggest you this link in French that you can translate. It answers your question directly.

Here is the abstract

A computational method for the pressure field of the two-dimensional unsteady flow of an inviscid and incompressible fluid is presented. The pressure is computed with a two steps procedure. In the first step, the part of the pressure field due to the velocity field alone is computed by solving a Poisson equation without accounting for the boundaries. This step is performed by means of a finite-volume scheme on a regular cartesian mesh. In the second step, an harmonic correction is applied in order to satisfy the boundary conditions, resulting in a second kind Fredholm integral equation. The properties of the method are illustrated through two examples, one starting from a computed velocity field and the other from a measured velocity field

 http://website.ec-nantes.fr/actesjh/images/12JH/Annexe/machrouki_jh12.pdf

With my best regards

Prof. Bachir ACHOUR

thanks Prof. Achour, but it is in french and I could not understand it. However, thanks for your note 

Dear Mr. Hamid,

I think you have to use the Navier-Stokes equations to compute the pressure field, but the way you do depends on the problem itself.

For example, if the pressure is known in the boundaries of the computational domain such as in FORCED FLOW IN PIPES in which the pressure is normally known at the pipes' inlet, you can use the x-component Navier-Stokes equation to compute directly p(x+dx,y) from p(x,y).

But if the pressure is unknown in the boundaries such as in FREE CONVECTION IN AN ENCLOSED CAVITY, I believe that you should use the discretized Navier-Stokes and continuity equations to derive a pressure equation in a similar way of how we get the pressure-correction equation of the SIMPLE algorithm but without omitting any term this time; then, you can solve the pressure equation via an iterative algorithm. Note that in this latter case you can obtain only the pressure gradient.

Dear Hamid, if you know velocity field, from Navier-Stokes equations you have the gradient of pressure; you can numerically integrated the gradient using a grid on domain (if possible, use a finite difference scheme) and a boundary condition on pressure for starting the numerical computation. A Poisson equation for pressure should not be necessary.  Gianluca

You can apply Bernoulli's Theorem where,

Cp = Pressure Coefficient

P = Static Pressure at x

Pref = Reference Static Pressure

rho = density

Vref = Reference Velocity Magnitude

q = Velocity Magnitude at x

As the equations will be as following :

Cp = (P - Pref) / (rho.Vref ^ 2 / 2) Cp = 1 - q ^ 2 / Vref ^ 2

Ahmed A. Mawgoud Hi, BernouBernoullili Eq cannot be applied to the turbulent flow filed. Thanks