hydrostaticPressure in two phase flow

multiphase

Hello everyone!I am a freshman in £ãÆ£Ä and I am doing multiphase flow with water and air.Now I have a confusing problem about the pressure.

In v monmentum equation,if we only consider invisid flow,the equation will be

d(rou*u*v)/dx+d(rou*v*v+p)/dy=-rou*g

if we consider u v are both equal to zero,then the equation becomes

d(p)/dy=-rou*g

for my case,I give initial guess as hydrostatic pressure -rou*g*y

So after derivative,it becomes -rou*g-d(rou)/dy*y

Therefore anyway there is something left!

I am using roe scheme and coupled solver.What I should do to give right correction or some other suggestions?

Thanks for any suggestions!