Pressure boundary condition
 

For a problem like laminar flow in a lid driven cavity, we specify the pressure boundary condition as dp/dn = 0. How do we arrive at this boundary condition?

I guess it's like one of Prandlt's boundary layer deductions, stattic pressure doesn't change with height (the normal), that's what the zero derivative means, no change. However, I don't recall well the cavity case.

the pressure gradient across the boundary layer is zero.
it means the pressure inside the boundary layer is equal to that outside the boundary layer.
therefore when you are to solve viscous flow passing a wall, pressure condition will be in fact the zero gradient pressure normal to wall.

regards

HI

Since the boundary layer thickness is small, it is assumed that within the boundary layer free stream pressure is impressed upon. Hence dp/dn normal to the wall is considered negligible and can be ignored.

Thanks
CCTech Pune