Well it's pretty easily understandable given that the whole stress-energy tensor goes into determining the gravitational field: pressure is just the diagonal components of the stress-energy tensor. I was actually puzzling over how this worked some time ago. The result is just that matter going either way through a surface make theAssuming I recall correctly, if for example you were to calculate the gravitational field inside a ball of gas, even the pressure of the gas has an effect on the resulting spacetime curvature and gravity. Not very intuitive at all, most definitely a case of "shut up and calculate" before trying to draw or guesstimate any conclusions.

*same*contribution to the momentum flux through that surface (the momentum flux has a velocity dependence that goes as $$\sim v^{2}$$), so the momentum flux can be non-zero even if the net flow of matter is zero.