In the incompressible model the system of PDE reduces to the momentum equation with the constraint div v = 0. This way, the only action of the pressure appears by means of the gradient in the momentum, no absolute value of the pressure is involved. On the other hand, what we denote as pressure in the momentum is not the thermodinamic pressure but only an auxiliary variable that makes the continuity fulfilled. Setting zero pressure at an outlet is just the way to fix the undetermined constant but it is not necessary at all to fix a Dirichlet condition for the pressure.

Thank you sir. when we simulating the in- compressible Naveir stokes equations for a bifurcating channel (with one perpendicular branch and other horizontal) with two outlets, do we need to fix some pressure at the horizontal branch outlet, to push fluid the perpendicular branch?.

From a general perspective, two outlets can produce different solutions depending on the flow rate subdivision. But the general issue for incompressible flows is that you can set either pressure or velocity BCs. The pressure condition in terms of a Dirichlet setting is mathematically correct as well as the Neumann condition. However, to assume a constant pressure at the outlet (no matter about its absolute value) you should also think to the physical problem: can you assume that the model realizes accurately this homogeneous pressure?

I think No, in bifurcating case to put pressure just at one outlet. I simulated the equations for such a channel and there was no fluid flow to the upper branch. I applied zero pressure at both outlets.

That is exactly a possibile solution for this problem. Who guarante that you have a certain amount of flow rate in the cross section? Have you some measured experiment?

Thank you so much sir. For the time being, i have no such materials. Anyway, this is my opinion for such simulation. i need some experimental work.