If I have understood the problem, by setting (du/dx=dp/dx=0), you are probably talking about a steady flow. In such case, then using the N-S equations and assuming a very long duct the velocity would be only in the x-direction, then the velocity would only depend on pressure gradient and the external forcing. Assuming the external forcing is in the x-direction, and by setting the pressure gradient equal to zero, then there will be a constant velocity varying with y and z only, which may be computed and therefore the velocity value is known at the inlet for a certain forcing leading to a Dirichlet boundary, whereas the du/dx originally is a Neumann boundary when the velocity cannot be computed explicitly. To summarise in such case the velocity may be computed at the inlet.

In most cases, pressure "gradient" is the major driving force for fluid flow motion. With no other driving force, I can't see how the fluid flows.

is it a free surface flow?

I mean duct flow

Hi Davood jan! No, it is a duct flow with bottom, top, front, and back wall boundaries.

Hi Shiuh-Hwa! the driving force is an external source acting on suspended particles.

Dr. Haghighi, could you be more specific as to what kind of driving force or external source?

you could, e.g., think of an external magnetic field exerting a force on suspended particles. please note that the question is whether a zero gradient BC for both velocity and pressure (du/dx=dp/dx=0) is mathematically sound?

To me, it is mathematically correct. Be sure to specify a reference pressure at one point. However, how do you physically apply a zero pressure gradient at both inlet and exit? I feel it is more easily to apply an equal pressure at both inlet and exit. 

I think periodic boundary conditions might be more suiltable because zero pressure gradient is not physical even for developed flow profile.

I think if your inlet and outlet is closed definitely you can use the zero gradient BC. But you should consider your flowfield whether you got reflected wave in outlet or not, in this case you might probably go for non reflective BC.

If you use a duct, you can't use it in the inlet /outlet together so that you can use it in the outlet only and in the inlet you can use (opening) as BC. You can found this BC if you use ANSYS CFX and can't found it in ANSYS FKUENT.

Ghassan

You finally must satisfy the continuity equation as a condition for convergence, so at inlet use either pressure or velocity inlet conditions.

To solve analytically the problem of the flow through a pipe (that yields a Poiseuille solution), I think you need to have boundary conditions at the inlet and the outlet (either over p or U).

Plus, it is sometimes unclear what the solver actually does with such "zero Gradient" boundary conditions...

Frédéric.

If I have understood the problem, by setting (du/dx=dp/dx=0), you are probably talking about a steady flow. In such case, then using the N-S equations and assuming a very long duct the velocity would be only in the x-direction, then the velocity would only depend on pressure gradient and the external forcing. Assuming the external forcing is in the x-direction, and by setting the pressure gradient equal to zero, then there will be a constant velocity varying with y and z only, which may be computed and therefore the velocity value is known at the inlet for a certain forcing leading to a Dirichlet boundary, whereas the du/dx originally is a Neumann boundary when the velocity cannot be computed explicitly. To summarise in such case the velocity may be computed at the inlet.

Dear Dr. Hejazi, many thanks for your thorough response which makes sense to me. Best, Erfan

Taking both velocity an pressure gradient as a Neumann boundary condition will leads to ill-posed mathematical solution which has either no solution or infunitedly many solutions