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You can't set both a pressure and a velocity boundary conditions at the inlet but you can accomplish what you want simply by imposing the constant velocity BC at the inlet (e.g. u=velocity) and setting a pressure BC at the outlet. In incompressible flow the actual value of the pressure is irrelevant, only the pressure difference matters.
Ozgur

In my problem, what is known is the pressure difference, not the inlet velocity.

Let me summarize:

case 1)
Given the INLET UNIFORM velocity and the OUTLET PRESSURE in the channel, the solver find naturally a solution for which the solved pressure is CONSTANT at the Inlet.

Case 2) (reverse case)
Given a constant PRESSURE and a UNIFORM "UNKNOWN" velocity (to be solved) at the inlet, and given the outlet pression, find the volocity field.

Theses 2 case should has the same solution in my opinion. This is not the value of the velocity that I want to set, but I want to set that this velocity must be a constant., i.e., du/dy = 0. however, this condition is not implemented in comsol, the default condition on the x and y velocity is "no viscouss stress" which is not what is needed in my problem.

I hope this will clarify my question!

Thank you for your effort and keep me posted

Ok I think I understand what you are trying to do. You don't know the uniform velocity boundary condition that will give you the correct pressure drop in advance.

Here is the easiest way that comes to my mind to tackle the problem if I understand it right. There are more elaborate ways using constraints but what I will outline is easiest way below although this is a little iterative but should still get you the answer quickly.

1- Solve the flow problem using only the pressure boundary conditions (e.g. outlet pressure =0, inlet pressure= your known pressure difference) and get a solution for flow field. This flow field may not have the plug flow (uniform) velocity profile at the inlet you want yet.

2- Calculate bulk average flow velocity from the above solution. Let's call this number U_bulk.

3- Now set up the same problem again by changing the inlet boundary condition to have a uniform velocity of U_inlet (literally, type in U_inlet there) and outlet pressure as 0.

4- run a parametric study where you vary U_inlet in a small range about U_bulk and solve the problem. Note that the whole point of the first 2 steps above were to get you a good starting point for U_inlet. If you already have a good idea what it should be you can skip those steps and start from step 3.

5- plot your calculated inlet pressure as a function of U_inlet parameter and from the plot identify the U_inlet value that would result in the correct pressure drop you want.

6- If you want you can re-run the problem with that correct velocity that would also give you the right pressure drop and you are done.

does this make sense?

As I said alternatively you can do it all in one shot using global constraints and constraining the inlet velocity to automatically satisy the pressure drop requirement but if you are not already familiar with this approach there will be a little bit of a learning curve and the above outlined approach is much simpler and intuitive.

Good luck,
Ozgur