Calculate flow rate through a porous cylinder

Hi all,
I would like to evaluate the Flow rate through a porous cylinder placed perpendicular to the flow as in the figure. Since the fluid can also enter from the faces of the cylinder I want to consider all the surfaces in this calculation (because the fluid can enter also from below or from the back).
I have to tried to use the integrate variables filter on the velocity magnitude but I don’t think it is correct since it does not take into account the normal component of the velocity. Do you have any exact way to compute it?
Thank you very much!

Here is the surface i have created to enclose the cylinder.