But you know pressure drop for a given mass flow. And you now the area of your porous baffle, and the density. So you can calculate a mean velocity. Better would be to have pressure drops for more than one mass flow because you have two unknowns

You have one equation with two unknowns. You need the force/pressure drop at two or more flow rates. Then you can curve fit the equation to the data.

I have one force value, but I don't have an associated flow rate for that force. How can I calculate the flow rate in the porous media?

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