??? Your question needs to be "clarified"
First, we assume you have some pipe or leak-proof vent duct with an in-line (axial) fan inside.
If there is no flow in the pipe, before the fan turns on, pressure upstream = pressure downstream = P0
If there is flow in the pipe, before the fan turns on, pressure upstream > pressure downstream due to flow losses through the fan blades. But this is meaningless, nobody can use a fan as a vent damper!
After the fan turns on, pressure upstream << pressure downstream calculated from the fan manufacturer tables of design efficiency at that pressure, temperature, gas type, and fan diameter. Pressure upstream will slightly less than the original static P0, but vent fans at normal flows and temperatures don't have a NPSH problem like fluid pumps do. Turbines can because they running near their max , vent fans "can" but only if they woefully sized wrong or the suction damper is shut.