That's because the volume of liquid is conserved - there is nowhere else for it to go except through every sequential part of the pipe, so no matter where you measure the flow, you get the same answer. If the pipe above is a water pipeline into your house, and there is no water being used in the house, the flow F will be zero. Both pressure meters will read 50 psi. You will find that P 2 will measure 30 psi while P 1 remains at 50 psi. If we want to quantify the behavior of the porous plug in a hydraulic context, we don't care about the pressure on either side, but only on the difference of pressures across the plug.
Hydraulic pressure is an across-variable .
The pressure meter is content to observe through tiny ports. You could even install a small valve at each of the ports, so that the the pressure meter could be removed without leaving holes. But the flowmeter has to be big enough to allow the whole flow in the pipe to pass through it, and even so we may worry if its internal workings in some way impede the flow. That's the trouble with measuring through-variables. Now that we've established that the behavior of the porous plug depends only on the pressure difference across it, and not the absolute pressure at either end, we can do a series of experiments on it.