OK, this is all over the place, pump that 'pushes' the flow through filters in Litres per minute?? therefore it is pumping dirty water before any filtration, correct?
is 3 x 20 inches the depth and circumference of each filter, which as they do their job and get dirty will require more pressure for the same flow
Then a secondary filtration through 4 filters no idea about .q meaning?, but what really has me puzzled is the pressure can be adjusted by a 'free flow waste' so does this restrict it and cause a back pressure?? presume 7 to 1 is in bar?
However it is very very simple, just like your wires in electricity, the maximum flow available will be at the most restrictive point, you can't push it any harder. So the circumference of the smallest pipe is all you'll get, look up the formula on Google. Once you know how much should be coming through 'free flow' then with the filters in you'll need a gauge to increase pump pressure to get the same reading.
i.e. fit a pressure gauge at the end of the filtration, take all filters out put pump up to max and note reading. Stop, dial pump back, put filters in then increase pump to get 1st reading. Eventually as filters clog you'll have to increase pressure to get max flow.
I'll add a bit more, there is a fixed relationship between the pressure (pump), volume of water flow and circumference of the pipe (discounting aeration). So your circumference is a constant, fixed by the pipe size, leaving the only variables pressure and volume (related to each other). You cannot push any more through it than it will take, because it is liquid and does not compress (unlike a gas), once it reaches maximum then that is it, no more.
I need to understand how the pressure is affected by this free flow waste, i.e. the relationship in the system. Is the pump constant pressure? i.e. non adjustable, because if it is as I stated earlier I suspect the waste acts like a resistor. If this is so then you are always getting full flow as that is what the pump is supplying, the waste is merely restricting (calming down) the full flow.
Give us a bit better description of the system please