Flowrates in gravity system + piston pump
I hope you can help me here. I am trying to model an elevated vat which is using gravity to supply water to a filler. The pipeline has filters and bends in it which lead to headlosses. The filler supplys a fixed volume of liquid to a bottle at set time intervals. The filler is basically a glass jar (of sorts) with a piston in it and every time it needs to fill a bottle the psiton moves up - thereby pulling water into it. Once it has been filled the inlet valve shuts, oulet valve opens and the piston moves down - thereby filling the bottle.
I previously calculated the flowrate of a simillar system assuming it was one vat draining into the other. Here i wrote all sources of headlosses in terms of Q, summed and equated these to the total available head and solved for Q. This was a straightforward method which provided me with good results.
However, with the inclusion of the filler and the suction head it provides at intervals i'm not sure how to calculate the flowrates. Essentially i am looking to see if there is enough head available to supply the filler with enough water.
Your thoughts are appreciated!