I am analyzing a hydraulic system that extends a single-acting cylinder. Due to a mechanical linkage, the force that the cylinder needs to exert decreases as it extends (and subsequently the pressure also decreases during extension). The pump's flow rate decreases as pressure increases, the flow rate can be described using:
Q=0.9-0.0027*p+3.7*(10^-6)*(p^2)-2.084*(10^-9)*(p^3) Q: flow rate (L/min) p: pressure (bar)
The pressure decrease from the cylinder extension is linear, The starting/ending pressures can vary, but for this case it decreases from 500 (not extended) to 350 bar (fully extended). The cylinder volume at max advance is 0.8L.
How would I go about calculating the time it takes for the cylinder to extend?