# How to calculate time it takes for a cylinder to extend, if the pressure is not constant and the pump flow rate varies by pressure?

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?

• Base it on the fluid delivered per unit time - the fluid, if liquid, is considered incompressible. Nov 8, 2022 at 12:53
• @SolarMike The fluid is indeed incompressible. If I'm not mistaken, your suggestion would imply using integration to calculate the time? Nov 8, 2022 at 12:59