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: 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?

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

1 Answer 1


You have to discretize the the pressure range and the volume flow range, attempt a very small step of 1 bar calculate the volume flow, then determine the amount of extension based on a small step of time 0.1 sec. Based on the extension read a new pressure. You can decrease steps appropriately till your results aren't sensitive to stepping.

  • $\begingroup$ This solved it, I used excel to calculate the filling of the cylinder in small steps as you suggested, with the pressure and flow calculted incrementally at each step. then counted the amount of steps at which the cylinder should be full to get the time. Thank you for your suggestion. $\endgroup$
    – David
    Nov 10, 2022 at 11:36

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