The following interactive graph plots out theoretical pressures of a hydraulic sytem composed of a differential area double-acting cylinder and a pilot-to-open check valve (please refer to the diagram below the graph). It is assumed that there is no back pressure in the return line (V2).
The term "Equivalent Pressure Differential" (horizontal axis) refers to the caculated pressure differential across the check valve - the valve is considered open when this pressure is higher than the check-valve cracking pressure.
The main purpose of this chart is interactivity, i.e. to demonstrate in a clear and graphical way how changing the key parameters of such a system (valve pilot ratio, cylinder area ratio, load induced pressure, trapped pressure, check valve cracking pressure and cylinder orientation) affects the numbers and can create conditions for overpressure and cylinder locking. The lines are plotted out beyond the magenta line for a clear illustration of the lines' slope (pressure development tendency), obviously in a real system the pressures would be immediately affected by the check-valve's opening.
Read more on the subject in Wrapping My Head Around the Pilot-Operated Check Valve Mounted on a Double-Acting Hydraulic Cylinder
Load Pressure refers to load induced pressure