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Define sudden. Let's assume the actuator is moving at 10 inches per second and the cylinder is moving 12 inches per second. Let's also assume the valve is mounted on the cylinder so the minimum of volume of trap oil is 0.A sudden jump in pressure at the cylinder's fill port suggests that the cylinder has stopped moving because it's hit a hard stop, the fill flow has gone to zero, and so has the pressure difference across the fill plumbing.
Excellent.Cd = 0.125 * (Nr)^0.5
Kv = Cd * A * (2/rho)^0.5
Q = Kv * (deltaP)^0.5
This is the classic flow makes it go equation. It is wrong ( actually incomplete ) because it doesn't explain how the mass is accelerated to the velocity in Q=V*A. Not only does it assume there is no friction. It assume there is no mass to accelerate and it assume there is not opposing force cause by pushing the oil the port on the other side of the cylinder. That isn't very realistic. Those that use V=Q/A screw up their hydraulic designs. Then I/we get calls from customers that ask why the motion controller isn't making the actuator move as fast as they want.Q=V*A.
Perhaps you should ask Dr Fitch and Dr Hong about 'flow makes it go'.Personal Note:
My background stints from having the opportunity to work with Dr. Fitch, the founder of the Fluid Power Research Center and Dr. Hong, his protege, specializing in hyrdaulic system design, service assurance and contamination control.