Hey everyone, Hope you're all doing well.

So I have been trying to wrap my head around this and seem to be stuck at this point, I am trying to determine what size hydraulic valve I need to incorporate into my system, the valve is intended to be a vent to open slip in logic valve, It will supply flow pushing a cylinder with a weight attached in order to accelerate the weight to a specific velocity. The accumulator will step in as the prime mover due to the short time of the cycle the pump will only supply a small amount of flow.

This is the data I have.
Final velocity needed of actuator
Surface area of piston
volume of blind and rod end (these are equal because the cylinder is double rod)
Minimum force to accelerate in given time/ distance ( this number can be flexible)
Supply pressure
Accumulator volume and precharge
Pump Flow constant
approximate flow from accumulator per 100 psi drop
fluid gravity
fluid temperature

So I have read about finding the "Cv" or flow coefficient however i am not sure how to apply it. I know that as my valve opens the pressure supplied via accumulator will drop this will in turn change the Cv no? furthermore, I don't fully understand how to calculate the demand from the actuator, I know how many gallons per minute it will require to accomplish the stroke I don't know how that will effect pressure or how to calculate a pressure drop. It seems like I will have to find a "median" point and go over/under IE size the valve for an average acceleration to meet my final velocity goal.