can someone please explain how does a pressure control/regulating valve regulate the static pressure downstream (at no flow condition).

Flow will continue through the control valve.  The flow into your piping system with no outlet flow will cause the pressure to rise.  That rise in pressure will cause the control valve loop to start to close the valve to maintain set-point (from your question, I'm assuming your control valve is for downstream pressure control).  

How fast the valve closes and what the final pressure for the system is is a function of the control loop tuning and system size but once it's closed, the pressure can't decrease until you remove material from downstream of the valve.  Also, the pressure will likely continue to increase unless your control valve is a bubble tight shut-off which I suspect is unlikely.

This is true for both a gas and liquid system but since a liquid system is essentially incompressible in many cases, the downstream pressure will increase much faster than for a gas.

The quick answer is no. A PRV (Pressure Relief Valve) will only prevent the pressure from reaching a setpoint. It prevents overpressure. A PRV will not control to a setpoint (the pressure may be lower). In any case, a PRV should not be used for control - it is considered a "safety" device.

Can you describe more in detail what it is you are trying to do? It is more efficient than asking what each of the devices are used for.

MORE NEWS