It depends on the fluid properties. It is the obligation of the Automatic Recirculation Control Valve manufacturer to analyze the system needs and supply a Back Pressure Regulator when warranted by the laws of fluid dynamics.
The requirement of backpressure is generic to all ARC pressure reducing applications. Pressure
reduction even by multiple stage cascading can minimize the requirement; however, no valve design will redefine a fluid’s physical properties.
In high pressure applications, the ARC system often does not provide adequate pressure
in the bypass line to prevent cavitation or flashing. Either of these conditions is undesirable because it can cause damage to both valves and the pipe system or cause a reduction in flow below the minimum desired, jeopardizing the pump protection system. All pressure reducing valves will experience a velocity-induced recovery effect that will limit the amount of pressure drop a valve can take and cause a reduction in flow capacity.
The size of the bypass pipe depends on flow and piping configuration. If the pressure
drop through the orifice results in flashing flow, the orifice should be located at the end of
the bypass piping and should discharge directly into the larger receiving tank or larger
downstream piping.
A more detailed answer to your query can not be made without knowledge of the application and fluid properties.