Final answer:
A reverse flow check with a PRV is mainly needed for safety, to prevent reverse flow that could close the PRV during a spike and to ensure proper functioning of the system during variable pressure conditions.
Step-by-step explanation:
A reverse flow check may be needed with a Pressure Relief Valve (PRV) primarily for safety reasons. When a pressure spike occurs, it could potentially close the PRV, which is intended to open in the event of high pressure to protect the system. Moreover, even though an extra valve might seem redundant, it is a critical component that ensures the correct operation of safety systems, particularly in complex setups such as piping systems with variable tube diameters or even in reactors where auxiliary cooling systems and pumps must be reliable in case of an accident. In these situations, the reverse flow check valve prevents the reverse flow of fluids, which could lead to system failures or accidents, much like how in complex fluid systems, resistance and turbulence can greatly impact the pressure downstream and hence the flow rates.