Positive displacement pump Positive displacement pumps, unlike centrifugal or roto-dynamic pumps, theoretically can produce the same flow at a given RPM no matter what the discharge pressure. Thus, positive displacement pumps are constant flow machines. However, a slight increase in internal leakage as the pressure increases prevents a truly constant flow rate. A relief or safety valve on the discharge side of the positive displacement pump is necessary. The relief valve can be internal or external. An external relief valve in the discharge line, with a return line back to the suction line or supply tank provides increased safety.