A positive displacement rotary pump including a housing having an internal chamber and inlet and discharge ports, a sealing land on the housing between a downstream end of the inlet port and an upstream end of the discharge port, and a rotating group in the internal chamber defining a plurality of pump chambers. The pump chambers traverse in succession and at regular intervals the inlet port and the sealing land and the discharge port. The housing has a stationary pre-charging passage which communicates with the discharge port and overlaps the sealing land. The rotating group includes a plurality of rotating pre-charging passages which communicate with respective ones of the pump chambers. As each rotating pre-charging passage attains overlap with the stationary pre-charging passage, the low pressure of the fluid trapped in the corresponding pump chamber sealed closed in the sealing land increases rapidly and induces a pulse in the fluid in the discharge port and in the fluid system connected to the discharge port. The angular separation between the rotating pre-charging passages is randomly unequal so that the intervals between pulses are irregular. The irregular intervals between the pulses suppresses tonal pump noise.