The method presented can be used to determine fluid flow and coolant pump speed transients in a nuclear reactor system. Included are transients due to power failure, starting pumps in idle loops, and the opening of an active pump's discharge valve. Parallel pumps in the system may be analysed independently of each other. Typical cases are presented for the N. S. Savannah (NMSR) and the Consolidated Edison Thorium Reactor (CETR). Partial failure of pumping power results in an unbalanced change in primary flow, i.e., flow in the active loops accelerates while flow in the failed loops decelerates rapidly. Maximum deceleration occurs when all pumps are operating and only one fails. The maximum rate of cold water is pumped into the reactor when the pumps in an idle loop are started while the discharge valve is open.