Abstract: The present invention provides a fluid flow measurement system for an oil well drilling system that includes a supply of drilling fluid to a wellbore under pressure and a return line carrying fluid leaving the wellbore during drilling of the wellbore. The system includes at least one floating sensor in the return line that provides a measure of the velocity of the fluid in the return line. The sensor may be a thermal sensor, an electromagnetic sensor or an ultrasonic sensor. A height sensor provides the fluid level in the return line and a density sensor provides the density of the returning fluid. A controller determines the inflow rate and out flow rate of the drilling fluid and further determines the presence of a kick and wash out from the flow rates. The system also determines the operating condition of the pumps supplying fluid to the wellbore.