Sensorless technologies for estimating the flow rate in rotary blood pumps are desirable in that they can enable the realization of cost-effective and compact circulation support systems without the need for flow meters. A simple method for estimating the flow rate in a centrifugal blood pump using the measured torque and rotational speed of the motor is proposed and tested. By utilizing the motor torque measured using a torque meter, the error in estimating the flow rate of water was found to be less than 0.51 L/min in the range from 0 to 10 L/min, which is about half the equivalent value using the torque estimated with the torque monitor function provided in a commercially available motor driver. Furthermore, to compensate for changes in blood viscosity, the outlet port of the pump was clamped and the viscosity was estimated using the measured torque and rotational speed of the motor. The error in estimating the viscosity was less than 0.16 mPa·s in the range from 0.75 to 3.29 mPa·s. The estimated flow rate, compensated by the estimated viscosity, showed an error of less than 0.77 L/min in the range up to 10 L/min. Although the proposed method for estimating flow rate is described by a simple equation and its calibration is easier, the accuracy is comparable to that of conventional methods.