A method and system for calibrating and controlling the withdrawal of a fluid, such as blood, from a fluid source, such as a blood vessel, includes a fluid pump, a pressure sensor, a flow rate sensor, and a microprocessor based flow control subsystem. The flow control subsystem optimizes the flow rate by sensing zero flow rate pressure within the subject, making a plurality of periodic flow path pressure measurements and extrapolating a calibration flow rate curve. A control curve is generated by utilizing the zero-flow rate pressure point, the slope of the calibration curve, and an empirically predetermined pressure. The blood pump is then operated at a maximum speed that is limited by the flow control curve to maximize flow without occlusion or collapse of the blood vessel during blood withdrawal. The method and system of the invention is particularly applicable to automated apheresis systems.