A flow control system is used in conjunction with a surgical handpiece for the removal of unwanted material in a very small enclosed operative site in which it is very critical to maintain a pressure within a certain range, such as in the surgical operation of the removal of a cataract lens from the human eye. The system includes an irrigation subsystem comprising a source of treatment fluid, such as an artificial aqueous solution, at a preselected constant pressure for supplying said fluid to the enclosed operative site via the handpiece. A suspension of the treatment fluid, including any unwanted material, is removed from the operative site by an aspiration subsystem. The aspiration subsystem comprises a pump used to remove the suspension and to overcome the friction and other losses throughout the entire fluid system, a flow transducer for measuring the rate of flow, and a vent valve to reduce the flow in the aspiration subsystem when necessary to assist in maintaining a relatively constant pressure within the operative site. An electronic flow control receives signals from the flow transducer and reacts to certain changes in flow signals by sending a signal to the venting valve.