A hemodialysis apparatus comprising diaphragm pumps for the movement of both dialysate and blood, and under the control of a controller, is capable of detecting blood flow conditions that give rise to an alarm and implement procedures to adjust, pause, or halt the pumping of dialysate and/or blood. The controller can direct the application of a time-varying pressure to fluid in the control chamber of a blood pump, and monitor the resulting pressure waveform during a fill stroke of the blood pump. A deviation of the measured pressure variation from an expected value can give rise to an alert to a user and to the initiation of an adjustment, pause, or cessation of the dialysate pump's activity.