Pressure is sensed in blood flow tubing by placing an aqueous, preferably isotonic, substantially cell-free solution into branch connection tubing that connects in branching relation with the blood flow tubing at one end. The branch connection tubing also connects in use with a pressure transducer unit at its other end. An air volume is maintained, occupying a portion of the branch connection tubing which is adjacent to the other end. One flows positively or negatively pressurized blood through the blood flow tubing, with the result that the pressure of the blood is communicated through the aqueous solution and the air volume in the branch connection tubing to the pressure transducer unit, with the blood being spaced from the air volume. Preferably, substantially all of the branch connection tubing containing the aqueous solution and air volume has an inner diameter of substantially no more than 5 mm. This facilitates the continued separation of blood and solution when pressurized blood enters the branch connection tubing through the one end.