A clamping apparatus is provided for use with a fluid flow device, such as a blood separation system. The clamping apparatus includes a clamp head at least partially defining first and second tube openings each to receive tubing. The clamping apparatus also includes a first actuator coupled to a first flow control member. The first flow control member is configured to be movable via the first actuator relative to the first tube opening to control fluid flow through tubing located in the first tube opening. The clamping apparatus further includes a second actuator coupled to a second flow control member. The second flow control member is movable via the second actuator relative to the second tube opening to control fluid flow through tubing located in the second tube opening.