A constant flow valve mechanism for use in an inkjet printer includes a valve. A first port, a second port, and a third port are in fluid communication with each other through the valve. A portion of the valve is moveable and associated with the first, second, and third ports to produce a change in fluid impedance between the first port and the second port and the first port and the third port such that the fluid impedance between the first port and the second port changes at the same rate and in an opposite direction as that of the fluid impedance between the first port and the third port.