An artificial lung is used during cardiopulmonary bypass to oxygenate blood and to control blood temperature. The pressure drop-flow rate characteristics of the membrane compartment in three hollow fiber membrane oxygenators were determined in vitro to characterize design features. Results are presented in a unique dimensionless relationship between Euler number, N(Eu) (ratio of pressure drop to kinetic energy), and Reynolds number, N(Re) (ratio of inertial to viscous forces), and are a function of the device porosity, epsilon, and a characteristic device length, xi, defined as the ratio of the mean blood path and manifold length: [equation in text]. This dimensionless approach allows us (1) to compare oxygenators independently, and (2) to relate water tests to blood.