An analysis of rotating flow in a rotor stator gap with axial through flow is presented. The analysis considers changes in mass, angular momentum, and static pressure that occur both between and across regions where cooling flow is injected, and may be applied to both smooth and rough rotors and stators. A simple calculation shows that most turbogenerator gap flows are undeveloped with sin average tangential velocity different than half the rotor speed. The analysis is compared to data from a recent set of experiments. Comparisons are made for gap flow with both a constant and varying axial through flow; the latter caused by air injection from the rotor. In both cases, the agreement is extremely good.