where  is the velocity of the fluid along a streamline far upstream, and  is the velocity of the fluid just prior to the rotor. Written in cylindrical polar co-ordinates, we have the following expression:
where  and  are the z-components of the velocity far upstream and just prior to the rotor respectively. This is exactly the same as the upstream equation from the Betz model.
As can be seen from the figure above, the flow expands as it approaches the rotor, a consequence of the increase in static pressure and the conservation of mass. This would imply that  upstream. However, for the purpose of this analysis, that effect will be neglected.