Interest is growing among utility companies and governments of maritime countries in assessing the power potential of tidal streams. While the latest assessment for Canadian coastlines estimates a resource of approximately 42 GW, these results are based on the average kinetic energy flux in the undisturbed state through the most constricted cross-section of a channel. It has been shown, however, that this method cannot be used to obtain the maximum extractable power for electricity generation. This work presents an updated theory for the extractable power from a tidal stream in a channel linking a bay to the open ocean. A mathematical model is developed for one-dimensional, non-steady flow through a channel of varying cross-sectional area, and includes flow acceleration, bottom surface drag, and exit separation effects in the dynamical balance. The model is applied to Masset Sound in Haida Gwaii, a remote island region, to determine the extractable power and its associated impacts to the tidal amplitude and flow rate through the channel.