Interest is growing worldwide 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 through the 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 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-section. Flow acceleration, bottom drag, and exit separation effects are included in the momentum balance. The model is applied to Masset Sound and Masset Inlet in Haida Gwaii, a remote island region, to determine the extractable power and its associated impacts to the tidal amplitude and volume flow rate through the channel.