Consider an idealized tidal reservoir of surface area A = 30 km² that fills and drains through a narrow channel of width w = 60 m and depth d = 20 m. Assume that the tidal range is h = 2.5 m. For simplicity, assume that the water flows uniformly throughout the channel and varies sinusoidally in time, with a 12 hour period, at a velocity v(t) = v₀ sinωt, where ω = 4π/24 hours. Compute the maximum speed v₀ needed for the reservoir to drain and fill completely on each tidal cycle and the power density of the water passing through the channel. Compute the total tidal stream energy passing through the channel daily. Consider installing four tidal stream turbines in the channel. Assume that they operate at 20% of the Betz limit, and that each has two rotors of radius 8 m. Estimate the average power output of the turbines. Compare this result with the energy extracted by a tidal barrage that utilizes both the ebb and flood tide with 50% efficiency.