Puget Power Plant No. 1 at Snoqualmie Falls, WA is a hydroelectric facility in which water is directed straight down through a pair of steel penstocks located upstream, passes through a set of generator turbines, and exits through a horizontal tunnel that emerges at the base of the falls. The parallel, vertical penstocks are each 8 ft in diameter and 270 ft long and the plant capacity is 11,900 kW.

(a) If viscous losses are negligible and the generator efficiency is 90%, what water flow rate is needed to run at full capacity? You may assume that the river depth at the inflow is 10 ft and that the cross-sectional area of the outflow tunnel equals the total for the two penstocks.

(b) Assuming fully developed flow in the penstocks, show that the viscous loss there is negligible. [Including also entrance effects would significantly increase the predicted loss, but it would remain small compared with the shaft work.]