A reservoir supplies water through 100 m of 30-cmdiameter cast iron pipe to a turbine that extracts 80 hp from the flow. The water then exhausts to the atmosphere.

Neglect minor losses.
(a) Assuming that ƒ≈ 0.019, find the flow rate (which results in a cubic polynomial). Explain why there are two legitimate solutions.
(b) For extra credit, solve for the flow rates using the actual friction factors.