Calculate the turbine specific speed of the turbine in Prob. 14–83. Provide answers in both dimensionless form and in customary U.S. units. Is it in the normal range for a Francis turbine? If not, what type of turbine would be more appropriate?

Data from Problem 14–83.

A Francis radial-flow hydro turbine is being designed with the following dimensions: r₂ = 2.00 m, r₁ =1.42 m, b₂ = 0.731 m, and b₁ = 2.20 m. The runner rotates at ṅ = 180 rpm. The wicket gates turn the flow by angle α₂ = 30° from radial at the runner inlet, and the flow at the runner outlet is at angle α₁ = 10° from radial (Fig. P14–83). The volume flow rate at design conditions is 340 m³/s, and the gross head provided by the dam is H_gross = 90.0 m. For the preliminary design, irreversible losses are neglected. Calculate the inlet and outlet runner blade angles β₂ and β₁, respectively, and predict the power output (MW) and required net head (m). Is the design feasible?

FIGURE P14–83

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