Calculate the turbine specific speed of the turbine in Prob. 14–85. 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 14-85

A Francis radial-flow hydroturbine has the following dimensions, where location 2 is the inlet and location 1 is the outlet: r₂ = 2.00 m, r₁ = 1.30 m, b₂ = 0.85 m, and b₁ = 2.10 m. The runner blade angles are β₂ = 71.4° and β₁ = 15.3° at the turbine inlet and outlet, respectively. The runner rotates at ṅ = 160 rpm. The volume flow rate at design conditions is 80.0 m³/s. Irreversible losses are neglected in this preliminary analysis. Calculate the angle α₂ through which the wicket gates should turn the flow, where α₂ is measured from the radial direction at the runner inlet (Fig. P14–83). Calculate the swirl angle α₁, where α₁ is measured from the radial direction at the runner outlet (Fig. P14–83). Does this turbine have forward or reverse swirl? Predict the power output (MW) and required net head (m).

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1 * "A.. V₂.n FIGURE P14-83 A W Control volume V₁.1