Calculate the turbine specific speed of the turbine of Example 1413 for the case where 1

Calculate the turbine specific speed of the turbine of Example 14–13 for the case where α₁ = 10°. 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 Example 14-13

A retrofit Francis radial-flow hydroturbine is being designed to replace an old turbine in a hydroelectric dam. The new turbine must meet the following design restrictions in order to properly couple with the existing setup: The runner inlet radius is r₂ = 8.20 ft (2.50 m) and its outlet radius is r₁ = 5.80 ft (1.77 m). The runner blade widths are b2 5 3.00 ft (0.914 m) and b₁ = 8.60 ft (2.62 m) at the inlet and outlet, respectively. The runner must rotate at ṅ = 120 rpm (ω = 12.57 rad/s) to turn the 60-Hz electric generator. The wicket gates turn the flow by angle α₂ = 33° from radial at the runner inlet, and the flow at the runner outlet is to have angle α₁ between 210° and 10° from radial (Fig. 14–99) for proper flow through the draft tube. The volume flow rate at design conditions is 9.50 × 10⁶ gpm (599 m³/s), and the gross head provided by the dam is H_gross = 303 ft (92.4 m).

(a) Calculate the inlet and outlet runner blade angles β₂ and β₁, respectively, and predict the power output and required net head if irreversible losses are neglected for the case with α₁ = 10° from radial (with-rotation swirl).

(b) Repeat the calculations for the case with α₁ = 0° from radial (no swirl).

(c) Repeat the calculations for the case with α₁ = 210° from radial (reverse swirl).