Question 14.13: Application of Turbine Affinity Laws A Francis turbine is be...
Application of Turbine Affinity Laws
A Francis turbine is being designed for a hydroelectric dam. Instead of starting from scratch, the engineers decide to geometrically scale up a previously designed hydroturbine that has an excellent performance history. The existing turbine (turbine A) has diameter D_{ A }=2.05 m , and spins at \dot{n}_{ A }=120 rpm \left(\omega_{ A }=12.57 rad / s \right) . At its best efficiency point, \dot{V}_{ A }=350 m ^{3} / s , H_{ A }=75.0 m of water, and b h p_{A}=242 MW . The new turbine (turbine B) is for a larger facility. Its generator will spin at the same speed (120 rpm), but its net head will be higher \left(H_{ B }=104 m \right) . Calculate the diameter of the new turbine such that it operates most efficiently, and calculate \dot{V}_{ B }, \text { bhp }_{ B } \text {, and } \eta_{\text {turbine, }} .
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