A turbine homologous to the turbine of Sample Prob. 16.9 has all dimensions one-half as large. For this turbine find the speed of rotation, flow rate, and brake horsepower when operating under the same net head of 81 ft.
Eq. (16.16): If h does not change, n \propto D^{-1}
Hence: \quad n_{2}=(2 / 1) n_{1}=(2 / 1) 150=300 \mathrm{rpm} \quad
Eq. (16.17): If h does not change, Q \propto D^{2}
Hence: \quad Q_{2}=(1 / 2)^{2} Q_{1}=(1 / 4) 200=50 \mathrm{cfs} \quad
Eq. (16.18): If h does not change, P \propto D^{2}
Hence: \quad P_{2}=(1 / 2)^{2} P_{1}=(1 / 4) 1600=400 \mathrm{hp} \quad
n \propto h^{1 / 2} / D \quad \text { or } \quad n=K_n h^{1 / 2} / D (16.16)
Q=K_Q h^{1 / 2} D^2 (16.17)
P=K_p h^{3 / 2} D^2 (16.18 )