a. A prototype Francis turbine is to be designed to operate at 375 rpm at a power specific speed of 0.8 (rad), with an effective head of 25 m. Assuming the overall efficiency is 92%, the mechanical efficiency is 99%, the runner tip speed to jet speed ratio is 0.68, and the flow at runner exit has zero swirl, determine
i. the shaft power developed;
ii. the volume flow rate;
iii. the impeller diameter and blade tip speed;
iv. the absolute and relative flow angles at runner inlet if the meridional velocity is constant and equal to 7.0 m/s.
b. Using Thoma's coefficient and the data in Figure 9.21, investigate whether the turbine is likely to experience cavitation. The vertical distance between the runner and the tailrace is 2.5 m, the atmospheric pressure is 1.0 bar, and the water temperature is 20°C.
