so I am still very much confused about the quantitative analysis of Francis turbine, so i wrote a small program. I have attached a copy of the results. Everything is fine, the results do match the normal circumstances. But upto speed 110, degree of reaction(R in the table) is negative, and over 440, it is over 1. I cross checked all the calculations by hand, and various values seemed to be OK. Is it really so practically?? I had the impression, it is always between 0 and 1(from its definition). And if it really is so, how can it be put forth qualitatively?? Second the relation between discharge and speed is sort of hyperbolic shape, whereas it is of drooping shape in the text book. I am confused about this. One more peculiar thing, I didn't have to feed anything to calculate discharge, when i did, program said the code is over specified, so i deleted the discharge as input and it calculated successfully!!! Only input i entered is head and rpm!! Qualitatively, in a pelton wheel, a spear is pulled back & forth to regulate the flow. What is the procedure for the Francis turbine?,is it guide blade angle? The angle which Vr1 makes with horizontal(also called the blade inlet angle), changes continuously as the rpm increases, so there is nothing as shock less entry, therefore the tip of the blade is always airfoil like(round). Am I correct??(I also noticed this in my fluid lab). Or is it that a turbine is designed to serve only at the optimum efficiency and these variations with rpm are neglected??