Tutorial prob#$3$

A Francis turbine operates at an overall efficiency of ${}_0=0\mathrm{.}94$ corresponding to a power specific speed of $0\mathrm{.}9$ rad $.$ The effective head across the turbine is $160$ m and the speed required for electrical generation is $750$ rpm $.$ The runner tip speed is $0\mathrm{.}7$ times the spouting velocity, the absolute flow angle at runner entry is $72$ from the radial direction, and the absolute flow at runner exit is without swirl. Assuming there are no losses in the guide vanes and the mechanical efficiency is $100\%,$ determine: $($assume density of water, $={10}^{3}k\frac{g}{m^3})$

a$.$ the turbine power and the volume flow rate;

b$.$ the runner diameter;

c$.$ the magnitude of the tangential component of the absolute velocity at runner inlet;

d$.$ the axial length of the runner vanes at inlet.