Tutorial prob#$4$

The power specific speed of a $4$ MW Francis turbine is $0\mathrm{.}8,$ and the hydraulic efficiency can be assumed to be $90\%.$ The head of water supplied to the turbine is $100$ m $.$ The runner vanes are radial at inlet and their internal diameter is three$-$quarters of the external diameter. The meridional velocities at runner inlet and outlet are equal to $25\%$ and $30\%,$ respectively, of the spouting velocity. Blade thickness effects can be neglected. Assume density of water, $={10}^{3}k\frac{g}{m^3}.$ Also, absolute flow is without swirl at exit and

Determine: mechanical losses are negligible.

a$.$ the rotational speed and diameter of the runner;

b$.$ the flow angles at outlet from the guide vanes and at runner exit;

c$.$ the widths of the runner at inlet and at exit.