Question $9$:

An axial flow pump has a rotor $600$ mm diameter and the ratio of the hub diameter to the rotor diameter is $0\mathrm{.}5.$ The flow rate produced is $0\mathrm{.}55\frac{m^3}{s}$ when the impeller speed is $650re\frac{v}{m}in.$ The vane angle at inlet $({}_1)$ is $20$ and at exit $({}_2)$ it is $40$ at all radii. Determine the vane angles needed for the guide vanes at inlet and outlet for the root and the tip. Calculate the diagram power at the root and tip for a unit mass flow rate. Using the mean of these, estimate the diagram, Power. Take the density as $1000k\frac{g}{m^3}.$