A velocity compounded, two$-$stage, impulse turbine was designed for an axial discharge of steam. The velocity of the steam leaving the turbine is $80$ m$/$s

The inlet angle of the moving blade of the second stage is $30.$

The inlet and outlet angles of the first row of moving blades are equal.

The inlet angle of the fixed blades is $35$

The relative velocity of the steam at the turbine outlet is $160$ m$/$s

The mass flow rate of the steam is $5$ kg$/$s

There is a $7\%$ loss of velocity across all blades due to friction.

$3\mathrm{.}1$ Use a scale of $1$cm $=40$ m$/$s and construct velocity diagrams for the turbine in your answer book. Indicate the length of all the lines as well as the magnitude of the angels on the diagrams. $(10)$

$3\mathrm{.}2$ Determine from the velocity diagrams

$3\mathrm{.}2\mathrm{.}1$ The blade velocity in m$/$s

$3\mathrm{.}2\mathrm{.}2$ The nozzle velocity in m$/$s

$3\mathrm{.}2\mathrm{.}3$ The exit angle of the fixed blades

$3\mathrm{.}2\mathrm{.}4$ The total axial thrust on the shaft in Newtons

$3\mathrm{.}2\mathrm{.}5$ The power developed by the turbine in kW$.$

$3\mathrm{.}2\mathrm{.}6$ The diagram efficiency