Problem $\backslash$# $1$

An impulse turbine at the mean radius is designed to provide $\backslash (185\backslash$mathrm$\{$~kJ$\}/\backslash$mathrm$\{$kg$\}\backslash )$ of specific work. The mean radius is $0\mathrm{.}275$ m and the hub to tip ratio is $0\mathrm{.}75.$ The axial velocity component of the flow is $\backslash (150\backslash$mathrm$\{$~m$\}/\backslash$mathrm$\{$s$\}\backslash ).$ Consider free vortex flow at the inlet of the rotor and no swirl at the exit.

a$)$ Determine the rotating speed of the rotor and find the leading and trailing edge angle of the rotor blade at the mean radius.

b$)$ Determine the guide nozzles blade exit angle at the mean radius.

c$)$ For the tip radius, determine the leading and trailing edge angle of the rotor blade and find the training edge angle of the guide nozzles.

d$)$ Find the degree of reaction at the tip radius.

e$)$ Find the total pressure ratio of the turbine stage if the total inlet temperature is $\backslash (1200\{\}^\{\backslash$circ$\}\backslash$mathrm$\{$C$\}\backslash )$ and the efficiency of the stage is $\backslash (84\backslash \%\backslash ).$ Consider $\backslash (\backslash$mathrm$\{$C$\}\_\{$p$\}=1\mathrm{.}124\backslash )\backslash (\backslash$mathrm$\{$kJ$\}/\backslash$mathrm$\{$kg$\}.\backslash$mathrm$\{$K$\}\backslash ),$ and $\backslash (\backslash$gamma$=1\mathrm{.}34\backslash ).$