For Problems $03$ and $04,$ consider hot gas flow at the inlet to the first stage rotor of turbine of a large, utility$-$scale gas turbine rotating at $3600$ RPM$.$ Ignore changes in primary$-$path flow rate because of coolant flow injections into the primary path for the first stator row airfoils. Assume no losses.

Gas constant

c$\_$P$/$c$\_$v

Hub radius

Tip radius

$287\frac{J}{k}g$ K

$1\mathrm{.}35$

$0\mathrm{.}67$ m

$0\mathrm{.}83$ m

Flow axial component of velocity $300\frac{m}{s}($on stationary frame$)$

Flow direction

at $70$ degrees from axial $($on stationary frame$)$

Static temperature

$1450$ K

Static pressure

$11$ bar

P$03.$ Calculate the blade or rotor peripheral $($or linear tangential$)$ speed, in $\frac{m}{s},$ at the mean diameter. $($Use the arithmetic mean for the mean as we have done in the class.$)$