Jet Propulsion/Stage temperature ratio

Euler equation rewritten with fluid angles and mass flows

$v_{1}=u_{1}\tan \beta _{r1}$

$v_{2}=u_{2}\tan \beta _{2}=\omega r_{2}-u_{2}\tan \beta _{r2}$

${\frac {T_{t2}}{T_{t1}}}=1+{\frac {(\omega r_{2})^{2}}{c_{p}T_{t1}}}[1-{\frac {u_{2}}{\omega r_{2}}}(\tan \beta _{r2}+{\frac {u_{1}r_{1}}{u_{2}r_{2}}}\tan \beta _{1})]$

The blade speed dimensionless group:

${\frac {(\omega r_{2})^{2}}{c_{p}T_{t1}}}$