Jet Propulsion/Stage temperature ratio

Euler equation rewritten with fluid angles and mass flows

$v_{1} = u_{1} \tan β_{r 1}$

$v_{2} = u_{2} \tan β_{2} = ω r_{2} - u_{2} \tan β_{r 2}$

$\frac{T_{t 2}}{T_{t 1}} = 1 + \frac{(ω r_{2})^{2}}{c_{p} T_{t 1}} [1 - \frac{u_{2}}{ω r_{2}} (\tan β_{r 2} + \frac{u_{1} r_{1}}{u_{2} r_{2}} \tan β_{1})]$

The blade speed dimensionless group:

$\frac{(ω r_{2})^{2}}{c_{p} T_{t 1}}$