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:

$$\frac{(\omega r_2)^2}{c_p T_{t1}}$$