Jet Propulsion/Stage temperature ratio

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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}}