Flow Velocity Triangle

Nomencalture

$\alpha_1$ - absolute flow angle at the rotor's inlet
$\alpha_2$ - absolute flow angle at the stator inlet
$c_x$ - meridional velocity in the radial and axial plane
$N$ - rotational speed
$r1$ - radius at the rotor's inlet

Velocity Triangle

calculates flow velocity triangle

$cx_1 = c_x$ - axial velocity at the rotor's inlet (m/s)

$U = (rpm \ to \ m/s)(r1,N)$ - blade velocity at the rotor's inlet (m/s)

$c_{\theta_1} = cx_1 \tan{\left(\alpha_1 \right)}$ - absolute tangential velocity at the rotor's inlet (m/s)

$c_1 = \frac{cx_1}{\cos{\left(\alpha_1 \right)}}$ - absolute velocity at the rotor's inlet (m/s)

$w_1 = \sqrt{U^{2} + cx_1^{2}}$ - relative velocity at the rotor's inlet (m/s)

$w_{\theta_1} = U - c_{\theta_1}$ - relative tangential velocity at the rotor's inlet (m/s)

$\beta_1 = \operatorname{atan}{\left(\frac{w_{\theta_1}}{cx_1} \right)}$ - relative flow angle at the rotor inlet (rad)

$cx_2 = c_x$ - axial velocity at the stator's inlet (m/s)

$c_{\theta_2} = cx_2 \tan{\left(\alpha_2 \right)}$ - absolute tangential velocity at the stator's inlet (m/s)

$c_2 = \sqrt{c_{\theta_2}^{2} + c_x^{2}}$ - absolute velocity at the stator's inlet (m/s)

$w_{\theta_2} = U - c_{\theta_2}$ - relative tangential velocity at the stator's inlet (m/s)

$w_2 = \sqrt{cx_2^{2} + w_{\theta_2}^{2}}$ - relative velocity at the stator's inlet (m/s)

$\beta_2 = \operatorname{atan}{\left(\frac{w_{\theta_2}}{cx_2} \right)}$ - relative flow angle at the stator inlet (rad)

$(w2/w1) = \frac{w_2}{w_1}$ - deHaller w2/w1 relationship (dimensionless)

alpha_m

calculates $\alpha_m$ flow angle parameter

$\alpha_m = \operatorname{atan}{\left(0.5 \tan{\left(\alpha_1 \right)} + 0.5 \tan{\left(\alpha_2 \right)} \right)}$ - $\alpha_m$ flow angle parameter (rad)