Blade angles, Reaction, Diffusion

[roldy]

I'm really confused about an in class example my professor did to show how to obtain the hub and tip degrees of reaction of a free-vortex compressor stage and the diffusion factor for the rotor tip

Given:
$$\frac{\Delta P_t}{\rho {W_0}^2}=0.9$$

$$\frac{r_t}{r_h}=2.646$$

$$^{\circ}R_m=0.5$$

$$\sigma_m=1.0$$

$$\frac{\omega r_h}{W_0}=0.5$$

His results:

$$D_{rotor,hub}=-.179$$

$$D_{rotor,tip}=0.56$$

$$D_{stator,hub}=.74$$

$$D_{stator,tip}=0.55$$

$$^{\circ}R_{tip}=0.714$$

$$^{\circ}R_{hub}=-1.0$$


The only values that I found where the $$^{\circ}R_{tip}$$ and $$^{\circ}R_{hub}$$.

For now, I'm just concentrating on figuring out the rotor tip diffusion. The equation that I have for the Diffusion of the rotor is as follows.

$$D_{rotor}=1-\frac{cos(\beta_1)}{cos(\beta_2)}+\frac{1}{2\sigma}(tan(\beta_1)-tan(\beta_2))cos(\beta_1)$$

I would assume that the beta angles are the beta tip angles. This is where I got stumped. I don't have $$\omega$$ or [tex]W_0[\tex] to help me solve for the missing things.

 

[Illmatic1]

I'm not sure if I'm missing something or if this is the wrong equation. Any help would be greatly appreciated.