Question 15.4: Compare between the specific power of axial and radial turbi......
Compare between the specific power of axial and radial turbines in the following case:
Axial flow turbine having the following angles \alpha_2=\beta_3=60 \text{ and }\alpha_3=\beta_2=0.
Radial inflow turbine with \alpha_2=60,\alpha_3=\beta_2=0, \text{ and } \beta_3=0.
The rotational speed U_2 is equal in both turbines.
The velocity triangles for both axial and radial turbines are shown in Figure 15.7.
(a) Axial flow turbine: Since \alpha_2=\beta_3=60 \text{ and }\alpha_3=\beta_2=0, and the specific work is
W_{\text{axial}}=U_2C_{\text{u}2}+U_3C_{\text{u}3} \\ W_{\text{axial}}=U^2_2
(b) Radial flow turbine: Since \alpha_2=60^\circ,\alpha_3=\beta_2=0, \text{ and }\beta_3=45^\circ and the specific work is
W_{\text{radial}}=U_2C_{\text{u}2}-U_3C_{\text{u}3} \\ W_{\text{radial}}=U_2U_2-U_3 \times 0 \\ W_{\text{radial}}= U_2^2 \\ \frac{W_{\text{axial}}}{W_{\text{radial}}} =\frac{U^2_2}{U^2_2} =1
Thus, in this special case the specific powers of both turbines are equal.
