Average flow angle and total pressure loss coefficient.

Question

(i) Derive the following expression for life (C₁) and drag (C_D) coefficients for flow with friction through  a compressor (axial flow type) cascades:

C_L = $2\frac{S}{C}$ (tan ${\color{Green} \alpha _{1}}-tan{\color{Green} \alpha _{2}} cos {\color{Green} \alpha _{m}}-C_{D} tan {\color{Green} \alpha _{m}}$

C_D = $\xi \frac{S}{C}.\frac{cos^{3}\alpha _{m}}{cos^{2}\alpha _{1}}$

Where S, C, $\alpha _{1}$,$\alpha _{2}, \alpha _{m}$ $\xi$  denote pitch, chord, inlet flow angle, outlet flow angle, average flow angle and total pressure loss coefficient.

(ii) Show the variation of C_L and C_D with incidence and discuss physical significance. 20