1. An axial-flow compressor stage with hub and tip radii r_h = 38 cm and r_t = 61 cm is designed with the following data: N = 6000 rpm, ΔT_0s = 19.5 K, C_x = 137 m/s, λ = 0.92, R_m = 0.5. Determine the flow angles at the hub, mean, and tip radii of both inlet and outlet of the rotor. Also calculate the degrees of reaction at both hub and tip.

2. Use the listed equations to solve the following problems:

ΔΡ_stage = ρU²Φ|Ψ|χ;  η_stage = ΔP_actual / ΔP_ideal = Φ_χ; 

x = {((R-Φ) x δ)/(Φ + δ x R) }

where : Φ = c_x/U ; Ψ = Δc_y/U

Ψ = blade loading coefficent t; R = degree of reaction

δ = drag to lift ration; U = rotor vlocity; ΔP = pressure gain

i- Employ the velocity diagram of Problem 1, determine the stage pressure rise and stage efficiency when the degree of reaction is 50% and drag to left coefficient 0.08. (Air density = 1.2 kg/m³).

ii- Each stage of axial compressor is of 0.5 reaction, flow ratio of 0.5, and blade speed of 300 m/s. If the inlet and outlet relative angles are 60 and 30 degrees respectively and drag to left coefficient 0.1, determine the blade loading coefficient, stage pressure rise and required energy input.(Air density = 1.2 kg/m³).

4. A 16-stage axial-flow compressor is to have a total pressure ratio of 6.3. Tests have shown that a stage efficiency of 90% can be obtained for each of the first 6 stages and 87% for the rest stages. Determine the compressor overall efficiency assuming constant work is done in each stage.