In an axial compressor stage, the Degree of Reaction ($R$) is defined as $0.50$ (50% symmetric stage). Which of the following conditions is satisfied across this stage?

(A) Static enthalpy rise in the rotor equals static enthalpy rise in the stator (symmetric velocity triangles)

(B) Static pressure rise occurs entirely across the rotor, with zero diffusion in the stator

(C) The rotor blade relative flow velocity is strictly axial with zero swirl

(D) Total temperature across the stage remains strictly constant

Answer Key:

A

### 5-Stage Derivation & Analytical Solution: 1. **Stage 1: Definition:** Degree of reaction $R = \frac{\Delta h_{rotor}}{\Delta h_{stage}} = \frac{h_2 - h_1}{h_3 - h_1}$. 2. **Stage 2: 50% Reaction Symmetry:** When $R = 0.5$, $\Delta h_{rotor} = \Delta h_{stator}$. The rotor and stator do equal aerodynamic diffusion work. 3. **Stage 3: Kinematic Consequence:** The rotor relative velocity triangle is a mirror image of the absolute velocity triangle ($W_1 = C_2$, $W_2 = C_1$). 4. **Stage 4: Distractor Analysis:** Option B corresponds to $R = 1.0$ (pure reaction rotor). Option D is physically impossible because compressors require shaft work input ($\Delta T_0 > 0$). 5. **Stage 5: Official Reference:** Jack D. Mattingly, *Elements of Propulsion: Gas Turbines and Rockets*, Chapter 9.

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