Which of the following statements regarding axial flow turbine stages are **CORRECT**?

(A) In a zero-reaction ($R = 0$) impulse turbine stage, the entire stage static pressure and static enthalpy drop occurs exclusively across the stationary nozzle guide vanes

(B) In an impulse turbine stage, the relative flow speed across the rotor blade remains constant ($W_2 = W_1$) in frictionless flow

(C) A 50% reaction turbine stage achieves higher aerodynamic isentropic efficiency than a pure impulse stage due to favorable accelerating flow gradients through both stator and rotor blades

(D) For a given mean blade speed $U$, an impulse stage extracts less work per stage than a 50% reaction stage

Answer Key:

Verified in official key

### 1. Strategy & Theoretical Principles 1. **Impulse Stage ($R = 0$):** - Degree of reaction $R = \frac{\Delta h_{\text{rotor}}}{\Delta h_{\text{stage}}} = 0$. - All expansion and pressure drop occurs in the stationary nozzle guide vanes ($h_1 - h_2 = \Delta h_{\text{stage}}$). - No expansion occurs in the rotor blade passages ($p_2 = p_3$). Therefore, relative velocity magnitude is conserved across the rotor: $W_3 = W_2$. 2. **50% Reaction Stage ($R = 0.50$):** - Expansion is split equally between stator and rotor ($50\%$ each). - Fluid accelerates through both blade passages, reducing boundary layer growth and flow separation, yielding superior isentropic efficiency. 3. **Stage Work Comparison:** - Maximum work extracted by an impulse stage is $w_{\max} = 2 U^2$ (at blade speed ratio $\nu = 0.50$). - Maximum work extracted by a $50\%$ reaction stage is $w_{\max} = U^2$ (at $\nu = 1.0$). - Therefore, an impulse stage extracts **twice as much work** per stage as a $50\%$ reaction stage for the same blade speed $U$. Hence Statement D is false. ### 2. Statement Evaluation - **Statements A, B, C:** **CORRECT.** - **Statement D:** **INCORRECT.** Impulse stages extract *more* work per stage (up to $2 U^2$), which is why impulse stages are often used as the first high-pressure turbine stage. ### 3. Exam Trap & Standard Reference - **Trap Alert:** Impulse stages extract higher work per stage ($2 U^2$), but $50\%$ reaction stages achieve higher aerodynamic efficiency. - **Standard Reference:** Saravanamuttoo, H.I.H., *Gas Turbine Theory*, Chapter 7.

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