Difficulty: Easy
Correct Answer: Relative velocity at rotor inlet equals relative velocity at rotor exit
Explanation:
Introduction / Context:
Impulse-stage kinematics are captured by velocity triangles. With friction neglected, certain components remain unchanged across the rotor, while others must change to allow work extraction. Understanding which components are conserved clarifies stage design and performance estimation.
Given Data / Assumptions:
Concept / Approach:
In an ideal impulse rotor, the magnitude of the relative velocity is unchanged across the rotor, i.e., Vr1 = Vr2, since no energy is added or removed in the rotor aside from direction change. Axial velocity is typically assumed constant (Va1 = Va2) for uniform flow area, while whirl components must change to produce torque: Vw1 ≠ Vw2 (indeed, Vw2 is often reduced toward zero for high efficiency). Absolute velocities generally differ in magnitude and direction between inlet and outlet due to the wheel speed and momentum change.
Step-by-Step Solution:
Recognize that with no friction: |Vr| is conserved through the rotor.Torque requirement demands ΔVw ≠ 0, so whirl cannot be equal.Absolute speeds differ because the vector sum with wheel speed changes between inlet and outlet.Therefore, the correct equality is Vr1 = Vr2.
Verification / Alternative check:
Many introductory derivations of diagram efficiency start from Vr1 = Vr2, Va1 = Va2, and analyze changes in Vw to compute work and power.
Why Other Options Are Wrong:
Absolute speeds equal (A) is not generally true; whirl equal (D) would imply zero work; (C) contradicts the common constant-axial-velocity design assumption.
Common Pitfalls:
Confusing absolute and relative components; forgetting that work in turbines comes from change in whirl velocity.
Final Answer:
Relative velocity at rotor inlet equals relative velocity at rotor exit
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