Relative velocity in ideal impulse rotors In an impulse turbine neglecting friction, the relative velocity of steam at the exit tip of the moving blade is ________ the relative velocity at the inlet tip.

Introduction / Context:
Impulse rotors ideally experience no pressure change across the moving blades; they simply turn the jet and extract work via change in whirl component. Understanding how relative velocity behaves in this ideal case is critical for constructing correct velocity triangles and estimating diagram efficiency limits.

Given Data / Assumptions:

• Impulse rotor: negligible pressure drop across moving blades.
• No friction (idealization), so no viscous dissipation in the rotor passage.
• Steady flow and correct incidence at blade entry.

Concept / Approach:

With no pressure change and no friction, the magnitude of the relative velocity vector should remain constant through the rotor passage; only its direction changes due to blade curvature. Hence w1 (at inlet) equals w2 (at exit) in magnitude. Real blades show a reduction (e.g., 10–15%) due to friction, but the ideal model preserves the magnitude.

Step-by-Step Solution:

Verification / Alternative check:

Euler's turbine equation shows rotor work depends on whirl change in absolute velocity, not on a change in relative speed magnitude for the ideal impulse rotor.

Why Other Options Are Wrong:

Less/greater than: would imply frictional loss or energy input, contradicting the ideal assumption.Half or twice: arbitrary and inconsistent with energy conservation in the relative frame.

Common Pitfalls:

Mixing real and ideal behavior; in practice, friction lowers w2, but the question explicitly neglects friction.

Final Answer:

equal to