Reaction Turbines — Effect of Unit Speed on Discharge How does the discharge through a reaction turbine vary with an increase in unit speed (speed at unit head)?

Introduction:Unit quantities normalize turbine performance to a head of 1 m, enabling comparisons across heads and scales. Understanding how unit speed relates to flow helps in model testing, selection, and regulation of reaction turbines.

Given Data / Assumptions:

• Reaction turbine operating under dynamic similarity.
• Definitions: unit speed Nu = N / H^0.5 and unit discharge Qu = Q / H^0.5.
• Geometrically similar settings and comparable guide-vane openings.

Concept / Approach:From similarity laws, peripheral velocity u ∝ N * D and flow rate Q ∝ V_f * A. Under similitude at fixed geometry, characteristic velocities scale with H^0.5 and with shaft speed. Consequently, Qu correlates with Nu; increasing unit speed implies a proportionate tendency for unit discharge to rise.

Step-by-Step Solution:Define Nu = N / H^0.5.Define Qu = Q / H^0.5.For similar operation, Qu ∝ Nu.Therefore, as unit speed increases, discharge increases correspondingly.

Verification / Alternative check:Performance curves (Qu vs Nu) for reaction turbines typically show a rising trend within the stable operating zone.

Why Other Options Are Wrong:remains same: contradicts similarity relations.decreases: opposite to observed and theoretical trend.depends only on gate opening: gate affects flow, but unit speed also influences it under similitude.

Common Pitfalls:Confusing absolute speed changes with unit-normalized quantities; unit variables remove the head effect but keep speed influence.

Final Answer:increases