Hydraulic turbines — definition of hydraulic efficiency (η_h) For a reaction turbine operating under steady conditions, hydraulic efficiency is defined as the ratio of what quantity to what reference energy? Choose the most standard textbook definition used in turbine theory.

Difficulty: Easy

Correct Answer: work done on the wheel to the energy (head of water) actually supplied to the turbine

Explanation:


Introduction:
Hydraulic efficiency is a key performance indicator for water turbines. It compares how effectively the hydraulic energy delivered by the water is converted into useful work on the runner (wheel). For reaction turbines, both pressure and kinetic energy changes occur across the runner, so the proper definition must reference the energy actually available at the runner inlet.

Given Data / Assumptions:

  • Steady, incompressible flow of water.
  • Losses may occur in nozzles, guide apparatus, and within the runner.
  • We are isolating the runner to define hydraulic efficiency.


Concept / Approach:
Let E_in be the specific hydraulic energy available at the runner entry plane (including appropriate pressure head and velocity head components relative to exit). The useful hydraulic work rate on the runner equals the runner torque times angular speed, which is the energy transfer predicted by Euler’s turbine equation. Hydraulic efficiency is therefore η_h = (work done on runner) / (hydraulic energy supplied to runner). This definition excludes mechanical losses (bearings, seals) and volumetric slip; those are captured by other efficiencies (mechanical, volumetric, overall).

Step-by-Step Solution:

Identify numerator: work rate on the runner (wheel) from fluid to shaft = torque * angular speed.Identify denominator: hydraulic power at runner inlet = ρgQ*H_available at runner (or its equivalent energy flux).Form definition: η_h = (work done on the wheel) / (energy actually supplied to the turbine (runner)).


Verification / Alternative check:
In textbooks, “hydraulic efficiency” explicitly omits mechanical losses and leakage; hence it cannot be “shaft power / water power at penstock.” That latter ratio corresponds to overall efficiency when combined with volumetric losses.

Why Other Options Are Wrong:

  • Power produced / energy actually supplied: mixes rate with energy basis ambiguously and often implies overall efficiency.
  • Actual work available to the turbine / energy imparted to the wheel: circular and imprecise.
  • None of the above: incorrect because the standard definition is available among the options.
  • Mechanical shaft power / water power: that is overall efficiency, not hydraulic efficiency.


Common Pitfalls:
Confusing hydraulic, mechanical, and overall efficiencies; using penstock head instead of runner-inlet available head; ignoring reaction effects through the runner.


Final Answer:

work done on the wheel to the energy (head of water) actually supplied to the turbine

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