Definition of hydraulic efficiency (impulse turbines) Hydraulic efficiency of an impulse turbine is the:

Introduction / Context:
Overall efficiency in a turbine is the product of hydraulic, mechanical, and volumetric efficiencies. For impulse turbines, hydraulic efficiency isolates how effectively the runner converts the jet’s kinetic energy into useful work on the wheel before mechanical losses are considered.

Given Data / Assumptions:

• Impulse action only (pressure at runner near atmospheric).
• Jet kinetic energy at inlet is the available hydraulic energy to the runner.
• Neglect mechanical and generator losses for the hydraulic efficiency definition.

Concept / Approach:
Hydraulic efficiency, η_h, is defined as (work done on the runner) / (kinetic energy of the jet at inlet). The numerator comes from momentum change (whirl component) across the runner; the denominator represents the energy content of the incident jet.

Step-by-Step Solution:
Energy available to runner = (1/2) * ρ * Q * V^2.Work done = torque * angular velocity = mass flow * change in whirl velocity * u.η_h = Work done / Jet KE at inlet.This definition cleanly separates hydraulic conversion from mechanical losses.

Verification / Alternative check:
Textbook derivations for Pelton wheels lead to η_h expressions dependent on speed ratio and bucket losses, all referenced to the jet’s inlet KE.

Why Other Options Are Wrong:
Option (a) mixes hydraulic with overall efficiency. Option (b) is close in spirit but ambiguous; the precise definition uses jet KE explicitly. Option (e) is meaningless for efficiency definition; (d) is incorrect because (c) is correct.

Common Pitfalls:
Confusing hydraulic with overall or mechanical efficiencies; using head instead of jet KE without clarifying the reference.

Final Answer:
ratio of work done on the wheel to the kinetic energy of the jet at inlet