Outlet behavior index: The ratio of the rate of change of an outlet’s discharge to the rate of change of discharge in the parent channel is termed as what?

Introduction / Context:
In canal irrigation, an outlet should ideally maintain a predictable proportion of the parent canal’s discharge. Several parameters describe outlet performance; among them, flexibility relates discharge responsiveness of the outlet to that of the parent channel.

Given Data / Assumptions:

• Parent channel discharge Q_p changes slightly.
• Outlet discharge q_o responds accordingly.
• Small-signal (differential) definition is used.

Concept / Approach:
Flexibility (often denoted F) is defined as (dq_o / q_o) / (dQ_p / Q_p) for fractional changes, or simply the ratio of the rates of change when using absolute rates in matched dimensions. It expresses how sensitively the outlet follows parent discharge changes and whether it is proportional (proportional outlet), less responsive (semi-modular), or independent (modular).

Step-by-Step Solution:
1) Consider a small change dQ_p in parent discharge.2) Measure resulting change dq_o in outlet discharge.3) Compute flexibility F = (dq_o/dt) / (dQ_p/dt) or the corresponding fractional form.

Verification / Alternative check:
Textbook definitions distinguish flexibility from sensitivity (which involves head changes). An ideal proportional outlet has F close to 1, meaning outlet discharge varies proportionally with canal discharge.

Why Other Options Are Wrong:

• Efficiency: head or energy conversion ratio, not outlet response.
• Sensitivity: relates to response with respect to head changes, not discharge changes.
• Modular limit: range over which outlet behaves as a module (near-constant discharge).

Common Pitfalls:

• Interchanging flexibility and sensitivity; they refer to different independent variables.
• Ignoring the operating head—modularity depends on head limits, not directly on flexibility magnitude.

Final Answer:
Flexibility.