The correct answer is option 'A' - Flexibility.

Flexibility is the ratio of the rate of change of discharge of an outlet to the rate of change of the discharge of the distribution channel. It is an important parameter in hydraulic engineering, particularly in the design and operation of water distribution systems.

Here is a detailed explanation of the answer:

1. Introduction:
- Flexibility is a measure of the ability of a distribution system to respond to changes in demand or supply.
- It quantifies the relationship between the discharge of an outlet and the discharge of the distribution channel.

2. Definition of Flexibility:
- Flexibility is defined as the ratio of the rate of change of discharge of an outlet (Q_out) to the rate of change of the discharge of the distribution channel (Q_channel).
- Mathematically, Flexibility (F) can be expressed as: F = (dQ_out / dt) / (dQ_channel / dt)

3. Significance of Flexibility:
- Flexibility provides insights into the dynamic behavior of a water distribution system.
- It helps in understanding how changes in demand or supply at an outlet affect the flow rates in the distribution network.
- It is useful for system design, operation, and maintenance.

4. Application in System Design:
- In the design of water distribution systems, flexibility is considered to ensure that the system can adapt to changes in demand patterns.
- High flexibility indicates that the system can handle variations in flow rates effectively.
- Designing a system with adequate flexibility helps in optimizing the performance and efficiency of the distribution network.

5. Application in System Operation:
- Flexibility is crucial for efficient system operation.
- It helps in managing peak demand periods by ensuring that sufficient water is available at all outlets.
- By understanding the flexibility of the system, operators can make informed decisions regarding the allocation and control of water flow.

6. Conclusion:
- Flexibility is an important parameter in hydraulic engineering, specifically in water distribution systems.
- It quantifies the rate of change of discharge of an outlet relative to the rate of change of the discharge of the distribution channel.
- It is essential for system design, operation, and optimization.
- By considering flexibility, engineers and operators can ensure the efficient and effective functioning of water distribution networks.