The correct answer is option 'C' - Flexibility.

Explanation:
- The ratio mentioned in the question is referred to as the flexibility of the system.
- Flexibility is a measure of how much the discharge of the outlet changes in response to a change in the discharge of the distributor channel.
- It determines the sensitivity of the outlet discharge to changes in the distributor channel discharge.

Factors affecting flexibility:
1. Channel geometry: The shape and dimensions of the channel affect the flexibility of the system. For example, wider channels tend to have lower flexibility compared to narrower channels.
2. Channel slope: The slope of the channel also influences the flexibility. Channels with steeper slopes usually exhibit higher flexibility.
3. Roughness of the channel: The roughness of the channel walls affects the flow resistance and, consequently, the flexibility of the system. Smoother channels generally have lower flexibility.
4. Channel material: The material of the channel can impact the flexibility. Different materials have different roughness properties, which influence the flow characteristics.

Importance of flexibility:
1. Design considerations: Understanding the flexibility of a system is crucial in designing efficient and responsive hydraulic structures. By considering the flexibility, engineers can optimize the design and ensure desired performance.
2. System operation: Flexibility helps in predicting the behavior of the system under various operating conditions. It allows for better control and management of water resources.
3. Risk assessment: Assessing the flexibility of a system is essential for evaluating the potential risks associated with changes in the distributor channel discharge. It helps in identifying vulnerable areas and implementing appropriate measures to mitigate any adverse effects.

To summarize, the ratio of the rate of change of discharge of the outlet to the rate of change of discharge of the distributor channel is known as flexibility. It is a measure of the system's sensitivity to changes in the distributor channel discharge and plays a crucial role in design, operation, and risk assessment of hydraulic systems.