Step 1: Understanding the Concept:
In hydrology, the "time of concentration" (\(T_c\)) is a key parameter used to design drainage systems, estimate peak runoff rates, and construct hydrographs.
It represents the response time of a watershed to a given rainfall event.
Step 2: Detailed Explanation:
The time of concentration is defined as the time required for a drop of water to travel from the hydraulically most distant point in a watershed to the watershed outlet or a specific design point.
When a rainfall event of uniform intensity occurs over a watershed:
- Runoff begins at the outlet from nearby areas.
- As time progresses, runoff from more distant areas reaches the outlet.
- At \(t = T_c\), runoff from the furthest point in the watershed reaches the outlet.
- At this point, the entire watershed is contributing to the flow at the outlet, and peak discharge is achieved under constant rainfall.
Factors affecting the time of concentration include the flow path length, watershed slope, soil permeability, and surface roughness (land cover).
It is mathematically modeled using various empirical equations, such as the Kirpich equation:
\[ T_c = 0.0195 L^{0.77} S^{-0.385} \]
Where \(L\) is the length of the channel and \(S\) is the average slope of the watershed.
Thus, Option (C) is the correct definition.
Step 3: Final Answer:
The correct option is (C).