Urban drainage hydrology: definitions related to peak runoff and time of concentration (Tc) when using the Rational Method for small catchments

Introduction / Context:
For small urban catchments the Rational Method is widely adopted to estimate peak runoff for drainage design. Knowing the correct terminology around peak discharge and time of concentration prevents misuse and improves sizing of sewers, roadside drains, and culverts.

Given Data / Assumptions:

• Small catchment (typically < 50 ha) with relatively uniform rainfall intensity during storm duration.
• Rational formula: Q = C * i * A with consistent units.
• Design intensity i is selected for a duration equal to Tc and chosen return period.

Concept / Approach:

Peak discharge occurs when the entire catchment contributes simultaneously—by definition, when storm duration equals or exceeds Tc. Hence Tc is both the travel time from the remotest point and the time after which full contributing area is effective at the outlet, making statements (c) and (d) equivalent descriptors of the same physical concept.

Step-by-Step Solution:

Verification / Alternative check:

Hydrograph methods (e.g., unit hydrograph) can be used to check peak runoff estimates for complex basins; for small, simple areas, the Rational Method is generally adequate.

Why Other Options Are Wrong:

Each individual statement (a–d) is correct; therefore the complete, correct choice is “All the above”.

Common Pitfalls:

Using i for durations much shorter than Tc (overestimation) or much longer (underestimation); applying the method to large, non-uniform basins.

Final Answer:

All the above.