Time of entry (inlet time) estimation: Overland flow from the critical point travels 8 km to the drain with a fall of 12.4 m. Estimate the inlet time from standard overland-flow relations and choose the closest option.

Introduction / Context:

Rainfall–runoff design uses the time of concentration, whose first component can be the overland (sheet) flow travel time, also called inlet time, from the hydraulically most distant point to the drainage inlet. Empirical formulas (e.g., Kirpich-type relations) relate length and slope to travel time for overland or shallow concentrated flow.

Given Data / Assumptions:

• Overland distance L = 8 km = 8000 m.
• Elevation drop ΔH = 12.4 m → slope S = ΔH / L = 12.4 / 8000.
• Use a standard empirical relation for overland/shallow flow; choose the closest option.

Concept / Approach:

A widely used empirical form is: t_min ≈ 0.0195 * L^0.77 * S^-0.385 (with L in metres, S dimensionless). This provides the overland travel time in minutes for typical rural surfaces and shallow flow conditions.

Step-by-Step Solution:

Verification / Alternative check:

The computed time aligns with expectations for a relatively long overland path on a very mild slope. Rounded to the nearest hour, 4 hours is the best match among given options.

Why Other Options Are Wrong:

• 2 or 3 hours: Underestimate travel time for such a long path and mild slope.
• 5 hours: Slight overestimate compared with the empirical output.
• 1 hour: Much too short.

Common Pitfalls:

• Using channel-flow velocities instead of overland-flow relations.
• Failing to convert units consistently.

Final Answer:

4 hours