The length of overland flow from the critical point to a drain mouth is 13.58 km, and the elevation drop is 10 m. Estimate the inlet time (time of concentration) to the drain using the Kirpich relation. Choose the nearest value.

Introduction / Context:Time of concentration (or inlet time) estimates how long runoff from the hydraulically most distant point takes to reach a drain. Empirical formulas such as Kirpich’s are commonly used when only length and slope are known.

Given Data / Assumptions:

• Length of overland/flow path L = 13.58 km = 13,580 m.
• Elevation drop H = 10 m → bed slope S = H / L.
• Use Kirpich formula in minutes: t_c = 0.01947 * L^0.77 * S^(-0.385), where L in m and S is dimensionless slope.

Concept / Approach:Kirpich's empirical relation links time of concentration to length and slope. Lower slopes and longer lengths increase travel time, raising peak arrival time at the drain.

Step-by-Step Solution:Compute slope S = H / L = 10 / 13,580.Calculate t_c (min) = 0.01947 * (13,580)^0.77 * (S)^(-0.385).Numerically, t_c ≈ 476 minutes.Convert to hours: 476 / 60 ≈ 7.94 hours ≈ 8 hours.

Verification / Alternative check:The very shallow slope (10 m drop over 13.58 km) implies slow runoff—an 8-hour inlet time is plausible. Any steeper slope would reduce the computed time markedly.

Why Other Options Are Wrong:

• 2 h and 4 h: too small for such a long, shallow path.
• 6 h: still underestimates travel time for the given gentle slope.
• 10 h: larger than the Kirpich estimate; not the nearest value.

Common Pitfalls:Mixing units (km vs. m) or confusing H/L with L/H. Always use L in metres and dimensionless slope S = H/L in the formula given.

Final Answer:8 hours.