Discussion
The time of concentration of a watershed is proportional to?
Answer: B
The time of concentration is proportional to \(S^{-0.385}\).
Kirpich's formula, the one usually taught for small agricultural watersheds, gives
\[ t_c = 0.0195\, L^{0.77} S^{-0.385} \]
with \(t_c\) in minutes, L the maximum length of travel in metres and S the slope. For a given length, \(t_c\) varies as \(S^{-0.385}\): the steeper the watershed, the quicker water reaches the outlet.
The exponent on L is 0.77, not 1.77, so the options with \(L^{1.77}\) are wrong, and \(S^{0.385}\) has the wrong sign, since a steeper slope shortens the time of concentration.
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