Runoff and Hydrographs MCQ with answer and solution

Concept

Instantaneous Unit Hydrograph

Formula

u(t) = dS/dt or u(t) = (1 / (K × Γ(n))) × (t/K)^n-1 × e^-t/K

Step-by-step solution

This is a conceptual question, so no mathematical calculation is required. Identify that an Instantaneous Unit Hydrograph (IUH) assumes rainfall occurs over an infinitely small duration (D → 0), naturally eliminating the need for uniform rainfall distribution over a storm duration.

Explanation

An Instantaneous Unit Hydrograph (IUH) assumes that rainfall occurs instantly over a time duration approaching zero. Because the rainfall happens in an instant, the standard unit hydrograph assumption that rainfall must be uniformly distributed throughout a storm's duration is not needed.

Shortcut

Remember: "Instant" (IUH) has zero duration, so uniform distribution over "storm duration" is not required.

Common mistake

Many students confuse spatial uniformity with temporal uniformity and incorrectly choose Option A (distribution over the basin) instead of Option B, forgetting that IUH specifically eliminates the duration element (D → 0) rather than the spatial distribution requirement.