Definition of a unit hydrograph (runoff depth basis) A unit hydrograph is the direct-runoff hydrograph produced by a rainstorm of a specified duration that generates a runoff depth of:
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A5 mm
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B10 mm (i.e., 1 cm)
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C20 mm
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D25 mm
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E30 mm
Answer
Correct Answer: 10 mm (i.e., 1 cm)
Explanation
Introduction / Context:The unit hydrograph (UH) concept is a cornerstone of surface-water hydrology. It represents the time distribution of direct runoff resulting from a unit depth of effective rainfall of a given duration over a catchment.
Given Data / Assumptions:
- Catchment is linear and time-invariant during the event (superposition and proportionality hold approximately).
- “Unit” depth conventionally means 1 cm (10 mm) of effective rainfall excess.
- Specified duration refers to the rainfall excess duration (e.g., 1 hour UH, 4 hour UH).
Concept / Approach:A UH is defined so that its ordinates scale linearly with rainfall excess. If a storm produces D cm of effective rainfall of the same duration, the resulting direct-runoff hydrograph is D times the UH ordinates.
Step-by-Step Solution:
State the definition: “unit” runoff depth is 1 cm = 10 mm.Specify that duration is fixed (e.g., T-hour UH).Thus, the correct option is the depth equal to 10 mm.Verification / Alternative check:Hydrology handbooks and standard texts uniformly adopt 1 cm as the unit runoff depth in metric practice; some analyses may use 1 inch in US customary units.
Why Other Options Are Wrong:
- 5, 20, 25, and 30 mm are not the conventional “unit” depth; they would define non-standard hydrographs.
Common Pitfalls:Confusing rainfall depth (gross) with effective rainfall (excess). The UH is tied to runoff excess after abstraction losses.
Final Answer:10 mm (i.e., 1 cm)