A direct runoff hydrograph of triangular shape, caused by a storm, has a time base of 100 hours and the peak flow of 50 cumec occurring at 30 hours from the start. If the catchment area is 150 km², the rainfall excess of the storm was:
- A5.6 cm
- B6.8 cm
- C7.2 cm
- D6 cmCorrect
Solution
Concept
The area under the direct runoff hydrograph equals the volume of rainfall excess over the catchment.
Formula
Runoff volume = (1/2) × Tb × Qp ; Rainfall excess depth = Volume / Catchment area
Step-by-step solution
1. Time base Tb = 100 h = 100 × 3600 = 360000 s. 2. Volume = (1/2) × 360000 × 50 = 9 × 106 m³. 3. Catchment area A = 150 km² = 150 × 106 m². 4. Rainfall excess depth = 9 × 106 / (150 × 106) = 0.06 m. 5. Depth = 6 cm.
Explanation
The area of the triangular hydrograph gives the total direct runoff volume. Dividing this volume by the catchment area gives the depth of rainfall excess. The time to peak (30 h) is not needed for the volume.
Why the other options are wrong
A, B and C come from wrong unit conversion or wrong area of the triangle; the correct value is 6 cm.
Shortcut
Depth (cm) = 0.36 × Qp × Tb(h) / (2 × A(km²)) = 0.36 × 50 × 100 / 300 = 6 cm.
Common mistake
Forgetting the 1/2 for triangle area or not converting hours to seconds and km² to m².
Correct answer: D) 6 cm