Section 4: Soil and Water Conservation Engineering
Hydrology
Subtopic: Infiltration – indices and equations
Question Statement:
The following figure presents the hyetograph for a 3-hour storm. The surface runoff for the event is estimated to be 38 mm. The phi-index for the event in mm h⁻¹ is
Figure (reconstructed): Hyetograph (reconstructed): six 30-min bars at rainfall intensities 10, 30, 40, 50, 25, 8 mm/h over the 180-minute storm, as given in the original question paper.
Options:
(A) 11.50
(B) 14.25
(C) 15.80
(D) 17.25
Official Answer Key:
D
Step-by-Step Solution & Explanation
The hyetograph gives six 30-minute intervals with intensities 10, 30, 40, 50, 25, 8 mm/h. The phi-index is the uniform infiltration-loss rate such that total rainfall in excess of φ, summed over the storm, equals the observed runoff (38 mm). Excess for interval i (only counted where intensity_i > φ) = (intensity_i − φ)×0.5 h. By trial: at φ = 17.25 mm/h, intervals with intensity > φ are 30,40,50,25 mm/h (10 and 8 mm/h are below φ and contribute nothing): excess = [(30−17.25)+(40−17.25)+(50−17.25)+(25−17.25)]×0.5 = [12.75+22.75+32.75+7.75]×0.5 = 76.0×0.5 = 38.0 mm ✓. So φ = 17.25 mm/h, matching option (D).
Practice This in Real CBT Exam Interface
Test yourself with the official TCS-iON palette, virtual calculator, and immediate performance analytics.