Section 4: Soil and Water Conservation Engineering
Hydrology
Subtopic: Hydrograph analysis, unit hydrograph theory and application
Question Statement:
Which of the following physical and mathematical assumptions form the basis of Sherman's Unit Hydrograph (UH) theory?
Options:
(A) Linear response: The ordinates of direct runoff are directly proportional to the volume of rainfall excess (principle of superposition and scaling)
(B) Time invariance: The direct runoff response from a given effective rainfall duration is invariable with time of occurrence
(C) Rainfall excess is uniformly distributed throughout the effective duration of the storm across the entire catchment
(D) The base period duration of direct runoff hydrograph is constant for all storms of the specified duration, regardless of rainfall excess depth
Answer Key:
A, B, C, D
Step-by-Step Solution & Explanation
All four statements represent the classic assumptions formulated by L.K. Sherman (1932):
- A: Linear system property (doubling rainfall excess doubles direct runoff ordinates).
- B: Time invariance (catchment transfer function does not drift with season).
- C: Spatial and temporal uniformity of rainfall excess.
- D: Base time $T_b$ of direct runoff is constant for a given duration $D$.