If the area of a storm hydrograph corresponds to 102 cm of effective rainfall depth, the ordinates of the 1-cm unit hydrograph are obtained by dividing the storm hydrograph ordinates by which factor?

Introduction: This question checks your understanding of unit hydrograph scaling. A unit hydrograph (UH) is defined as the direct runoff hydrograph (DRH) produced by 1 cm of effective rainfall (excess) uniformly distributed over the catchment for a specified duration.

Given Data / Assumptions:

• The storm (direct runoff) hydrograph integrates to an effective rainfall depth of 102 cm over the basin for the same effective rainfall duration as the desired UH duration.
• We need the 1-cm unit hydrograph.

Concept / Approach: Unit hydrograph linearity states that if a storm produces D cm of effective rainfall, then the corresponding DRH ordinates are D times the ordinates of the 1-cm UH for the same duration. Therefore, the 1-cm UH ordinates are obtained by dividing the DRH ordinates by D.

Step-by-Step Solution: Step 1: Identify the effective rainfall depth D from the storm hydrograph area: D = 102 cm. Step 2: Apply linear scaling: UH_1cm ordinate = DRH ordinate / D. Step 3: Substitute D = 102 to get the divisor as 102.

Verification / Alternative check: If you multiply the obtained 1-cm UH ordinates by 102, you should recover the original storm DRH ordinates, confirming internal consistency (superposition and proportionality).

Why Other Options Are Wrong:

• 51: Would imply D = 51 cm; not given by the problem.
• 10.2: Would correspond to D = 10.2 cm (i.e., 102 mm), which is not the stated value.
• 204: Double the stated D; incorrect.
• 1: Dividing by 1 would leave the storm hydrograph unchanged; it would not be a 1-cm UH.

Common Pitfalls:

• Confusing millimetres and centimetres. Always keep units consistent with the UH definition.
• Trying to change the duration; duration must match between the storm hydrograph and the UH.

Final Answer: 102.