gen-define-the-unit-hydrograph-and-give-one-short-worked-example-c6b3

Define the unit hydrograph and give one short worked example.

# Unit Hydrograph ## Definition A **unit hydrograph** is the direct runoff hydrograph resulting from 1 unit (typically 1 inch or 1 cm) of effective rainfall (excess rainfall) occurring uniformly over a watershed at a constant rate for a specified duration. ### Key Characteristics: - Represents watershed response to unit depth of excess rainfall - Specific to a particular duration - Assumes linear watershed response - Can be used to derive hydrographs for other rainfall amounts --- ## Worked Example **Problem:** A 6-hour unit hydrograph for a watershed has the following ordinates. Find the direct runoff hydrograph for a storm with 3 cm of excess rainfall. **Given 6-hr Unit Hydrograph:** | Time (hr) | Unit Hydrograph (m³/s) | |-----------|------------------------| | 0 | 0 | | 6 | 20 | | 12 | 40 | | 18 | 30 | | 24 | 15 | | 30 | 0 | **Solution:** Since we have **3 cm of excess rainfall** (instead of 1 cm), we apply the principle of linearity: **Direct Runoff Hydrograph = 3 × Unit Hydrograph** | Time (hr) | Unit Hydrograph (m³/s) | Direct Runoff (m³/s) | |-----------|------------------------|----------------------| | 0 | 0 | 0 × 3 = **0** | | 6 | 20 | 20 × 3 = **60** | | 12 | 40 | 40 × 3 = **120** | | 18 | 30 | 30 × 3 = **90** | | 24 | 15 | 15 × 3 = **45** | | 30 | 0 | 0 × 3 = **0** | **Answer:** The peak discharge is **120 m³/s** at 12 hours.