Section 4: Soil and Water Conservation Engineering
Hydrology
Subtopic: Hydrograph analysis, unit hydrograph theory and application
Question Statement:
A $4$-hour unit hydrograph of a watershed has a peak discharge of $25\text{ m}^3/\text{s}$. A storm produces $6\text{ cm}$ of total rainfall with a constant $\phi$-index of $0.5\text{ cm/h}$ uniformly over the 4-hour duration. Assuming a constant baseflow of $5\text{ m}^3/\text{s}$, the peak discharge of the resulting flood hydrograph is ________ $\text{m}^3/\text{s}$ (answer in integer).
Answer Key:
105
Step-by-Step Solution & Explanation
1. Infiltration loss during the 4-hour storm:
$\text{Loss} = \phi \times t = 0.5\text{ cm/h} \times 4\text{ h} = 2.0\text{ cm}$
2. Direct Runoff Excess ($ER$):
$ER = P - \text{Loss} = 6.0\text{ cm} - 2.0\text{ cm} = 4.0\text{ cm}$
3. Peak Direct Runoff Hydrograph ($DRH$):
$Q_{p, \text{DRH}} = Q_{p, \text{UH}} \times ER = 25\text{ m}^3/\text{s} \times 4.0 = 100\text{ m}^3/\text{s}$
4. Peak of Total Flood Hydrograph:
$Q_{p, \text{Total}} = Q_{p, \text{DRH}} + \text{Baseflow} = 100 + 5 = 105\text{ m}^3/\text{s}$