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 catchment of area $360\text{ km}^2$ is triangular in shape with a base period of $60\text{ hours}$. The peak discharge of the Unit Hydrograph in $\text{m}^3\text{/s}$ is ________ (round off to 1 decimal place).
Answer Key:
33.3
Step-by-Step Solution & Explanation
1. For a 1-cm Unit Hydrograph, the total volume of direct runoff $V$:
$V = A \times 1\text{ cm} = 360 \times 10^6\text{ m}^2 \times 0.01\text{ m} = 3.60 \times 10^6\text{ m}^3$
2. Area of triangular hydrograph:
$\text{Volume} = \frac{1}{2} \times Q_p \times B$
Base period $B = 60\text{ hours} = 60 \times 3600\text{ s} = 216,000\text{ s}$.
$3.60 \times 10^6 = \frac{1}{2} \times Q_p \times 216000 = 108000 Q_p$
$Q_p = \frac{3.60 \times 10^6}{108000} = \frac{3600}{108} = 33.33\text{ m}^3\text{/s} \approx 33.3\text{ m}^3\text{/s}$