Watershed Drainage Coefficient Calculation Explained

This problem requires calculating the design discharge for a watershed given its area and drainage coefficient. We need to carefully convert units and apply the appropriate hydrological relationship.

Given Data

• Watershed Area: $A = 720$ ha
• Drainage Coefficient: $C = 1.2$ cm

Objective

Calculate the design discharge ($Q$) in m$^3$/s.

Calculation Steps

1. Convert Area Units: The area is given in hectares (ha), but discharge calculations typically use square meters (m$^2$). The conversion factor is $1 \text{ ha} = 10000 \text{ m}^2$. $A = 720 \text{ ha} \times 10000 \frac{\text{m}^2}{\text{ha}} = 7,200,000 \text{ m}^2$ Alternatively, $A = 7.2 \times 10^6 \text{ m}^2$.
2. Convert Drainage Coefficient Units: The drainage coefficient is given in centimeters (cm), which represents runoff depth. Convert this to meters (m). The conversion factor is $1 \text{ cm} = 0.01 \text{ m}$. Runoff Depth $d = 1.2 \text{ cm} = 1.2 \times 0.01 \text{ m} = 0.012 \text{ m}$.
3. Determine Time Period: The term "drainage coefficient" often implies a runoff depth over a specific time period. Given the context and the typical calculation for average discharge, we assume this depth corresponds to a 24-hour period (1 day). Time Period $T = 1 \text{ day} = 24 \text{ hours} = 24 \times 3600 \text{ seconds} = 86400 \text{ s}$.
4. Calculate Total Runoff Volume: The total volume ($V$) of runoff is the product of the watershed area ($A$) and the runoff depth ($d$). $V = A \times d$ $V = (7.2 \times 10^6 \text{ m}^2) \times (0.012 \text{ m}) = 86400 \text{ m}^3$.
5. Calculate Design Discharge: The average design discharge ($Q$) is the total runoff volume ($V$) divided by the time period ($T$). $Q = \frac{V}{T}$ $Q = \frac{86400 \text{ m}^3}{86400 \text{ s}} = 1.0 \text{ m}^3/\text{s}$.