Land use (%) Soil group Curve number Residential, 40% C 83 Open space- good condition, 25% D 80 Commercial and business, 20% C 94 Industrial, 15% D 93
Runoff Depth Calculation Using SCS Method
This solution details the calculation of runoff depth for a watershed based on given rainfall, land use distribution, soil types, and curve numbers (CN), using the Soil Conservation Service (SCS) method.
Weighted Curve Number Calculation
First, we calculate the weighted average Curve Number ($CN_{avg}$) for the watershed, considering the percentage area and CN for each land use type.
| Land Use | Area (%) | Soil Group | Curve Number (CN) | Weighted CN ($CN \times \%Area$) |
|---|---|---|---|---|
| Residential | 40% | C | 83 | $83 \times 0.40 = 33.2$ |
| Open space | 25% | D | 80 | $80 \times 0.25 = 20.0$ |
| Commercial and business | 20% | C | 94 | $94 \times 0.20 = 18.8$ |
| Industrial | 15% | D | 93 | $93 \times 0.15 = 13.95$ |
| Total Weighted CN ($CN_{avg}$) | $33.2 + 20.0 + 18.8 + 13.95 = 85.95$ | |||
Potential Maximum Retention (S) Calculation
The potential maximum retention ($S$) is calculated using the weighted average Curve Number ($CN_{avg}$). The formula is:
$S = \frac{25400}{CN_{avg}} - 254$
Substituting the calculated $CN_{avg}$:
$S = \frac{25400}{85.95} - 254 \approx 295.52 - 254 = 41.52 \text{ mm}$
Initial Abstraction ($I_a$) Calculation
The initial abstraction ($I_a$) is given as 0.2 times the potential maximum retention ($S$).
$I_a = 0.2 \times S$
$I_a = 0.2 \times 41.52 = 8.304 \text{ mm}$
Runoff Depth (Q) Calculation
The rainfall ($P$) is 152.4 mm. Since $P > I_a$ ($152.4 > 8.304$), runoff occurs. The SCS runoff equation is:
$Q = \frac{(P - I_a)^2}{P - I_a + S}$
Plugging in the values:
$Q = \frac{(152.4 - 8.304)^2}{(152.4 - 8.304) + 41.52}$
$Q = \frac{(144.096)^2}{144.096 + 41.52}$
$Q = \frac{20763.73}{185.616} \approx 111.866 \text{ mm}$
Final Result
Rounding the runoff depth to two decimal places:
$Q \approx 111.87 \text{ mm}$
This value falls within the range specified (111.8 to 112).
Important Questions from Runoff Estimation
- A $0.80\text{ km}^2$ agricultural watershed has a slope of $0.30\%$ and the maximum length of travel of water is $1\text{ km}$. The 10-year maximum depth of rainfall is tabulated below:
Duration (minutes) 5 10 20 30 40 60 Maximum depth of rainfall (mm) 16 24 39 50 60 65
Half of the watershed has row crops (runoff coefficient = $0.40$), whilst the other half of the watershed has pasture (runoff coefficient = $0.35$). The peak flow rate for the watershed (in $\text{m}^3\text{.s}^{-1}$) for the 10-year return period is ________. (Rounded off to two decimal places) - The mass curve of a rainfall event of 100 min duration over a catchment is given in the table.
If the initial loss is 0.6 cm and $\phi$-index is 0.6 cm/hour, the total surface runoff from the catchment is ______ cm (rounded off to one decimal place).Time from start of rainfall (min) 0 20 40 60 80 100 Cumulative rainfall (cm) 0 0.5 1.2 2.6 3.3 3.5 - The Rational method is used to estimate
- A $100 \text{ ha}$ watershed received rainfall at a rate of $5 \text{ cm h}^{-1}$ for $2 \text{ hours}$. If the runoff generated by the storm was at the rate of $1 \text{ m}^3 \text{ s}^{-1}$ for $10 \text{ hours}$, the runoff coefficient for the watershed would be
The Curve Number (CN) of a watershed of $40$ ha area under given hydrologic soil group, land use and management practices, and Antecedent Moisture Condition (AMC)-II is $80$. The initial abstraction is $20$% of maximum retention. For the rainfall event of $40$ mm, the direct runoff in mm (round off to $2$ decimal places) is _____________
