Calculate Direct Runoff Volume using Phi-Index
This solution calculates the direct runoff volume for a given watershed using the phi-index method based on the provided rainfall data.
Watershed Rainfall Analysis
- Watershed Area: 10 ha
- Rainfall Duration: 4 hours
- Rainfall Intensities: $I_1 = 2$ cm/h, $I_2 = 1$ cm/h, $I_3 = 1.5$ cm/h, $I_4 = 1$ cm/h
- Phi-Index ($\phi$): 1 cm/h
Step 1: Determine Effective Rainfall
Calculate the excess rainfall for each hour where intensity ($I$) exceeds the phi-index ($\phi$). The excess rainfall depth is $I - \phi$.
- Hour 1: $I_1 = 2$ cm/h. Since $2 > 1$, Excess = $2 - 1 = 1$ cm.
- Hour 2: $I_2 = 1$ cm/h. Since $1 \le 1$, Excess = 0 cm.
- Hour 3: $I_3 = 1.5$ cm/h. Since $1.5 > 1$, Excess = $1.5 - 1 = 0.5$ cm.
- Hour 4: $I_4 = 1$ cm/h. Since $1 \le 1$, Excess = 0 cm.
The total depth of direct runoff ($R$) is the sum of the hourly excesses: $R = 1 + 0 + 0.5 + 0 = 1.5$ cm.
Step 2: Calculate Runoff Volume
Convert the watershed area and runoff depth to compatible units (meters).
- Area ($A$) = 10 ha = $10 \times 10,000$ m$^2$ = 100,000 m$^2$.
- Runoff Depth ($R$) = 1.5 cm = 0.015 m.
Calculate the volume ($V$) using the formula $V = A \times R$.
$V = 100,000 \text{ m}^2 \times 0.015 \text{ m}$
$V = 1500 \text{ m}^3$.
Result
The volume of direct runoff is 1500 m$^3$.
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 _____________
