A watershed of area 80 ha has a runoff coefficient of 0.3. A storm of intensity $5 \text{ cm h}^{-1}$ occurs for a duration more than the time of concentration of the watershed. The peak discharge in $\text{m}^3 \text{ s}^{-1}$ (rounded off to two decimal places) is _____________________.
Calculating Peak Discharge Using the Rational Method
This problem requires calculating the peak discharge from a watershed during a storm using the Rational Method. The method relates peak flow to watershed area, runoff coefficient, and rainfall intensity.
Identifying Given Parameters
- Watershed Area: $A = 80 \text{ ha}$
- Runoff Coefficient: $C = 0.3$
- Rainfall Intensity: $I = 5 \text{ cm h}^{-1}$
- Storm duration is greater than the time of concentration, ensuring maximum runoff.
Applying the Rational Method Formula
The Rational Method formula, adapted for the given units (Area in hectares, Intensity in cm/h, Discharge in m³/s), is:
$ Q_p = \frac{C \times I \times A}{36} $
Where:
- $Q_p$ = Peak Discharge in $\text{m}^3 \text{ s}^{-1}$
- $C$ = Runoff Coefficient
- $I$ = Average Rainfall Intensity in $\text{cm h}^{-1}$
- $A$ = Watershed Area in ha
Peak Discharge Calculation
Substitute the given values into the formula:
$ Q_p = \frac{0.3 \times 5 \text{ cm h}^{-1} \times 80 \text{ ha}}{36} $
First, calculate the numerator:
$ 0.3 \times 5 \times 80 = 1.5 \times 80 = 120 $
Now, divide by 36:
$ Q_p = \frac{120}{36} \text{ m}^3 \text{ s}^{-1} $
$ Q_p = \frac{10}{3} \text{ m}^3 \text{ s}^{-1} $
$ Q_p \approx 3.333... \text{ m}^3 \text{ s}^{-1} $
Final Answer Rounding
The question asks for the peak discharge rounded to two decimal places.
Rounding $3.333...$ to two decimal places gives $3.33$.
The calculated peak discharge is 3.33 $\text{m}^3 \text{ s}^{-1}$.
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 _____________
