Rational Method Purpose
The Rational method is a fundamental formula used in hydrology and stormwater management.
Its primary and specific purpose is to estimate the peak runoff rate, which is the maximum flow rate of water expected from a specific drainage area during a rainfall event.
Understanding Peak Runoff Rate
The method calculates the highest instantaneous discharge (flow) that occurs at the outlet of a watershed.
- It does not calculate the total volume of runoff over a period.
- It does not determine the average runoff depth across the area.
- It focuses solely on the maximum flow intensity, crucial for designing drainage structures like culverts, storm sewers, and channels to handle the worst-case scenario.
The commonly used formula is $Q = \frac{CiA}{360}$ (where Q is peak flow in m3/s, C is the runoff coefficient, i is the rainfall intensity in mm/hr, and A is the drainage area in hectares) or $Q = CiA$ (using appropriate unit conversions). The output 'Q' represents the peak runoff rate.
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 - 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 _____________
- A 10 ha watershed received a 4-hour rainfall storm with rainfall intensity of 2, 1, 1.5, and 1 cm.h$^{-1}$ in each subsequent hour, respectively. Assuming phi-index ($\phi$) of 1 cm.h$^{-1}$, the volume of direct runoff, in m$^3$, is _________. (Rounded off to 2 decimal places)
