💧 Rational Formula for Runoff Estimation
The Rational Formula is one of the most widely used methods to estimate the peak rate of runoff from small catchment areas. It is based on the assumption that rainfall intensity is uniform and steady across the drainage area for the duration equal to the time of concentration.
Q = C × i × A
where Q = Peak discharge (m³/s), C = Runoff coefficient, i = Rainfall intensity (mm/hr), A = Catchment area (hectares)
- C (Runoff Coefficient): Depends on the surface type — concrete surfaces have higher values than grassy or soil areas.
- i (Rainfall Intensity): The average rainfall rate (mm/hr) for a storm with a duration equal to the time of concentration.
- A (Area): The total drainage area contributing to runoff, typically measured in hectares.
⚙️ The Rational Method is most accurate for small urban or semi-urban catchments (usually less than 200 hectares).
EXAMPLE
Rainwater Collection (Rational Method)
Given Parameters
- Catchment Area (A):
- Rainfall Intensity (I):
- Rainfall Duration (D):
- Runoff Coefficient (C): 0.95 (for impervious steel roof)
Formula Used (Volume in Liters)
Step 1: Calculate Total Rainfall Depth (R)
Using the relation ( R = Intensity X Duration ):
Convert to meters:
Step 2: Calculate Collected Volume (V) in m³
Step 3: Convert Volume to Liters
Since ( 1m^3 = 1000 Liters):
✅ Total Water Collected:
From a 100 m² steel roof during a light, one-hour rainfall.