For a catchment area of 120 km², the equilibrium discharge in m³/hour of an S-curve obtained by the summation of 6 hour unit hydrograph is

Solution (By Examveda Team)

The correct answer is Option A: 0.2 x 10⁶
The question involves understanding S-curve hydrographs and their relationship to unit hydrographs.
An S-curve hydrograph is created by summing an infinite series of unit hydrographs, each lagged by a duration equal to the unit hydrograph duration.
In this case, we have a 6-hour unit hydrograph.
The equilibrium discharge of the S-curve represents the constant rate of runoff when the rainfall continues indefinitely at a rate of 1 cm (or 1 unit) over the basin for the duration of the unit hydrograph.
The equilibrium discharge (Q_eq) is calculated as:
Q_eq = (Area of catchment x Rainfall depth) / Duration of Unit Hydrograph
Where, Area = 120 km² = 120 x 10⁶ m²
Rainfall depth = 1 cm = 0.01 m
Duration = 6 hours
Q_eq = (120 x 10⁶ m² x 0.01 m) / 6 hours
Q_eq = (1.2 x 10⁶ m³) / 6 hours
Q_eq = 0.2 x 10⁶ m³/hour
Therefore, the equilibrium discharge of the S-curve is 0.2 x 10⁶ m³/hour.