Problem Diagram

Rain falls at a uniform rate of 2 cm/hr over a 1 km x 1 km field, the water infiltrates into the soil at a rate of 1 cm/hr. At the downstream end of the field, the small channel carries a flow of 0.01 m³/s. If all rates remain constant, determine if ponding occurs.

Rain falls at: i = 2 cm/hr = 0.02 m/hr over an area of
A = 1 km² = 1,000,000 m²

Infiltration rate: 1 cm/hr = 0.01 m/hr

A small channel causes runoff = 0.01 m³/s = 36 m³/hr

For ponding, rainfall must exceed infiltration plus runoff (conservation of mass for a constant density fluid)

     rainfall volume
     = (rainfall intensity)(area) = iA
     = (0.02)(1,000,000) = 20,000 m³/hr

     infiltration volume + runoff volume
     = (0.01)(1,000,000) + 36
     = 10,036 m³/hr

Since rainfall volume > (infiltration volume + runoff volume), ponding will occur at a rate of (20,000 - 10,036) = 9,964 m³/hr

Note: system is not at steady state. For it to be at steady state, the outflow would need to increase to 10,000 m³/hr, at which point there would be zero ponding.