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FLUID MECHANICS - EXAMPLE

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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.

   
  Solution

 

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.

     
   
 
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