EROSION BY RAIN IMPACTED FLOW

When a raindrop penetrates the flow to the bed, it lifts particles up into the flow and these particles move down stream with the flow. As particles fall back to the bed they are subjected to horizantal and vertical forces. The major downward force is gravity. Horizantal forces are provided by the flow.

While the distance traveled downstream (x_pz) depends on the height to which a particle is lifted (z), for simplicity consider that each particle of size p travels a distance x_pd as a result of the impact of a drop of size d.

Since the particles move only a distance x_pd after a drop impact, only drop impacts that affect an area within a distance x_pd of a downsteam boundary cause particles of size p to cross that downstream boundary. The sediment discharge of particles of size p and density D being transported by the impact of drops of size d is given by

q_sR(p,D,d) = M_pDd [F_d x_pDd]

where M_pDd is the mass of p sized particles with density D lifted by into the flow by each drop impact, and F_d is the frequency of the drop impacts within the distance x_pDd of the boundary. Since soil is usually made up of particles of different sizes and density, and rain is made up of different sized drops, the sediment discharge is the sum of the values of q_sR(p,D,d) obtained for the various values of p, D and d that occur for the soil and rain.  

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