THE EFFECT OF FLOW DEPTH
qsR(p,D,d) = MpDd [Fd xpDd]
where MpDd is the mass of p sized particles lifted by into the flow by each drop impact, and Fd is the frequency of the drop impacts within the distance xpDd of the boundary. xpDd = tp u, where tp is the time the particle is suspended in the flow and u is flow velocity. Consequently,
qsR(p,D,d) = MpDd [Fd tp u]
The water layer absorbs energy during drop impact and reduces the energy applied to the underlying surface. The deeper the flow, the more energy absorbed. Flow depth thus influences the amount of material lifted into the flow (MpDd) and the height to which particles are lifted. The height to which particles are lifted affects tp. Alternatively,
qsR(p,D,d) = k(p,D) Id u f[h,d]
where k(p,D) is a coefficient depending on particle size and density when HR=1, Id is the intensity of rain made up of drops of size d, and f[h,d] is a function that varies with flow depth.When flow depth (h) is in mm and drop size (d) is in mm, this function is given by
f[h,d] = h exp (-0.207h)..................................., h < hc
f[h,d= = h exp (-0.207h - bd(h - hc)) ................, h > or = hc
where
hc = 1.017 +4.11 ln (d)
bd = exp (0.585 - 0.387 d)
The equation for sediment concentration (rather than sediment discharge) is
csR(p,D,d) = k(p,D) Id f[h,d]/h
(Kinnell (1993). Sediment concentrations resulting from flow depth/drop size interactions. Trans. A.S.A.E. 36,1099-1103)
The effects of flow depth on f[h,d] and f[h,d]/h are shown in the figures below.
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The common relationship for all drop sizes when h < hc results from the surface of the flow being low enough to restrict the height to which particles can be lifted in the flow.
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RD-RIFT, RD-FT and side-slope erosion
Detachment and transport systems
Effect of previously detached particles (intro)