Figure 4.8. Pressure correction (Einstein 1950).
In the preceding calculations for the bed sediment load, the shear velocity is based on the
hydraulic radius of the bed due to grain roughness Rb′. Its computation is explained in the
following paragraph.
Total resistance to flow is composed of two parts, surface drag and form drag. The
transmission of shear to the boundary is accompanied by a transformation of flow energy into
energy turbulence. The part of energy corresponding to grain roughness is transformed into
turbulence that stays at least for a short time in the immediate vicinity of the grains and has a
great effect on the bed load motion. Whereas, the other part of the energy which
corresponds to the form resistance is transformed into turbulence at the interface between
wake and free stream flow, or at a considerable distance away from the grains. This energy
does not contribute to the bed load motion of the particles and may be largely neglected in
the sediment transportation.
Einstein's equation for mean flow velocity V in terms of V*′ is
V / V*′ = 5.75 log(12.26R′ / ∆)
(4.42a)
b
or
V / V*′ = 5.75 log(12.26R′ / k s X)
(4.42b)
b
4.17
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