ABSTRACT
Ordinary differential equations (ODEs) come up in a number of fields in
engineering, For example, in describing sediment transport in streams or in the sea
it is possible to write a differential equation that describes the change in sediment
concentration over the water depth. For the simple case, where the conditions are
constant in the direction along the bed, the concentration can be assumed to vary
only in the vertical, in which case it is possible to write:
ε
wc
dz
dc
−= (13.2)
where c is the concentration, z the vertical axis, w the fall velocity of the particles
and ε the eddy viscosity which is related to the turbulence. The equation comes
directly from Fick’s law that relates the flux of a material to the product of a
there are
direction as
value of
to a more
A typical concentration profile, for the case of uniform conditions in the
horizontal, based on solution of Equation (13.2), is shown in Figure 13.4.
