c V 1 [g(y 1 3 ∆y/2∆y^2 /2y 1 )]1/2 (8.16)which for small surges (e.g. in navigation canals) results in
c≈ V 1 [g(y 1 3 ∆y/2)]1/2. (8.17)For the flow velocity V 1 0 and small ∆y, equation (8.17) reduces to
c(gy 1 )1/2(see also Chapter 14).
8.2.3 Sediment transportA full discussion of sediment transport in open channels is clearly outside
the scope of this brief text, but a few fundamental aspects have to be
included here.
From the point of view of source sediment, transport can be divided
into washload comprising very fine material moving in rivers and canals in
suspension and bed material load moving as bedload and suspended load
depending on sediment size and velocity. For river engineering and navi-
gation canals bedload is the important element of sediment transport, as it
determines the morphological erosion and sedimentation aspects; sus-
pended load may be important in river engineering only in reservoir sedi-
mentation and, exceptionally, in sedimentation at canal intakes.
The important properties of sediment and sediment transport are the
sediment size (d), shape, density (^) s(usually 2650 kg m^3 ), fall velocity (ws),
bulk density and porosity, and sediment concentration (C) (volumetric,
ppm, or mg l^1 ). According to size, we usually distinguish clay
(0.5 μmd5 μm), silt (5 μmd60 μm), sand (0.06 mmd2 mm) and
gravel (2 mmd60 mm).
The fall velocity can be approximately expressed by the equation
ws(4gd∆/3CD)1/2 (8.18)
where∆( (^) s )/ andCDis a drag coefficient dependent on the Reynolds
numberRewsd/v. For values of Re1 (very fine sediment) CD24/Re
which leads to Stokes law, while for larger sizes with Re 103 CDbecomes
constant and is a function of grain shape only (usually CD≈1.3 for sand parti-
cles). The fall velocity varies therefore with d1/2tod^2.
The threshold of sediment motion (incipient motion) is given by a
critical value of the shear stress which, for a plane sediment bed, is given
by the Shields criterion:
cc( (^) s )gd (8.19)
where, according to various authors, cvaries between 0.04 and 0.06. The