Lammers and Bledsoe (2018) based on Bagnold sediment relationship, introduced the unit discharge q defined as
q ¼ Q=w
ð6:156Þ
which is directly related to flow depth
Q
wU
¼
q
U
¼ h
ð6:157Þ
where q is the unit discharge (m
2 s
−1 ), U is the average water flow velocity (ms
−1 ),
w is the channel width (m) and Q is the discharge rate (m
3 s
−1 ). Thus, flow depth
and unit discharge are only equal at a constant velocity. Flow depth is also influenced by surface roughness and this influence is neglected by replacing depth with
unit discharge.
In all this context, Lammers and Bledsoe (2018) based on extensive
meta-analysis and database treatment, proposed two empirical equations for bedload q b (kgm
−1 s
−1 ) and total sediment load transport Q t (ppm) as follows:
q b ¼ a 1 ½x À x c
3=2 D
À1=2
s
q
1=2
ð6:158Þ
and
Q t ¼ a 2 ½x À x c
3=2 D
À1
s q
À5=6
ð6:159Þ
where the coefficient a 1 is 0.0044 if x and x c are expressed in kg m
−1 s
−1 units. The
value of x c , indicative of a threshold of a motion, can be obtained from Eq. (6.155)
by assuming the value of 0.1 for x
Ã
c . In Eq. (6.160), expressing x and x c in kg
m
−1 s
−1 units, the coefficient a 2 is 0.66. These two equations for values of bedload
and total sediments transport rates ranged between 10
–4 and 10
2 kgm
−1 s
−1 and 10
–1
and 10
5 ppm, respectively, showed good agreements, under residual metrics, with
data from direct measurements on available databases and from four alternative
models.
Sensitivity analysis showed that discharge and channel slope had the largest
influence on transport rates either with bedload or with total load sediments. On
transport rates of both loads, channel width, grain size, and x
Ã
c showed having a
small effect only.
Among theoretical approaches for analyzing sediment tQransport in rivers it is
worth mention those developed by Lamb et al. (2008) and Ferguson (2005, 2012).
Lamb et al. (2008) established equations for quantifying the influence of critical
shear stress in fluvial sediment transport on balance equilibrium in the coordinate
system parallel to the streambed between the system forces composed by buoyancy,
6.5 Mass Transfer
227
q ¼ Q=w
ð6:156Þ
which is directly related to flow depth
Q
wU
¼
q
U
¼ h
ð6:157Þ
where q is the unit discharge (m
2 s
−1 ), U is the average water flow velocity (ms
−1 ),
w is the channel width (m) and Q is the discharge rate (m
3 s
−1 ). Thus, flow depth
and unit discharge are only equal at a constant velocity. Flow depth is also influenced by surface roughness and this influence is neglected by replacing depth with
unit discharge.
In all this context, Lammers and Bledsoe (2018) based on extensive
meta-analysis and database treatment, proposed two empirical equations for bedload q b (kgm
−1 s
−1 ) and total sediment load transport Q t (ppm) as follows:
q b ¼ a 1 ½x À x c
3=2 D
À1=2
s
q
1=2
ð6:158Þ
and
Q t ¼ a 2 ½x À x c
3=2 D
À1
s q
À5=6
ð6:159Þ
where the coefficient a 1 is 0.0044 if x and x c are expressed in kg m
−1 s
−1 units. The
value of x c , indicative of a threshold of a motion, can be obtained from Eq. (6.155)
by assuming the value of 0.1 for x
Ã
c . In Eq. (6.160), expressing x and x c in kg
m
−1 s
−1 units, the coefficient a 2 is 0.66. These two equations for values of bedload
and total sediments transport rates ranged between 10
–4 and 10
2 kgm
−1 s
−1 and 10
–1
and 10
5 ppm, respectively, showed good agreements, under residual metrics, with
data from direct measurements on available databases and from four alternative
models.
Sensitivity analysis showed that discharge and channel slope had the largest
influence on transport rates either with bedload or with total load sediments. On
transport rates of both loads, channel width, grain size, and x
Ã
c showed having a
small effect only.
Among theoretical approaches for analyzing sediment tQransport in rivers it is
worth mention those developed by Lamb et al. (2008) and Ferguson (2005, 2012).
Lamb et al. (2008) established equations for quantifying the influence of critical
shear stress in fluvial sediment transport on balance equilibrium in the coordinate
system parallel to the streambed between the system forces composed by buoyancy,
6.5 Mass Transfer
227