Sediment Movement in Alluvial Rivers - River Dynamics and Integrated River Management - page 279

1

(5.28)

U R

2 / 3

s

1 / 2

n

Manning's n is used in this topic for the discussion of resistance.
For alluvial streams, especially sandy streams, the pattern of roughness is much more complex. The
comprehensive resistance is the result of the joint action of the grain sizes, bed form, banks and
floodplain, channel shape, and human structures. Among the factors contributing to the resistance, several
depend on the flow condition, and not only on the boundary characteristics. In particular, the status of the
bed configuration significantly affects the roughness. The roughness may increase by several hundred
percent for streams with various bed configurations. In such cases, the roughness coefficient is surely not
a constant.
In order to correctly understand the mechanism of resistance in alluvial streams, one must treat the
resistance components individually, i.e. study the relation between them and the flow, and determine how
the components combine together to produce the total resistance to flow in alluvial streams. Similarly, if
the total resistance has been estimated from experimental data, one must also identify each component of
the comprehensive resistance, especially the grain friction. Only then can one calculate the rate of
sediment transport in alluvial streams through the mechanical relation between the grain friction and
sediment movement.
For convenience, a simple river channel with a rectangular cross section of flow area A and wetted
perimeter P ( B+2h ), where B is the width, is considered initially. In a unit distance, due to the boundary
friction to flow, the resistance to the flow is P W 0 , in which, W 0 is the average shear stress on the boundary.

For uniform flow, the energy slope, J , is identical to the bed slope, s , and the flow is not accelerating;
hence

(5.29)
This flow resistance actually has two parts, one is the bank resistance acting on the two bank walls,
expressed by W w , the other is the bed resistance acting on the bed, expressed by W b . The wetted perimeter
of the former is P w = 2 h , and for the latter, P b = B . Both parts can be expressed by a formula similar to Eq.
(5.14) in which the variables correspond to the component parts of the resistance.
As shown in Fig. 5.20, the energy slope is taken as a constant but the hydraulic radius is divided
according to the resistance components. For the above example, the expressions for the bed resistance
and bank resistance are

W J Rs

0

WJ
WJ

RJ
RJ

¾

w w

(5.30)

¿ b b

Fig. 5.20 Division of the energy and resistance. The energy consumed on the left wall ab is from the potential
energy of water body abf . The energy consumed on the bed is from the potential energy of water body bcef . The energy
consumed on the right wall cd is from the water body ced . (after Qian and Wan, 1983)