with
c 0 , c 1 , c 2
(c 0 c 1 c 2 1).
In the original Muskingum method Kandx(which are assumed to
be constant for a given channel) are determined empirically from a plot of
VagainstxI(1 x)O(equation (8.39)) selecting the plot which for a
chosen value of xgives the best approximation to a straight line (Vis
determined from the previously known IandOhydrographs). However,
Cunge (1969) has shown that
K∆L/w (8.41a)
and
x0.5 (8.41b)
(wis the average speed of the flood peak Qp,∆Lthe length of the reach, S
the average bed slope and B ̄the average channel width), giving a better
physical interpretation of the routing parameters.
8.7 River improvement
8.7.1 General
The objectives of river improvement works are to aid navigation, to
prevent flooding, to reclaim or protect land or to provide water supply for
irrigation, hydropower development or domestic and industrial use.
The design of river improvements works in general builds upon
the principles discussed in Sections 8.2 and 8.3 and should be based on
fluvial geomorphology and wider river engineering aims (Thorne, Hey and
Newson, 1997) and river mechanics (Hey, 1986; Yalin, 1992; Knighton,
1998; Yalin, Ferreira and da Silva, 2001; Julian, 2002).
It is extremely important in river training to adopt a holistic
approach and to incorporate environmental impact assessment and socio-
economic considerations in any design.
Flood-protectionworks include high-water river training (mainly by
dykes), diversion and flood-relief channels with or without control struc-
tures, and flood-control reservoirs. Flood protection schemes require a
careful cost–benefit analysis to determine a suitable design discharge
which depends on the type of land, structures and property to be protected
Q ̄p
2 SB ̄w∆L
K Kx 0.5∆t
K Kx0.5∆t
Kx0.5∆t
K Kx0.5∆t
Kx 0.5∆t
K Kx0.5∆t
342 RIVER ENGINEERING
