R1/2S"d. (8.27)
In contrast, the critical tractive force theory leads to (equation (8.19))
B"Q0.46, (8.28a)
y"Q0.46, (8.28b)
S"Q^ 0.46 (8.28c)
and
RS"d. (8.29)
Both the régime concept and critical tractive force theory lead to a
relatively weak dependence of velocity on discharge. The régime concept
results in
V"Q1/6 (8.30)
and the critical tractive force theory in
V"Q0.08. (8.31)
Generally, the critical tractive force approach would be more associ-
ated with coarse material (gravel) and upland river reaches, and the
régime concept with fine material in lowland river reaches and canals.
The above relationships apply to changes in cross-section in the
downstream direction. At any one river section different ‘at a station’ rela-
tionships apply. Characteristically, they are (Leopold, Wolman and Miller,
1964)
B"Q0.26, (8.32a)
y"Q0.4, (8.32b)
V"Q0.34, (8.32c)
S"Q0.14. (8.32d)
Braided river reaches are usually steeper, wider, and shallower than indi-
vidual reaches with the same Q; indeed, braiding may be regarded as the
incipient form of meandering (Petersen, 1986).
In a river with constantly changing values of Q, the problem arises as
to what to consider as an appropriate discharge in the above equations.
330 RIVER ENGINEERING
