Geoscience Reference
In-Depth Information
channel flows. The Manning equation has the form:
1
n S 0 . o R 0 . 67
v =
(5.7)
h
where R h is the hydraulic radius and S o is the local slope angle. Recall that the hydraulic radius is defined
as the cross-sectional area of the flow, A , divided by the wetted perimeter, P . Thus, for flows that are
wide compared with their depth R h =
A/P
Wh/W
h where W is the width of the flow and h is the
local flow depth. The discharge can then be calculated as
1
n WS 0 . o h 1 . 67
Q
=
vhW
=
(5.8)
This has the general form of the power law storage-discharge relationship used in Box 5.7 (where an
equivalent expression is developed for the Darcy-Weisbach uniform flow equation)
q = bh a
(5.9)
where the specific discharge q
1 . 67. The
kinematic wave velocity or celerity c is equal to the rate of change of discharge with storage (here dq
=
Q/W and, for Manning's equation, b
=
S 0 . o /n and a
=
dh ). It
is an expression of the rate at which the effects of a local disturbance propagate downslope or downstream.
For the power law, c = ( abh 1 a ) and this wave velocity always increases with discharge if a> 1 . For
a = 1, q is a linear function of h and both the flow velocity and the wave speed c are constant with
changing discharge.
Other relationships may show different types of behaviour. Wong and Laurenson (1983) show, for a
number of Australian river reaches, how the form of the relationship between wave speed and flow in a
river channel may change as the flow approaches bankfull discharge and goes overbank (Figure 5.10).
Figure 5.10 Wave speed-discharge relation on the Murrumbidgee River over a reach of 195 km between
Wagga Wagga and Narrandera (after Wong and Laurenson, 1983, with kind permission of the American
Geophysical Union): Q b 1 is the reach flood warning discharge; Q b 2 is the reach bankfull discharge.
Search WWH ::




Custom Search