1288 WATER FLOW
and momentum are applicable to each subsection individu-
ally as well as to the entire channel cross-section.Composite Roughness EquationThe Reynolds form of the Navier-Stokes equation was used
to develop the shear distribution and the velocity profile
was obtained using the Prandtl-von Karman mixing length
theory. In addition, a channel momentum equation and the
flow resistance formula of Manning were utilised to derive
the relationship for the division surface separating the two
flow subsections as(. )()
066 ()1
1116
12121223R 16
NNNq/
//
//
g /
l
laal−
[] (91)in which R hydraulic radius of entire channel, N 1 , N 2
Manning’s roughness for the bed and cover respectively, g
acceleration due to gravity, l R 1 / R 2 is hydraulic radius
ratio of the bed subsection to the cover subsection, a P 1 / P
is the wetted perimeter ratio of the entire channel to the bed
subsection. The division surface is found by solving for l
using Eq. (91).
The complete roughness, N, of an ice-covered channel
is given byN
NN
N1 53 1
2[] 11 ()al ⎡a() 1 a l^53.
⎣⎢⎤⎦⎥/ / (92)REFERENCES- Ackers, P., Experiments on small streams in alluvium, proceedings,
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S.P. CHEE
University of WindsorFIGURE 14 Ice covered channel.P 221P 1C023_003_r03.indd 1288C023_003_r03.indd 1288 11/18/2005 11:12:15 AM11/18/2005 11:12:15 AM