101

IWA Publishing 2004

Robert J. Sobey

The concept of uniform flow is traditionally associated with a cross-section-integrated description of

Department of Civil and Environmental

channel flow. In some analyses of flow in wide channels, it may be appropriate to adopt a

Engineering,

Imperial College London,

depth-integrated description. The ensuing lateral structure of the depth-integrated flow is

London SW7 2AZ,

UK

investigated at uniform flow. The steady state ordinary differential equation for the lateral structure

E-mail: *r.j.sobey@imperial.ac.uk*

is established, along with the formulation as a boundary value problem. An integral part of the

formulation is the relationship between the channel resistance models for cross-section-integrated

and depth-integrated descriptions, respectively. Predictions are shown for a rectangular channel and

for an irregular channel.

| uniform flow, natural channels, lateral profile, eddy viscosity

mass and momentum fluxes in both the longitudinal and

Uniform flow in a channel is a flow state that is rarely

lateral directions. The vector momentum equations must

experienced but it is nonetheless influential in character-

also include lateral momentum transfer, without which

izing channel flows. In particular, it has a fundamental

there would be slip at lateral boundaries and no lateral

role in characterizing channel friction. The familiar chan-

boundary layer structure. Channel resistance is here

nel resistance closure models, Chezy, DarcyWeisbach

`

characterized by a bottom friction factor (C or *f *or *n*) to

and Manning, are uniform flow formulae. In steady

represent shear in the vertical and an eddy viscosity *e *to

gradually varied flow, uniform flow is the asymptotic state.

represent shear in the horizontal. Together, the bottom

In unsteady flow, steady gradually varied flow is the local

friction factor and the horizontal eddy viscosity assume

time-averaged flow.

the role of the cross-section-averaged friction factor in the

The traditional analysis of uniform flow is based on a

cross-section-integrated description.

cross-section-integrated description of channel flow. The

A depth-integrated description provides the oppor-

flow is characterized by the cross-section-integrated flow

tunity to predict the lateral flow structure at uniform flow.

As context, this paper will initially review the traditional

is characterized by a constant cross-section-averaged

cross-section-integrated prediction of uniform flow con-

friction factor, C, *f *or *n*, depending on the closure

ditions in a natural channel. It will then consider the

model. At uniform flow, *Q*, the flow cross-section *A*

definition of uniform flow conditions with a depth-

and the water surface slope *∂h*/*∂x *are all constant.

integrated description of channel flow. An ordinary differ-

There is no prediction of flow structure within the cross

ential equation is established to describe the lateral flow

section.

structure *q*x(*y*) at uniform flow. The associated boundary

A depth-integrated description of channel flow pro-

value problem is formulated, and solved numerically. An

vides some flow structure. The flow is characterized by

depth-integrated flows *q*x in the longitudinal direction and

integral part of the analysis is the relationship between the

cross-section-integrated friction factor and the combi-

elevation *h*. The conservation equations must now include

nation of bottom friction factor and horizontal eddy

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