Science of Water : Concepts and Applications

Water Hydraulics 75
In this section, water passage in open channels, which allow part of the water to be exposed to
the atmosphere, is discussed. This type of channel—an open-fl ow channel—includes natural waterways,
canals, culverts, fl umes, and pipes fl owing under the infl uence of gravity.
CHARACTERISTICS OF OPEN-CHANNEL FLOW
McGhee (1991) points out that basic hydraulic principles apply in open-channel fl ow (with water
depth constant) although there is no pressure to act as the driving force. Velocity head is the only
natural energy this water possesses, and at normal water velocities, this is a small value (V 2 /2g).
Several parameters can be (and often are) used to describe open-channel fl ow. However, we
begin our discussion with a few characteristics including laminar or turbulent, uniform or varied,
and subcritical, critical, or supercritical.
LAMINAR AND TURBULENT FLOW
Laminar and turbulent fl ow in open channels is analogous to that in closed pressurized conduits
(i.e., pipes). It is important to point out, however, that fl ow in open channels is usually turbulent.
In addition, there is no important circumstance in which laminar fl ow occurs in open channels in
either water or wastewater unit processes or structures.
UNIFORM AND VARIED FLOW
Flow can be a function of time and location. If the fl ow quantity is invariant, it is said to be steady.
Uniform fl ow is fl ow in which the depth, width, and velocity remain constant along a channel. That
is, if the fl ow cross section does not depend on the location along the channel, the fl ow is said to be
uniform. Varied or nonuniform fl ow involves a change in these, with a change in one producing a
change in the others. Most circumstances of open-channel fl ow in water/wastewater systems involve
varied fl ow. The concept of uniform fl ow is valuable, however, in that it defi nes a limit that the varied
fl ow may be considered to be approaching in many cases.
√ Note: Uniform channel construction does not ensure uniform fl ow.
CRITICAL FLOW
Critical fl ow (i.e., fl ow at the critical depth and velocity) defi nes a state of fl ow between two fl ow
regimes. Critical fl ow coincides with minimum specifi c energy for a given discharge and maximum
discharge for a given specifi c energy. Critical fl ow occurs in fl ow measurement devices at or near
free discharges, and establishes controls in open-channel fl ow. Critical fl ow occurs frequently in
water/wastewater systems and is very important in their operation and design.
√ Note: Critical fl ow minimizes the specifi c energy and maximizes discharge.
PARAMETERS USED IN OPEN-CHANNEL FLOW
The three primary parameters used in open-channel fl ow are hydraulic radius, hydraulic depth, and
slope, S.
Hydraulic Radius
The hydraulic radius is the ratio of area in fl ow to wetted perimeter.
r
H
A
P
(3.23)