Water Hydraulics - Mathematics and Statistics for the Environment - page 600

22.6.2 u niForm and v aried F loW
Flow can be a function of time and location. If the flow quantity is invariant, it is said to be steady.
Uniform flow is flow in which the depth, width, and velocity remain constant along a channel; that
is, if the flow cross-section does not depend on the location along the channel, the flow is said to
be uniform. Varied or nonuniform flow involves a change in these variables, with a change in one
producing a change in the others. Most circumstances of open-channel flow in water and wastewater
systems involve varied flow. The concept of uniform flow is valuable, however, in that it defines a
limit that the varied flow may be considered to be approaching in many cases.

22.6.3 C ritiCal F loW
Critical flow (i.e., flow at the critical depth and velocity) defines a state of flow between two flow
regimes. Critical flow coincides with minimum specific energy for a given discharge and maximum
discharge for a given specific energy. Critical flow occurs in flow measurement devices at or near
free discharges and establishes controls in open-channel flow. Critical flow occurs frequently in
water/wastewater systems and is very important in their operation and design.

22.6.4 p arameters u sed in o pen C hannel F loW
The three primary parameters used in open channel flow are hydraulic radius , hydraulic depth , and
slope ( S ).

22.6.4.1 Hydraulic Radius
The hydraulic radius is the ratio of area in flow to wetted perimeter:

A
P

r

H =

(22.22)

where
r H = Hydraulic radius.
A = Cross-sectional area of the water.
P = Wetted perimeter.

Consider, for example, that in open channels it is of primary importance to maintain the proper
velocity. This is the case, of course, because if velocity is not maintained then flow stops (theoreti-
cally). To maintain velocity at a constant level, the channel slope must be adequate to overcome
friction losses. As with other flows, calculation of head loss at a given flow is necessary, and the
Hazen-Williams equation is useful ( Q = 0.435 × C × d 2.63 × S .54 ). Keep in mind that the concept of
slope has not changed. The difference? We are now measuring, or calculating for, the physical slope
of a channel (ft/ft), equivalent to head loss.
The preceding seems logical and makes sense, but there is a problem. The problem is with the
diameter. In conduits that are not circular (e.g., grit chambers, contact basins, streams, rivers) or in
pipes only partially full (e.g., drains, wastewater gravity mains, sewers), where the cross-sectional
area of the water is not circular, there is no diameter. Without a diameter, what do we do? Another
good question. Because we do not have a diameter in situations where the cross-sectional area of the
water is not circular, we must use another parameter to designate the size of the cross-section and
the amount of it that contacts the sides of the conduit. This is where the hydraulic radius ( r H ) comes
in. The hydraulic radius is a measure of the efficiency with which the conduit can transmit water.
Its value depends on pipe size, and amount of fullness. We use the hydraulic radius to measure how
much of the water is in contact with the sides of the channel or how much of the water is not in
contact with the sides (see Figure 22.5).