Water Hydraulics - Mathematics and Statistics for the Environment - page 601

Wetted
perimeter

Wetted area

FIGURE 22.5 Hydraulic radius. (From Spellman, F.R. and Drinan, J., Water Hydraulics , Technomic,
Lancaster, PA, 2001.)

22.6.4.2 Hydraulic Depth
The hydraulic depth is the ratio of area in flow to the width of the channel at the fluid surface (note
that other names for hydraulic depth are hydraulic mean depth and hydraulic radius ):

A
w

d

H =

(22.23)

where
d h = Hydraulic depth.
a = Area in flow.
w = Width of the channel at the fluid surface.

22.6.4.3 Slope
The slope ( S ) in open-channel equations is the slope of the energy line. If the flow is uniform, the
slope of the energy line will parallel the water surface and channel bottom. In general, the slope can
be calculated from the Bernoulli equation as the energy loss per unit length of channel:

D
D

h
l

S = (22.24)

22.7 OPEN-CHANNEL FLOW CALCULATIONS
The calculation for head loss at a given flow is typically accomplished by using the Hazen-Williams
equation. In addition, in open-channel flow problems, although the concept of slope has not changed,
a problem again rises with the diameter. In pipes only partially full where the cross-sectional area of
the water is not circular, we have no diameter to work with, and the hydraulic radius is used for these
noncircular areas. In the original version of the Hazen-Williams equation, the hydraulic radius was
incorporated. Moreover, similar versions developed by Chezy (pronounced “Shay-zee”), Manning,
and others incorporated the hydraulic radius. For use in open channels, Manning's formula has
become the most commonly used:

15 .

066 . 0 5 .

Q = AR × × s (22.25)

n