Page 499 - Fair, Geyer, and Okun's Water and wastewater engineering : water supply and wastewater removal

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Chapter 13

Hydraulics of Sewer Systems

13.1 NATURE OF FLOW

Hydraulically, wastewater collection differs from water distribution in the following three
essentials: (a) Sewers, although most of them are circular pipes, normally flow only par-
tially filled and hence as open channels; (b) tributary flows are almost always unsteady and
often nonuniform; and (c) sewers are generally required to transport substantial loads of
floating, suspended, and soluble substances with little or no deposition, on the one hand,
and without erosion of channel surfaces on the other hand. To meet the third requirement,
sewer velocities must be self-cleansing yet nondestructive.
As shown in an earlier chapter, the design period for main collectors, interceptors, and
outfalls may have to be as much as 50 years because of the inconvenience and cost of en-
larging or replacing hydraulic structures of this nature in busy city streets. The sizing of
needed conduits becomes complicated if they are to be self-cleansing at the beginning as
well as the end of the design period. Although water distribution systems, too, must meet
changing capacity requirements, their hydraulic balance is less delicate; the water must
transport only itself, so to speak. It follows that velocities of flow in water distribution sys-
tems are important economically rather than functionally and can be allowed to vary over
a wide range of magnitudes without markedly affecting system performance. In contrast,
performance of wastewater systems is tied, more or less rigidly, to inflexible hydraulic gra-
dients and so becomes functionally as well as economically important.

13.2 FLOW IN FILLED SEWERS
In the absence of precise and conveniently applicable information on how channel rough-
ness can be measured and introduced into theoretical formulations of flow in open chan-
nels, engineers continue to base the hydraulic design of sewers, as they do the design of
water conduits, on empirical formulations. Equations common in North American practice
are the Kutter-Ganguillett formula of 1869 and the Manning formula of 1890. In principle,
these formulations evaluate the velocity or discharge coefficient c in the Chézy formula of
1775 in terms of invert slope s (Kutter-Ganguillet only), hydraulic radius r, and a coeffi-
cient of roughness n. The resulting expressions for c are as follows:
-3
(41.65 + 2.81 * 10 >s) + 1.811>n
c Kutter-Ganguillet = (13.1)
-3
(41.65 + 2.81 * 10 >s)(n>r 1>2 ) + 1
c Manning = 1.486 r 1>6 >n (13.2)

Of the two, Manning’s equation is given preference in these pages, because it satisfies
experimental findings fully as well as the mathematically clumsier Kutter-Ganguillet for-
mula. Moreover, it lends itself more satisfactorily to algebraic manipulation and graphical
representation.

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