Page 179 - Water Engineering Hydraulics, Distribution and Treatment

5.7 Location
Air released from the water and trapped at high points
+
Cumulative departures of mean
daily temperatures from 32°F
reduces the waterway, increases friction, and may interrupt
flow unless an air relief valve or vacuum pump is installed.
True siphons should be avoided if possible. However, if the
height of rise above the hydraulic grade is confined to less
0
Freezing index, F
than 20 ft (6 m) and the velocity of flow is kept above 2 ft/s
(0.60 m/s), operating troubles will be few. For best results,
the line should leave the summit at a slope less than that of
the hydraulic gradient.
Time in days
In practice, possible locations of supply conduits are
examined on available maps of the region; the topographic
and geologic sheets of the US Geological Survey are use- Figure 5.24 Determination of the freezing index of soils as the 157
◦
ful examples. Route surveys are then carried into the field. cumulative departure of the mean daily temperature from 323 F.
Topography and geology are confirmed and developed in
needed detail, possibly by aerial surveys, borings, and seis-
the 45th parallel the depth increases to 7 ft (2 m). The follow-
mic exploration. Rights of way, accessibility of proposed
ing equation approximates Shannon’s (1945) observations of
routes, and the nature of obstructions are also identified. The
frost depth:
use of joint rights-of-way with other utilities may generate
economies. d = 1.65F 0.468 (US customary units) (5.41a)
where d is the depth of frozen soil, in.; and F, the freez-
ing index, is the algebraic difference between the maxi-
mum positive and maximum negative cumulative departures,
5.7.2 Vertical and Horizontal Curves
◦
Σ(T − 32), of the daily mean temperatures (T )from32 F.
d d
In long supply lines, changes in direction and grade are Accumulation, as shown in Fig. 5.24, begins with the first day
effected gradually in order to conserve head and avoid unbal- on which a freezing temperature is recorded. In concept, the
anced pressures. Masonry conduits built in place can be freezing index is analogous to the degree day, which describes
brought to any desired degree of curvature by proper form the heat requirements of buildings during the heating season.
work. Cast iron and other sectional pipelines are limited in The authors of this book have developed the following frost
curvature by the maximum angular deflection of standard depth equation using the SI units:
lengths of pipe at which joints will remain tight. The desired 0.468
d = 55.18F (SI units) (5.41b)
curve is built up by the necessary number of offsets from the
tangent. Sharper curves can be formed by shorter or shortened where d is the depth of frozen soil, mm; and F is the freezing
pipes. The smaller the pipe, the sharper can be the deflection. index, which is the algebraic difference between the maxi-
Welded pipelines less than 15 in. (400 mm) in diameter are mum positive and maximum negative cumulative departures,
◦
sufficiently flexible to be bent in the field. The ends of larger Σ(T − 0), of the daily mean temperatures (T ) from 0 C.
d d
steel pipe must be cut at an angle that depends on the type of In the absence of daily readings, the value of F may be
transverse joint, the thickness of the steel plate, and the size approximated, in North America, from the mean monthly
of the pipe. temperatures as follows:
For sharp curves, transitions, and branches, special fit-
F = (32n −ΣT )30.2 (US customary units) (5.42a)
m
tings are often built up or manufactured of the same materials
as the main conduit. F = (0 −ΣT )30.2 (SI units) (5.42b)
m
Here n is the number of months during which the tem-
◦
◦
perature is less than 32 F(0 C); ΣT is the sum of the mean
m
◦
◦
temperatures For C during each of these months; and 30.2
5.7.3 Depth of Cover
is the mean number of days in December, January, February,
Conduits that follow the surface of the ground are generally and March.
laid below the frost line, although the thermal capacity and Pipes laid at depths of 2–3 ft (0.60–0.90 m) are safe
latent heat of water are so great that there is little danger of from extremes of heat and ordinary mechanical damage, but
freezing as long as the water remains in motion. To reduce it is wise to go to 5 ft (1.5 m) in streets or roads open
the external load on large conduits, only the lower half may to heavy vehicles. Otherwise, structural characteristics of
be laid below frost. Along the 42nd parallel of latitude, which conduits determine the allowable depth of cover or weight
describes the southern boundaries of Massachusetts, upper of backfill. Some conduits may have to be laid in open cut
New York, and Michigan in the United States, frost seldom to keep the depth of backfill below the maximum allowable
penetrates more than 5 ft (1.5 m) beneath the surface; along value.