Page 164 - Fair, Geyer, and Okun's Water and wastewater engineering : water supply and wastewater removal

JWCL344_ch04_118-153.qxd 8/2/10 9:18 PM Page 126

126 Chapter 4 Quantities of Water and Wastewater Flows
successive saturation estimates L, which are eventually verified graphically by lying
closely in a straight line on a logistic-arithmetic plot. The percentage saturation P is
P 100 y>L 100>[1 p exp(–qt)] and
ln[(100 P)>P] ln p qt
The straight line of best fit by eye has an ordinate intercept ln p and a slope q when
ln[(100 P)>P] is plotted against t or values of n[(100 P)>P] are scaled in either direc-
tion from a 50th percentile or middle ordinate.
Graphical forecasts offer a means of escape from mathematical forecasting. However,
even when mathematical forecasting appears to give meaningful results, most engineers
seek support for their estimates from plots of experienced and projected population growth
on arithmetic or semilogarithmic scales. Trends in rates of growth rather than growth itself
may be examined arithmetically, geometrically, or graphically with fair promise of suc-
cess. Estimates of arithmetic and semilogarithmic straight-line growth of populations and
population trends can be developed analytically by applying least-squares procedures, in-
cluding the determination of the coefficient of correlation and its standard error.
At best, since forecasts of population involve great uncertainties, the probability that
the estimated values turn out to be correct can be quite low. Nevertheless, the engineer
must select values in order to proceed with planning and design of works. To use uncer-
tainty as a reason for low estimates and short design periods can lead to capacities that are
even less adequate than they otherwise frequently turn out to be. Because of the uncertain-
ties involved, populations are sometimes projected at three rates—high, medium, and low.
The economic and other consequences of designing for one rate and having the population
grow at another can then be examined.

4.2.5 Simplified Method for Population Forecasts
The following are two simple equations that are used by consulting engineers for comput-
ing the rate of population increase and the future population forecast:
P P (1 R) n (4.17)
n
o
P P (1 R) n (4.17a)
p
o
where
P n future population
P o present population
P p past population
R probable rate of population increase per year
n number of years considered.
When population data (P , P , and n) for the past are available, the value of R in the
p
o
preceding equations can be computed. In case the rate of population increase per year is
changing, several R values can be calculated in order to obtain an average for the future
population forecast (P ) using the known data (R, P , and n).
o
n
4.2.6 Population Distribution and Area Density
Capacities of water collection, purification, and transmission works and of wastewater outfall
and treatment works are a matter of areal as well as population size. Within communities their
individual service areas, populations, and occupancy are the determinants. A classification of
areas by use and of expected population densities in persons per acre is shown in Table 4.4.
Values of this kind are founded on analyses of present and planned future subdivisions of