Wastewater, Volumes and Composition
Log-normally distributed data will be on a straight line when plotted on logarithmic
graph paper with a logarithmically divided x-axis. By plotting, the average (mean
value) and spread can be found. It should be noted that the mean value in a
log-normal distribution does not correspond to a 50 per cent probability, but it must
be calculated from the formula in Table 1.1.
Normal distribution
Log-normal distribution
(straight line on logarithmic graph paper
(straight line on logarithmic graph paper
with normal X-axis)
with logarithmic X-axis)
Mean value,
x = f(SO%)
log X = log f(SO%) + 1.1513. s 2
Spread
s = f(84%)- f(SO%)
s = log (f(84%)) -log (f(SO%))
or
or
s = f(SO%)- f(16%)
s = log (f(SO%)) -log (f(16%))
Table 1.1
Determination of mean value and spread plotted on logarithmic graph paper.
Fig 1.4 shows the plot of the influent measurements for the Sjc:else treatment plant
(Denmark) on a piece of logarithmic graph paper. It is seen that the maximum
hours, Qh,m.m and the diurnal influent can be assumed to be log-normally distributed whereas the maximum seconds values are not on a regular straight line.
In Fig 1.5 the maximum hourly flow to the Ejby Melle treatment plant (Denmark)
has been plotted for a number of dry-weather days. The points are reasonably linear,
and hence they can be assumed to be normally distributed as ordinary logarithmic
graph paper has been used for the plotting. The average maximum hourly flow rate,
Qh,ma~ can be read for 50 per cent probability
Qh,max= 3,175 m 3 /h
% of the hou111, when the wastewater now is less
th
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2600 2800 3000 3200 3400 3600
wastewater now, ah,max
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Ejby Millie Wastewater Treatment Plant Denmar1<
975 - 1978
1
Fig 1.5
Influent Ejby Molle wastewater treatment plant, Odense, (Denmark), data for
dry-weather 24-hour periods /20/.
15