William Streets outlet sewer at the intersection of Alexander Street and
University Avenue. The tributary drainage area of 132.96 acres is
chiefly a well developed residential district, with a few large buildings
and apartment houses. Most of the dwellings are large and stand rather
close together on lots of medium size. The average density of popula-
tion is about thirty-six per acre. Every street is sewered and graded, and
the roadways are nearly all improved with macadam or gravel, but there
is not a single first-class pavement in the whole district. The soil is gen-
erally of a loamy character, with some clay, gravel and muck in difl"erent
portions; its surface is somewhat undulating, the iDrevailiug slope, how-
ever, being towards the north and east; the average grade of the streets
36 KUICHLING ON" RAINFALL AND DISCHARGE OF SEWERS.
is about 1 in 151, and the sewer grades range from 1 in 51 to 1 in 400.
The outlet sewer is of ordinary rubble masonry, with a flat bottom exca-
vated in the limestone rock and trimmed to the sloi:)e; hence it is not well
adapted to the gauging except when running at considerable de^jths.
From the general character of this district, a relatively large percent-
age of discharge may be expected.
District XVII. — Discharge measured by gauge No. 30 in the Griffith
Street sewer at the intersection of Broadway. The tributary drainage
area of 92.27 acres is well sewered and developed, «,nd the average den-
sity of population may be taken at about 35 per acre. Almost every
street has been improved, about one-fifth of the aggregate length being
paved with asphalt, one-fourth with stone blocks, and the remainder
with macadam and gravel. The territory contains a number of large
business blocks and apartment houses, but the greater portion is occu-
pied by detached residences standing on lots of medium width. In one
district of about twenty-five acres the lots are very deep and afford op-
portunity for additional streets. The soil is mainly a clayey loam; its
surface slopes generally to the south, but in the aggregate one-half of
the whole area is quite flat. The average grade of the streets is 1 in 240,
and the sewer grades vary from 1 in 100 to 1 in 350. The sewerage is
not of the best description, and the outlet has frequently been over-
charged. It is reasonable to infer that the projjortion of rainfall reaching
the sewers is less than in the preceding district.
The foregoing five districts have been selected from the entire num-
ber available because they rej^reseut not only the best developed and
most i3oi)ulous localities on the east side, but also the largest and most
accessible outlet sewers. It is greatly regretted that much doubt with
respect to the bottom slojie of some of the other sewers, or of the same
sewers at other gauges, prevents the iitilization of the records obtained
until such time as the nominal grades may be tested by numerous exca-
vations; but the computations for several of these other districts show
such wide differences and improbabilities as to greatly imjiair their
value ; furthermore, most of these districts include large tracts of agri-
cultural or unimproved territory, and are therefore of minor interest in
connection Avith the discharge from i^opulous areas. The combined
flow from a series of contiguous districts was measured a number of
times by gauges 9 and 10, 11, 12 (a) and 13, and 12 (b) ; but as it was
impracticable to determine each comiionent separately, the gaugings
must necessarily relate to large territories, and can serve only to check
the comi)utations made for the smaller areas in which the essential ele-
ments were known with reasonable certainty. For these reasons only a
KUICHLIlSrG ON" RAINFALL AISTD DISCHARGE OF SEWERS. 37
part of all the records secured are now of use, while the remainder must
be laid aside until the sewer grades can be properly verified hereafter.
Some of the details of the discharge computations for the afore-
said five districts are given in the appended tables, Nos. 5, 6, 7, 8
and 9, while Table No. 10 shows the computed percentages of the
heaviest rainfall so discharged during the period of maximum flow.
To exhibit these important results in more convenient and compact
form, however, they are herewith submitted in the table on the follow-
ing page.
It will be noticed that there are numerous discordances in this
table, most of which can fairly be ascribed to imperfect estimates
of the maximum intensity of the rainfall, while the remainder have
doitbtless arisen from errors made in observing the flood-marks left on
the sewer gauges. Fortunately, however, the data are sufficiently
numerous to admit of comj^arison; and by averaging the results obtained
for similar durations of heavy rain it is probable that the majority of the
discrepancies will be equalized, and that the mean values of the per-
centages of the rainfall so removed by the sewers will afford a clue to
the general laws which govern such discharge. For facilitating the
study of the problem, these average values for each of the dis-
tricts were plotted as ordinates with the corresponding durations
of the maximum rainfall as abscissas, thus obtaining a series
of five somewhat irregular curves shown in Plate Xo. II. ; and
upon carefully examining these diagrams in conjunction with the
explanatory remarks relating to both the rainfall and the sewer
gaugings, the irregularities were corrected or equated by suitably
fitting regular lines or curves to the various points obtained as stated.
These new lines or curves accordingly represent a more or less close
apijroximation to the actual relation of the rainfall to the flood flow in
the sewers of populous districts; and while the numerical results thus
reached may not be absolutely correct, the diagrams nevertheless point
unmistakably to the following general conclusions:
First. — The percentage of the rainfall dischai'ged from any given
drainage area is nearly constant for rains of all considerable intensities
and lasting equal periods of time. This circumstance can be attributed
only to the fact that the amount of impervious surface on a definite
drainage area was also practically constant during the time occupied by
the experiments.
38 KUICHLING ON EAINFALL AND DISCHARGE OF SEWERS.
TABLE E.
Showing the computed percentages of tlie heaviest rainfall discharged
from live different city districts by the resiDective outlet sewers
during the jjeriod of maximum flow, also the average values of such
percentages. Arranged with reference to duration of heaviest
rainfall.
Maximum in-
tensity of rain-
fall, inches per
hour.
Duration of rain at
maximum intensity,
minutes.
Percentages of rainfall discharged.
Date.
Dist. I.— Gauge
2; trib. area,
356.94 acres.
^ S on
c3 ^ (U
rj
» -
5 « Q)
EC 03
§ ^ S
X «i O
â– !?<'"â– "
.;i T-t rH
Q
Dist. XVII.-
Ga u g e 30 ;
trib. area,
92.27 acres.
December 10th, 1887
September 16th, 1888....
0.31*
0.47t
60
50
13.8
19.8
24.1
38.2
58.2
41.6
26.0
37.2
Averages
55
35
30
30
16.8
10.4
10.4
11.0
31.1
26.2
15.5
15.8
58.2
52.1
35.3
41.6
29.0
38.2
29.6
31 6
May 9th, 1888
1.315|to0.75t
0.24*
0.30*
26.0
20 8
Aiiril 5th 1888
Hjay 12th 1888
17.0
â–
30
20
20
10.7
6.3
14.3
15.7
21.1
28.7
35.3
32. 0§
35.2
34.9
13. 2§
35.2
18.9
June 24th 1888
2.62+
0.80*
11. 8§
37.4
June 28th 1888
Averages
20 10.3 1 54.9
33.6
41.2
24.7
24.2
37.5
21.8
18.0
24.6
June 2(1, 1888
0.40t
0.76tt
1.616f
15
15
15
5.5
7.4
4.7
9.0
15.8
12.5
8.71[
19 4
July 11th 1888
August 16th, 1888
19. 1§
Averages
15
13
13
12
.14
5.9
6.8
8 6
4.6
4.0
12.4
14.4
25.911
10.0
12.2
32.9
64.8ir
31.8
33. 5§
25.8
36.iir
18.7
15.0
13. 8§
19.2
May 4th, 1888
0.30*
1.00*
l.OOt
2.50t
28.2ir
11 7
May 26th, 1888
August 4th, 1888
August 26th, 1888
13.8
12. 3§
Averages
13
10
10
6.0
7.6
5.5
12.2
12.2
8.7
32.6 15.8
25.0 14.8
18.4 1 11.9
12 6
July 18th. 1888
0.75*
1.33+
10 3
August 17th, 1888
8.9
Averages
10
6.5
10.4
21.7 13.3
9 6
Probable time required
for concentration of
flow at gauges, min-
44
26
16
23
24
* Preceded and followed by lighter rain.
+ Sudden shower, followed by lighter rain.
1 1 Heavy shower, preceded by lighter rain.
t Intensity roughly eKtimatcd.
§ Sewer here ran under head; percentage is computed from maximum discharge without
head j)revlou8 to surcharge.
H Figures obviously too high or low and rejected in deriving averages.
KUICHLTXG ON" RAINFALL AND DISCHARGE OF SEWERS. 39
Second. — The said percentage varies directly with the degree of urban
development of the district; or, in other words, with the amount of im-
pervious surface thereon. This fact is clearly shown by the large per-
centages derived from the relatively best developed District X, in con-
trast with the smaller percentages obtained from the relatively less im-
proved Districts IX, IV and XVII, and to the still smaller results yielded
by the least improved District I; and it also serves to account for the
constancy of the percentage discharged from any particular district for
rainfalls of the same duration. â–
Third. — The said percentage increases rapidly, and directly or uni-
formly, with the duration of the maximum intensity of the rainfall,
until a period is reached which is equal to the time required for the con-
centration of the drainage waters from the entire tributary area at the
point of observation; but if the rainfall continues at the same intensity
for a longer period, the said percentage will continue to increase for the
additional interval of time at a much smaller rate than previously. This
circumstance is manifestly attributable to the fact that the permeable
surface is gradually becoming saturated and is beginning to shed some
of the water falling u^jon it; or, in other words, the proportion of imper-
vious surface slowly increases with the duration of the rainfall.
Fourth. — The said percentage becomes larger when a moderate rain
has immediately preceded a heavy shower, thereby partially saturating the
permeable territory and correspondingly increasing the extent of imper-
vious surface.
Fifth. — The sewer-discharge varies promptly with all appreciable
fluctuations in the intensity of the rainfall, and thus constitutes an ex-
ceedingly sensitive index of the rain and its variations of intensity.
Sixth. — The diagrams also show that the time when the rate of increase
in the said percentages of discharge changes abruptly from a high to a
low figure, agrees closely with the computed lengths of time required for
the concentration of the storm-waters from the whole tributary area; and
hence the said percentages at such times may be taken as the proportion
of impervious surface upon the respective areas. For example, the
percentage curves for District IV and XVII are seen to be practically
coincident, whence it might be inferred that the projiortions of imper-
vious surface are alike in both ai-eas; as a fact, this conclusion is fully
warranted by an examination of the two territories, which are separated
by a large intermediate area.
40 KUICHLING ON RAINFALL AND DISCHARGE OF SEWERS.
The relation between the maximum sewer-discharge and the rainfall
has thus been approximately established for five different districts in
this city, and it has been seen that the flood-volume stands in direct
Ijroportion to the magnitude of the impervious surface on the drainage
area, and to the intensity and duration of the rain; also that such flood-
volume reaches practically a maximum when the precipitation continues
uniformly for a sufficient length of time to secure the concentration of
the storm-waters from all i3ortions of the area. The element of time,
therefore, enters twice into the determination of the flood-volume, and
from the relation between duration and maximum intensity of the rain-
fall in this locality heretofore established, we may accordingly find the
duration of that particular rainfall for which the sewer-discharge will
become an absolute maximum. With the following notation: (r) = maxi-
mum intensity of the rainfall in inches per hour; (;!)= duration in
minutes of such intensity; (§) = sewer discharge in cubic feet per
second; (A) = magnitude of the entire drainage area in acres; (?») = pro-
portion of imi3ervious surface on said area, which is also substantially
the same as the proportion of the rainfall discharged during the period
of greatest flow; and with (a, b and c)^ certain empirical constants, we
will have —
(1st) Q=mAr;
(2d) 771 = at;
(Sd) r = h — ct;
(4th) q = Aat [b—ct);
and for the usual condition under which (§) will become a maximum,
we obtain:
(5th) Aa (/;— 2 c/) = 0, whence: . 1 = ^^'
But in the foregoing it was shown that the values of the em23irical
constants [b) and (c) were, for rainfalls lasting less than one hour in the
locality of Rochester, b = 2.10 and c = 0.0205; hence the duration (/) of
the heaviest rain which will cause {Q) to become an absolute maximum
is: / = 51 minutes. This solution, however, is to be regarded simply as
a crude ai^jiroximation and valid only imder certain circumstances ; but
it suflBces to show that in drainage areas of moderate size, the heaviest
discharge always occurs when the rain lasts long enough at its maxi-
mum intensity to enable all portions of the area to contribute to the
flow. For large areas, on the other hand, a more elaborate analysis be-
comes necessary in order to find under what conditions the absolute
KUICHLING 0]Sr RAINFALL AND DISCHARGE OF SEWERS. 41
maximum discharge will occur, although the method of procedure
above indicated will remain the same.
The present percentages of the rainfall discharged from the afore-
said urban districts cannot, however, be regarded as permanent, since
improvements are constantly being made by the construction of new
buildings, pavements and sewers ; hence not only is the proportion of
impervious surface on these districts steadily growing, but the time re-
quired for the concentration of the storm-water in the outlet-sewers is
also becoming materially reduced. In planning new sewers, therefore,
it will be necessary to provide for the drainage from districts which,
sooner or later, will be much better developed than any of those de-
scribed above ; and in the absence of more trustworthy data, we may be
justified in concluding that the greatest percentages of discharge from
such improved districts will continue to be practically equal to the i^er-
centages of impervious surface thereon, as was found to be the case
with the five districts described.
The results of the flood gaugings are thus seen to be in general accord
with the above described process, suggested by the writer for com-
puting the necessary capacity of sewers on the "combined" system,
and hence the method may be considered as reasonably accurate. To
indicate what figures the writer adopted in computing the maximum
flow in the several sections of the proi^osed east side trunk sewer, it may
be stated that four different classes of territory were taken into account,
as follows : Class I, with 50 persons per acre and 55 per cent, of imper-
vious surface; Class II, with 40 persons per acre and 46 per cent, of im-
pervious surface; Class III, with 25 persons per acre and 27 per cent, of
impervious surface, and Class IV, with 15 persons per acre and 14 per
cent, of impervious surface. It should also be stated that the central
districts of the city, which will in the future undoubtedly alford a con-
siderably higher percentage of impervious surface than has been as-
signed to Class I, are not embraced in the drainage area of said trunk
sewer ; furthermore, that in the estimate of these percentages a much
better condition of the roadways and i^avements has been assumed than
now i^revails.
In conclusion, it may be of interest to make an application of the
above method and compare the result with the results given by the
four formulas mentioned. For this i^urpose, let us consider District I,
already described, with an area of 360 acres, which may, in the future,
42 KUICHLING ON RAINFALL AND DISCHARGE OF SEWERS.
be constituted as follows : 60 acres of Class I, 90 acres of Class II, 120
acres of Class III, aad 90 acres of Class IV, tlius giving 119.4 acres, or
33 per cent., of impervious surface, and a population of 10 950, or an
average density of about thirty persons per acre ; these conditions -will
doubtless be recognized as'representiug medium urban territory, to which
any of the four formulas are directly applicable; furthermore, let it be
assumed that the time required for the concentration of the storm -waters
at the lower end of this district is : Z = 44 minutes, and that the average
surface elope of the streets is .s= xj u, with sewer grades ranging from
1 in 50 to 1 in 900, the main collector, however, having an average grade
of 1 in 500. For the probable maximum intensity of the rainfall con-
tinuously during forty-four minutes we will have from Equation 3 r
/• — 2.10 — 0.0205 ;( = 1.20 inches per hour (or cubic feet per acre per
second), and hence the volume of storm-water running oflf into the sewers
from the 119 . 4 acres of impervious surface will at first be = 119 .4x1.2
= 143 . 3 cubic feet per second ; but as the rain lasts uniformly for so long
a time, it may be considered that the permeable area has become par-
tially saturated, and will toward the close of the rain be contributing
about 15 per cent, of the precipitation thereon to the sewers, thus
giving an additional. quantity of 240 x 1.2 x 0.15 =43.2 cubic feet per
second, or a total storm-flow of 186.5 cubic feet per second. With a
Avater-supply of 100 gallons per head per day, and one-half of this
amount flowing oflf as sewage uniformly in six hours, the volume of
sewage will be about 3.5 cubic feet per second ; and hence the required
capacity of the sewer at the lower end of said district should be, accord-
ing to the writer's method : Q = 190 cubic feet per second.
On the other hand, we will obtain from Hawksley's formula, which
predicates that r = 1.0, and that (s) is the sine of the slope of the out-
let-sewer, or in this case s = j-Jq:
(1) § = 3.946 A M^ = 68.97 cubic feet per second; or, if the
formula be taken as above transcribed, with ?â– = 1.2 and (s) denoting the
sine of the average surface slo]>e, or s = xixr:
(1*) Q =3.946 Ar 1^ = 106.66 cubic feet per second.
From Biirkli-Ziegler's transcribed formula, with the average value of
the co-efficient = 3.515, /• = 1.2 and s = yj-u. 'we find:
-^'â– ;|7.=
(2) § = 3.515 Ar - = 99.44 cubic feet per second.
kuichlinct on rainfall and discharge of sewers. 43
The difficulty here is to determine what value shall be given to {r),
since Biirkli-Ziegier distinctly states that it should be the maximum which
obtains during the continuance of the storm, and assigns to it for cen-
tral Europe values ranging from 1.75 to 2.75. If an irregular rain last-
ing forty -four minutes be assumed, it is easy to see that a maximum
intensity of 2.40 inches per hour might prevail for a few minutes, with
lesser rates for the remainder of the time, and giving an average of
1.2 inches, as above computed; and with r = 2.40 we would have double
the discharge just computed, or practically the same as the volume cal-
culated by the writer's method.
From Colonel Adams' formula, as transcribed, and which originally
predicates ?• = 1.0 and (s) as denoting the sine of the slope of the sewer,
or in this case, s = -^^-jj, we have:
(3) § = 1.035 A "-^2-= 83.23 cubic feet per second; whereas, if
we use the values r = 1.2 and s = y^o, as before, we will obtain:
(3*) § = 1.035 Ar ^N-ttT2 = 107.05 cubic feet per second.
In like manner we will find from the transcribed McMath formula,
for the average co-eflScient = 2.488 and r = 1.2, with s = tto:
(4) Q = 2A88 Ar . /— = 121.41 cubic feet per second; but if (r)
were taken at the value adopted for St. Louis, i. e., r = 2.75, the dis-
charge would be increased to about 278 cubic feet per second, or nearly
fifty per cent, more than the volume computed by the writer's method.
In the choice of the several processes of estimating the required
capacity of a combined sewer for a populous district, it must be remem-
bered that with the heavy rains of frequent occurrence in this country,
the proportioning of sewers by Hawksley's formula has usually resulted
in floodings, and that an extensive experience with the other formulas
has not yet been gained. The above investigations, moreover, show that
larger quantities of storm-water run ofi" from urban surfaces than is
commonly supposed, and hence it is obvious that a more rational method
of sewer computation is urgently demanded. Much room for improve-
ment in this direction is still left, and it is sincerely hojaed that the
efforts of the >vriter wiU be amply supplemented by many valuable sug-
gestions and experimental data which other members of the Society
may generously contribute.
44 KUICHLIN'G ON RAINFALL AND DISCHARGE OF SEWERS.
O
w
CQ
pi
O
03
P4
5tt
M
o
w
02
O S lO
a â– = s Si
S ° te !=*
S fci f* P
p .2
^S
lO IQ tH (M M
X CO '* t- rH
'^ (*« a; t- 1-H
Ci -* t- « CO
lO CM O C^ GO
CO 1-1 iH tH
(M -W OOO O
OOt-COOr-tOfM'^OOQOlOOO
i-Hi-('*i-l C0CC4OW
t-HXt-c^iOt-t^OTHOOi-i'— ico-ri
â– ^ClOCOC^OOOOi-fi-ICli-IOO-^Ci
> CO i-( iH iH T
•OX-<*t'^OC^-t«'*OOC0O
t
,-( O ** X 1-1
lO X O O ?t -sO c?
C? CI X - O -* -J 1-1
X ^^ O tH X o -^
CO 1-1 C^ '^ ;0 CO
fH OO no t- Oi iH M
O «D X X X O
W rH t- «
r^ Ci X t- t- '^
t- CO (M X X -H
X cs t- t- t- c?
CI "^ «-H 1-1 C- CI
l-O ti t- b- O X
CI 1-1 tr- t f ^
,-H T-l T-t ^ C4 1-1
I CI d CI CI CO
Sec
• DO.
)5 oc
• O o
• *^ ^
|6o
oaa
â– " 5 .2 â–
S -S .S; -w u
OO
^4M
. ^ ° O
0) ^ o -J
^ o a 3
^ — * "^
S S :j o
O 3 3
Pl!
o S
30
3 s i; > >-
^ & -r j^ .^
"' â– '* ^ ^
3 "2 .5 3 j5
o
^ S o ®
•?> 3 > >
P 3
3 d
o
<<â–
^ f>. »-a ♦- -t^
55'
o c
o OS
a .-3 — 2
^^_^ -SS-^'C
ooH^'pCa S S S S S o
>^ S a a
" C "^ »^ b» ^ t-H i-< ^ ^ k^ n >-< t-i t-^ k
■»r
KUICHLING OX RAINFALL AXD DISCHARGE OP SEWERS. 45
4) .-;
60 6E
S £ t- ■"
to M ^ a =s
JJ 3 3 — ^
^ w r* >
So
ca . c8
d ' °
â– ~ HO
O ,c^
a rt "" ^
9 a ^"^
S « c o
a h >ui
." a
ra ,• C8 ,•
3 ^ a ^ 3 >> a
tn' fe a BE «- ?
03—00
S '-'2 g >?
S â– " S -^
Q) O CD s p<
325-=
«■« a
:.2 0.2-^
:'S-£'d g o
: a |3 ai3^3
, o s o p.—
â– a ai;
o O •
o .2 .H 6:
p-i tc >. Ec-S « ^ &
fc, c p o 7- ^ (»>."
a J; a I; *- o g p.
o.S o-S •• fc; S
aci S =S ~ m c« >
3,2 a^ ''S a -a
;oooo^g|«
o ®
>■■a ''• d "-^ a
0:tig.t;oS7;:^
*j '^ -^ "^ i '^ 11''^
o S c
I, g i
a 3 . »
a sJ o tt,o u,
— ' ca 3 o a «
"S a "^ .S "^ .S
|||a|a,2
^ .-g oO OS
i m â– ?; s -3 a ,i^ a
> o S e 2 2 °
- ° i o fti^ "s^.-S
- ^ tn _ 'G '
>.^
®3 «3
,:: a J3 c3
3 g a o
•S P<
a-s a^
o M 3 =a
iCoO
"2 ° .2
o S "S'—
ti ,:h .-^ .^
R Clh
^ " S E
QQ ^ .
a
[ii b (^ Ph
o r- m
sEoS
0)25 a
o
2"°
5«
O (N o
C* C4 « CO
ii C»
l-H ^ CO
CI -H ^H
-H r-< la
1-t tH r-l CI
O t- OJ ^
:i a
ft, c3
iH CO O
C< CI d o
"" a s >•' d 2 t-'' ^ s s" >' > 5 ri
46 KUICHLING ON" RAINFALL AND DISCHARGE OF SEWERS.
o
^25
o
P5
«S 00
00
CO
r-4
I— 1
o
,^
;^i
02
l-H
S
d
o
B
«
(J
Ho
Q
to a sh
Q TO o) . .
Q W
c.2-3.9.2«
-^ e3 t^ ^ c^ a
â– * 3 O O lO lO
O t- — ' CO -H «
T-H O 0^ o o o
o o o o o o
'3 .'S .'3 .'S
-gfc,ai.at. = .=
.-I m c- 00 «o o -.r CJ
oooooooo
ocoooooo
oi ira o o o to
o CO -^ CO :c <-<
O O CO o o o
o o o o o o
o o o o o o
CO O O O CO o
7 I I I I I
s .a