The Sewerage of Sea Coast Towns
by
Henry C. Adams
Part 1 out of 3
Produced by Tiffany Vergon, Ted Garvin, Charles Franks
and the Online Distributed Proofreading Team.
THE SEWERAGE OF SEA COAST TOWNS
BY
HENRY C. ADAMS
CONTENTS
CHAPTER
I. THE FORMATION OF TIDES AND CURRENTS
II. OBSERVATIONS OF THE RISE AND FALL OF TIDES
III. CURRENT OBSERVATIONS
IV. SELECTION OF SITE FOR OUTFALL SEWER.
V. VOLUME OF SEWAGE
VI. GAUGING FLOW IN SEWERS
VII. RAINFALL
VIII. STORM WATER IN SEWERS
IX. WIND AND WINDMILLS
X. THE DESIGN OF SEA OUTFALLS
XI ACTION OF SEA WATER ON CEMENT
XII. DIVING
XIII. THE DISCHARGE OF SEA OUTFALL SEWERS
XIV. TRIGONOMETRICAL SURVEYING
XV. HYDROGRAPHICAL SURVEYING
PREFACE.
These notes are internal primarily for those engineers who,
having a general knowledge of sewerage, are called upon to
prepare a scheme for a sea coast town, or are desirous of being
able to meet such a call when made. Although many details of
the subject have been dealt with separately in other volumes,
the writer has a very vivid recollection of the difficulties he
experienced in collecting the knowledge he required when he was
first called on to prepare such a scheme, particularly with
regard to taking and recording current and tidal observations,
and it is in the hope that it might be helpful to others in a
similar difficulty to have all the information then obtained,
and that subsequently gained on other schemes, brought together
within a small compass that this book has written.
60, Queen Victoria St,
London, E.C.
CHAPTER I.
THE FORMATION OF TIDES AND CURRENTS.
It has often been stated that no two well-designed sewerage
schemes are alike, and although this truism is usually applied
to inland towns, it applies with far greater force to schemes
for coastal towns and towns situated on the banks of our large
rivers where the sewage is discharged into tidal waters. The
essence of good designing is that every detail shall be
carefully thought out with a view to meeting the special
conditions of the case to the best advantage, and at the least
possible expense, so that the maximum efficiency is combined
with the minimum cost. It will therefore be desirable to
consider the main conditions governing the design of schemes
for sea-coast towns before describing a few typical cases of
sea outfalls. Starting with the postulate that it is essential
for the sewage to be effectually and permanently disposed of
when it is discharged into tidal waters, we find that this
result is largely dependent on the nature of the currents,
which in their turn depend upon the rise and fall of the tide,
caused chiefly by the attraction of the moon, but also to a
less extent by the attraction of the sun. The subject of sewage
disposal in tidal waters, therefore, divides itself naturally
into two parts: first, the consideration of the tides and
currents; and, secondly, the design of the works.
The tidal attraction is primarily due to the natural effect of
gravity, whereby the attraction between two bodies is in direct
proportion to the product of their respective masses and in
inverse proportion to the square of their distance apart; but
as the tide-producing effect of the sun and moon is a
differential attraction, and not a direct one, their relative
effect is inversely as the cube of their distances. The mass of
the sun is about 324,000 times as great as that of the earth,
and it is about 93 millions of miles away, while the mass of
the moon is about 1-80th of that of the earth, but it averages
only 240,000 miles away, varying between 220,000 miles when it
is said to be in perigee, and 260,000 when in apogee. The
resultant effect of each of these bodies is a strong "pull" of
the earth towards them, that of the moon being in excess of
that of the sun as 1 is to 0.445, because, although its mass is
much less than that of the sun, it is considerably nearer to
the earth.
About one-third of the surface of the globe is occupied by
land, and the remaining two-thirds by water. The latter, being
a mobile substance, is affected by this pull, which results in
a banking up of the water in the form of the crest of a tidal
wave. It has been asserted in recent years that this tidal
action also takes place in a similar manner in the crust of the
earth, though in a lesser degree, resulting in a heaving up and
down amounting to one foot; but we are only concerned with the
action of the sea at present. Now, although this pull is felt
in all seas, it is only in the Southern Ocean that a sufficient
expanse of water exists for the tidal action to be fully
developed. This ocean has an average width of 1,500 miles, and
completely encircles the earth on a circumferential line 13,500
miles long; in it the attraction of the sun and moon raises the
water nearest to the centre of attraction into a crest which
forms high water at that place. At the same time, the water is
acted on by the centripetal effect of gravity, which, tending
to draw it as near as possible to the centre of the earth, acts
in opposition to the attraction of the sun and moon, so that at
the sides of the earth 90 degrees away, where the attraction of
the sun and moon is less, the centripetal force has more
effect, and the water is drawn so as to form the trough of the
wave, or low water, at those points. There is also the
centrifugal force contained in the revolving globe, which has
an equatorial diameter of about 8,000 miles and a circumference
of 25,132 miles. As it takes 23 hr. 56 min 4 sec, or, say,
twenty-four hours, to make a complete revolution, the surface
at the equator travels at a speed of approximately 25,132/24 =
1,047 miles per hour. This centrifugal force is always
constant, and tends to throw the water off from the surface of
the globe in opposition to the centripetal force, which tends
to retain the water in an even layer around the earth. It is
asserted, however, as an explanation of the phenomenon which
occurs, that the centripetal force acting at any point on the
surface of the earth varies inversely as the square of the
distance from that point to the moon, so that the centripetal
force acting on the water at the side of the earth furthest
removed from the moon is less effective than that on the side
nearest to the moon, to the extent due to the length of the
diameter of the earth. The result of this is that the
centrifugal force overbalances the centripetal force, and the
water tends to fly off, forming an anti-lunar wave crest at
that point approximately equal, and opposite, to the wave crest
at the point nearest to the moon. As the earth revolves, the
crest of high water of the lunar tide remains opposite the
centre of attraction of the sun and moon, so that a point on
the surface will be carried from high water towards and past
the trough of the wave, or low water, then past the crest of
the anti-lunar tide, or high water again, and back to its
original position under the moon. But while the earth is
revolving the moon has traveled 13 degrees along the elliptical
orbit in which she revolves around the earth, from west to
east, once in 27 days 7 hr. 43 min, so that the earth has to
make a fraction over a complete revolution before the same
point is brought under the centre of attraction again This
occupies on an average 52 min, so that, although we are taught
that the tide regularly ebbs and flows twice in twenty-four
hours, it will be seen that the tidal day averages 24 hr. 52
min, the high water of each tide in the Southern Ocean being at
12 hr. 26 min intervals. As a matter of fact, the tidal day
varies from 24 hr. 35 min at new and full moon to 25 hr. 25 min
at the quarters. Although the moon revolves around the earth in
approximately 27-1/3 days, the earth has moved 27 degrees on
its elliptical orbit around the sun, which it completes once in
365+ days, so that the period which elapses before the moon
again occupies the same relative position to the sun is 29 days
12 hr. 43 min, which is the time occupied by the moon in
completing her phases, and is known as a lunar month or a
lunation.
Considered from the point of view of a person on the earth,
this primary tidal wave constantly travels round the Southern
Ocean at a speed of 13,500 miles in 24 hr. 52 min, thus having
a velocity of 543 miles per hour, and measuring a length of
13,500/2 = 6,750 miles from crest to crest. If a map of the
world be examined it will be noticed that there are three large
oceans branching off the Southern Ocean, namely, the Atlantic,
Pacific, and Indian Oceans; and although there is the same
tendency for the formation of tides in these oceans, they are
too restricted for any very material tidal action to take
place. As the crest of the primary tidal wave in its journey
round the world passes these oceans, the surface of the water
is raised in them, which results in secondary or derivative
tidal waves being sent through each ocean to the furthermost
parts of the globe; and as the trough of the primary wave
passes the same points the surface of the water is lowered, and
a reverse action takes place, so that the derivative waves
oscillate backwards and forwards in the branch oceans, the
complete cycle occupying on the average 12 hr. 26 min Every
variation of the tides in the Southern Ocean is accurately
reproduced in every sea connected with it.
Wave motion consists only in a vertical movement of the
particles of water by which a crest and trough is formed
alternately, the crest being as much above the normal
horizontal line as the trough is below it; and in the tidal
waves this motion extends through the whole depth of the water
from the surface to the bottom, but there is no horizontal
movement except of form. The late Mr. J. Scott Russell
described it as the transference of motion without the
transference of matter; of form without the substance; of force
without the agent.
The action produced by the sun and moon jointly is practically
the resultant of the effects which each would produce
separately, and as the net tide-producing effect of the moon is
to raise a crest of water 1.4 ft above the trough, and that of
the sun is 0.6 ft (being in the proportion of I to 0.445), when
the two forces are acting in conjunction a wave 1.4 + 0.6 = 2
ft high is produced in the Southern Ocean, and when acting in
opposition a wave 1.4 - 0.6 = 0.8 ft high is formed. As the
derivative wave, consisting of the large mass of water set in
motion by the comparatively small rise and fall of the primary
wave, is propagated through the branch oceans, it is affected
by many circumstances, such as the continual variation in width
between the opposite shores, the alterations in the depth of
the channels, and the irregularity of the coast line. When
obstruction occurs, as, for example, in the Bristol Channel,
where there is a gradually rising bed with a converging
channel, the velocity, and/or the amount of rise and fall of
the derivative wave is increased to an enormous extent; in
other places where the oceans widen out, the rise and/or
velocity is diminished, and similarly where a narrow channel
occurs between two pieces of land an increase in the velocity
of the wave will take place, forming a race in that locality.
Although the laws governing the production of tides are well
understood, the irregularities in the depths of the oceans and
the outlines of the coast, the geographical distribution of the
water over the face of the globe and the position and declivity
of the shores greatly modify the movements of the tides and
give rise to so many complications that no general formulae can
be used to give the time or height of the tides at any place by
calculation alone. The average rate of travel and the course of
the flood tide of the derivative waves around the shores of
Great Britain are as follows:--150 miles per hour from Land's
End to Lundy Island; 90 miles per hour from Lundy to St.
David's Head; 22 miles per hour from St. David's Head to Holy
head; 45-1/2 miles per hour from Holyhead to Solway Firth; 194
miles per hour from the North of Ireland to the North of
Scotland; 52 miles per hour from the North of Scotland to the
Wash; 20 miles per hour from the Wash to Yarmouth; 10 miles per
hour from Yarmouth to Harwich. Along the south coast from
Land's End to Beachy Head the average velocity is 40 miles per
hour, the rate reducing as the wave approaches Dover, in the
vicinity of which the tidal waves from the two different
directions meet, one arriving approximately twelve hours later
than the other, thus forming tides which are a result of the
amalgamation of the two waves. On the ebb tide the direction of
the waves is reversed.
The mobility of the water around the earth causes it to be very
sensitive to the varying attraction of the sun and moon, due to
the alterations from time to time in the relative positions of
the three bodies. Fig. [Footnote: Plate I] shows
diagrammatically the condition of the water in the Southern
Ocean when the sun and moon are in the positions occupied at
the time of new moon. The tide at A is due to the sum of the
attractions of the sun and moon less the effect due to the
excess of the centripetal force over centrifugal force. The
tide at C is due to the excess of the centrifugal force over
the centripetal force. These tides are known as "spring" tides.
Fig. 2 [Footnote: Plate I] shows the positions occupied at the
time of full moon. The tide at A is due to the attraction of
the sun plus the effect due to the excess of the centrifugal
force over the centripetal force. The tide at C is due to the
attraction of the moon less the effect due to the excess of the
centripetal force over centrifugal force. These tides are also
known as "spring" tides. Fig. 3 [Footnote: Plate I] shows the
positions occupied when the moon is in the first quarter; the
position at the third quarter being similar, except that the
moon would then be on the side of the earth nearest to B, The
tide at A is compounded of high water of the solar tide
superimposed upon low water of the lunar tide, so that the sea
is at a higher level than in the case of the low water of
spring tides. The tide at D is due to the attraction of the
moon less the excess of centripetal force over centrifugal
force, and the tide at B is due to the excess of centrifugal
force over centripetal force. These are known as "neap" tides,
and, as the sun is acting in opposition to the moon, the height
of high water is considerably less than at the time of spring
tides. The tides are continually varying between these extremes
according to the alterations in the attracting forces, but the
joint high tide lies nearer to the crest of the lunar than of
the solar tide. It is obvious that, if the attracting force of
the sun and moon were equal, the height of spring tides would
be double that due to each body separately, and that there
would be no variation in the height of the sea at the time of
neap tides.
It will now be of interest to consider the minor movements of
the sun and moon, as they also affect the tides by reason of
the alterations they cause in the attractive force. During the
revolution of the earth round the sun the successive positions
of the point on the earth which is nearest to the sun will form
a diagonal line across the equator. At the vernal equinox
(March 20) the equator is vertically under the sun, which then
declines to the south until the summer solstice (June 21), when
it reaches its maximum south declination. It then moves
northwards, passing vertically over the equator again at the
autumnal equinox (September 21), and reaches its maximum
northern declination on the winter solstice (December 21). The
declination varies from about 24 degrees above to 24 degrees
below the equator. The sun is nearest to the Southern Ocean,
where the tides are generated, when it is in its southern
declination, and furthest away when in the north, but the sun
is actually nearest to the earth on December 31 (perihelion)
and furthest away on July I (aphelion), the difference between
the maximum and minimum distance being one-thirtieth of the
whole.
The moon travels in a similar diagonal direction around the
earth, varying between 18-1/2 degrees and 28-1/2 degreed above
and below the equator. The change from north to south
declination takes place every fourteen days, but these changes
do not necessarily take place at the change in the phases of
the moon. When the moon is south of the equator, she is nearer
to the Southern Ocean, where the tides are generated. The new
moon is nearest to the sun, and crosses the meridian at midday,
while the full moon crosses it at midnight.
The height of the afternoon tide varies from that of the
morning tide; sometimes one is the higher and sometimes the
other, according to the declination of the sun and moon. This
is called the "diurnal inequality." The average difference
between the night and morning tides is about 5 in on the east
coast and about 8in on the west coast. When there is a
considerable difference in the height of high water of two
consecutive tides, the ebb which follows the higher tide is
lower than that following the lower high water, and as a
general rule the higher the tide rises the lower it will fall.
The height of spring tides varies throughout the year, being at
a maximum when the sun is over the equator at the equinoxes and
at a minimum in June at the summer solstice when the sun is
furthest away from the equator. In the Southern Ocean high
water of spring tides occurs at mid-day on the meridian of
Greenwich and at midnight on the 180 meridian, and is later on
the coasts of other seas in proportion to the time taken for
the derivative waves to reach them, the tide being about three-
fourths of a day later at Land's End and one day and a half
later at the mouth of the Thames. The spring tides around the
coast of England are four inches higher on the average at the
time of new moon than at full moon, the average rise being
about 15 ft, while the average rise at neaps is 11 ft 6 in.
The height from high to low water of spring tides is
approximately double that of neap tides, while the maximum
height to which spring tides rise is about 33 per cent. more
than neaps, taking mean low water of spring tides as the datum.
Extraordinarily high tides may be expected when the moon is new
or full, and in her position nearest to the earth at the same
time as her declination is near the equator, and they will be
still further augmented if a strong gale has been blowing for
some time in the same direction as the flood tide in the open
sea, and then changes when the tide starts to rise, so as to
blow straight on to the shore. The pressure of the air also
affects the height of tides in so far as an increase will tend
to depress the water in one place, and a reduction of pressure
will facilitate its rising elsewhere, so that if there is a
steep gradient in the barometrical pressure falling in the same
direction as the flood tide the tides will be higher. As
exemplifying the effect of violent gales in the Atlantic on the
tides of the Bristol Channel, the following extract from "The
Surveyor, Engineer, and Architect" of 1840, dealing with
observations taken on Mr. Bunt's self-registering tide gauge at
Hotwell House, Clifton, may be of interest.
Date: Times of High Water. Difference in
Jan 1840. Tide Gauge. Tide Table. Tide Table.
H.M. H.M.
27th, p.m....... 0. 8 ....... 0. 7 ..... 1 min earlier.
28th, a.m....... 0.47 ....... 0.34 ..... 13 min earlier.
28th, p.m....... 11.41 ....... 1. 7 ..... 86 min later.
29th, a.m....... 1.29 ....... 1.47 ..... 18 min later.
29th, p.m....... 2.32 ....... 2.30 ..... 2 min earlier.
Although the times of the tides varied so considerably, their
heights were exactly as predicted in the tide-table.
The records during a storm on October 29, 1838, gave an
entirely different result, as the time was retarded only ten or
twelve minutes, but the height was increased by 8 ft On another
occasion the tide at Liverpool was increased 7 ft by a gale.
The Bristol Channel holds the record for the greatest tide
experienced around the shores of Great Britain, which occurred
at Chepstow in 1883, and had a rise of 48 ft 6 in The
configuration of the Bristol Channel is, of course, conducive
to large tides, but abnormally high tides do not generally
occur on our shores more frequently than perhaps once in ten
years, the last one occurring in the early part of 1904,
although there may foe many extra high ones during this period
of ten years from on-shore gales. Where tides approach a place
from different directions there may be an interval between the
times of arrival, which results in there being two periods of
high and low water, as at Southampton, where the tides approach
from each side of the Isle of Wight.
The hour at which high water occurs at any place on the coast
at the time of new or full moon is known as the establishment
of that place, and when this, together with the height to which
the tide rises above low water is ascertained by actual
observation, it is possible with the aid of the nautical
almanack to make calculations which will foretell the time and
height of the daily tides at that place for all future time. By
means of a tide-predicting machine, invented by Lord Kelvin,
the tides for a whole year can be calculated in from three to
four hours. This machine is fully described in the Minutes of
Proceedings, Inst.C.E., Vol. LXV. The age of the tide at any
place is the period of time between new or full moon and the
occurrence of spring tides at that place. The range of a tide
is the height between high and low water of that tide, and the
rise of a tide is the height between high water of that tide
and the mean low water level of spring tides. It follows,
therefore, that for spring tides the range and rise are
synonymous terms, but at neap tides the range is the total
height between high and low water, while the rise is the
difference between high water of the neap tide and the mean low
water level of spring tides. Neither the total time occupied by
the flood and ebb tides nor the rate of the rise and fall are
equal, except in the open sea, where there are fewer disturbing
conditions. In restricted areas of water the ebb lasts longer
than the flood.
Although the published tide-tables give much detailed
information, it only applies to certain representative ports,
and even then it is only correct in calm weather and with a
very steady wind, so that in the majority of cases the engineer
must take his own observations to obtain the necessary local
information to guide him in the design of the works. It is
impracticable for these observations to be continued over the
lengthy period necessary to obtain the fullest and most
accurate results, but, premising a general knowledge of the
natural phenomena which affect the tides, as briefly described
herein, he will be able to gauge the effect of the various
disturbing causes, and interpret the records he obtains so as
to arrive at a tolerably accurate estimate of what may be
expected under any particular circumstances. Generally about 25
per cent. of the tides in a year are directly affected by the
wind, etc., the majority varying from 6 in to 12 in in height
and from five to fifteen minutes in time. The effect of a
moderately stiff gale is approximately to raise a tide as many
inches as it might be expected to rise in feet under normal
conditions. The Liverpool tide-tables are based on observations
spread over ten years, and even longer periods have been
adopted in other places.
Much valuable information on this subject is contained in the
following books, among others--and the writer is indebted to
the various authors for some of the data contained in this and
subsequent chapters--"The Tides," by G. H. Darwin, 1886;
Baird's Manual of Tidal Observations, 1886; and "Tides and
Waves," by W. H. Wheeler, 1906, together with the articles in
the "Encyclopaedia Britannica" and "Chambers's Encyclopaedia."
Chapter II
Observations of the rise and fall of tides.
The first step in the practical design of the sewage works is
to ascertain the level of high and low water of ordinary spring
and neap tides and of equinoctial tides, as well as the rate of
rise and fall of the various tides. This is done by means of a
tide recording instrument similar to Fig. 4, which represents
one made by Mr. J. H. Steward, of 457, West Strand, London,
W.C. It consists of a drum about 5 in diameter and 10 in high,
which revolves by clockwork once in twenty-four hours, the same
mechanism also driving a small clock. A diagram paper divided
with vertical lines into twenty-four primary spaces for the
hours is fastened round the drum and a pen or pencil attached
to a slide actuated by a rack or toothed wheel is free to work
vertically up and down against the drum. A pinion working in
this rack or wheel is connected with a pulley over which a
flexible copper wire passes through the bottom of the case
containing the gauge to a spherical copper float, 8 inches
diameter, which rises and falls with the tide, so that every
movement of the tide is reproduced moment by moment upon the
chart as it revokes. The instrument is enclosed in an ebonized
cabinet, having glazed doors in front and at both sides, giving
convenient access to all parts. Inasmuch as the height and the
time of the tide vary every day, it is practicable to read
three days' tides on one chart, instead changing it every day.
When the diagrams are taken of, the lines representing the
water levels should be traced on to a continuous strip of
tracing linen, so that the variations can be seen at a glance
extra lines should be drawn, on the tracing showing the time at
which the changes of the moon occur.
Fig. 5 is a reproduction to a small scale of actual records
taken over a period of eighteen days, which shows true
appearance of the diagrams when traced on the continuous strip.
These observations show very little difference between the
spring and neap tides, and are interesting as indicating the
unreliability of basing general deductions upon data obtained
during a limited period only. At the time of the spring tides
at the beginning of June the conditions were not favourable to
big tides, as although the moon was approaching her perigee,
her declination had nearly reached its northern limit and the
declination of the sun was 22 IN The first quarter of the moon
coincided very closely with the moon's passage over the
equator, so that the neaps would be bigger than usual. At the
period of the spring: tides, about the middle of June, although
the time of full moon corresponded with her southernmost
declination, she was approaching her apogee, and the
declination of the sun was 23 16' N., so that the tides would
be lower than usual.
In order to ensure accurate observations, the position chosen
for the tide gauge should be in deep water in the immediate
vicinity of the locus in quo, but so that it is not affected by
the waves from passing vessels. Wave motion is most felt where
the float is in shallow water. A pier or quay wall will
probably be most convenient, but in order to obtain records of
the whole range of the tides it is of course necessary that the
float should not be left dry at low water. In some instances
the float is fixed in a well sunk above high water mark to such
a depth that the bottom of it is below the lowest low water
level, and a small pipe is then laid under the beach from the
well to, and below, low water, so that the water stands
continuously in the well at the same level as the sea.
The gauge should be fixed on bearers, about 3 ft 6 in from the
floor, in a wooden shed, similar to a watchman's box, but
provided with a door, erected on the pier or other site fixed
upon for the observations. A hole must be formed in the floor
and a galvanized iron or timber tube about 10 in square
reaching to below low water level fixed underneath, so that
when the float is suspended from the recording instrument it
shall hang vertically down the centre of the tube. The shed
and tube must of course be fixed securely to withstand wind and
waves. The inside of the tube must be free from all projections
or floating matter which would interfere with the movements of
the float, the bottom should be closed, and about four lin
diameter holes should be cleanly formed in the sides near to
the bottom for the ingress and egress of the water. With a
larger number of holes the wave action will cause the diagram
to be very indistinct, and probably lead to incorrectness in
determining the actual levels of the tides; and if the tube is
considerably larger than the float, the latter will swing
laterally and give incorrect readings.
A bench mark at some known height above ordnance datum should
be set up in the hut, preferably on the top of the tube. At
each visit the observer should pull the float wire down a short
distance, and allow it to return slowly, thus making a vertical
mark on the diagram, and should then measure the actual level
of the surface of the water below the bench mark in the hut, so
that the water line on the chart can be referred to ordnance
datum. He should also note the correct time from his watch, so
as to subsequently rectify any inaccuracy in the rate of
revolution of the drum.
The most suitable period for taking these observations is from
about the middle of March to near the end of June, as this will
include records of the high spring equinoctial tides and the
low "bird" tides of June. A chart similar to Fig. 6 should be
prepared from the diagrams, showing the rise and fall of the
highest spring tides, the average spring tides, the average
neap tides, and the lowest neap tides, which will be found
extremely useful in considering the levels of, and the
discharge from, the sea outfall pipe.
The levels adopted for tide work vary in different ports.
Trinity high-water mark is the datum adopted for the Port of
London by the Thames Conservancy; it is the level of the lower
edge of a stone fixed in the face of the river wall upon the
east side of the Hermitage entrance of the London Docks, and is
12 48 ft above Ordnance datum. The Liverpool tide tables give
the heights above the Old Dock Sill, which is now non-existent,
but the level of it has been carefully preserved near the same
position, on a stone built into the western wall of the Canning
Half Tide Dock. This level is 40 ft below Ordnance datum. At
Bristol the levels are referred to the Old Cumberland Basin
(O.C.B.), which is an imaginary line 58 ft below Ordnance
datum. It is very desirable that for sewage work all tide
levels should be reduced to Ordnance datum.
A critical examination of the charts obtained from the tide-
recording instruments will show that the mean level of the sea
does not agree with the level of Ordnance datum. Ordnance datum
is officially described as the assumed mean water level at
Liverpool, which was ascertained from observations made by the
Ordnance Survey Department in March, 1844, but subsequent
records taken in May and June, 1859, by a self-recording gauge
on St. George's Pier, showed that the true mean level of the
sea at Liverpool is 0.068 ft below the assumed level. The
general mean level of the sea around the coast of England, as
determined by elaborate records taken at 29 places during the
years 1859-60, was originally said to be, and is still,
officially recognised by the Ordnance Survey Department to be
0.65 ft, or 7.8 in, above Ordnance datum, but included in these
29 stations were 8 at which the records were admitted to be
imperfectly taken. If these 8 stations are omitted from the
calculations, the true general mean level of the sea would be
0.623 ft, or 7.476 in, above Ordnance datum, or 0.691 ft above
the true mean level of the sea at Liverpool. The local mean
seal level at various stations around the coast varies from
0.982 ft below the general mean sea level at Plymouth, to 1.260
ft above it at Harwich, the places nearest to the mean being
Weymouth (.089 ft below) and Hull (.038 ft above).
It may be of interest to mention that Ordnance datum for
Ireland is the level of low water of spring tides in Dublin
Bay, which is 21 ft below a mark on the base of Poolbeg
Lighthouse, and 7.46 ft below English Ordnance datum.
The lines of "high and low water mark of ordinary tides" shown
upon Ordnance maps represent mean tides; that is, tides halfway
between the spring and the neap tides, and are generally
surveyed at the fourth tide before new and full moon. The
foreshore of tidal water below "mean high water" belongs to the
Crown, except in those cases where the rights have been waived
by special grants. Mean high water is, strictly speaking, the
average height of all high waters, spring and neap, as
ascertained over a long period. Mean low water of ordinary
spring tides is the datum generally adopted for the soundings
on the Admiralty Charts, although it is not universally adhered
to; as, for instance, the soundings in Liverpool Bay and the river
Mersey are reduced to a datum 20 ft below the old dock sill, which
is 125 ft below the level of low water of ordinary spring tides.
The datum of each chart varies as regards Ordnance datum, and in the
case of charts embracing a large area the datum varies along the coast.
The following table gives the fall during each half-hour of the
typical tides shown in Fig, 6 (see page 15), from which it will
be seen that the maximum rate occurs at about half-tide, while
very little movement takes place during the half-hour before
and the half-hour after the turn of the tide:--
Table I.
Rate of fall of tides.
State of Eqionoctial Ordinary Ordinary Lowest
Tide. Tides. Spring Tides. Neap Tides. Neap Tides.
High water -- -- -- --
1/2 hour after 0.44 0.40 0.22 0.19
1 " " 0.96 0.80 0.40 0.31
1-1/2 " " 1.39 1.14 0.68 0.53
2 " " 1.85 1.56 0.72 0.59
2-1/2 " " 1.91 1.64 0.84 0.68
3 " " 1.94 1.66 0.86 0.70
3-1/2 " " 1.94 1.66 0.86 0.70
4 " " 1.91 1.64 0.84 0.68
4-1/2 " " 1.35 1.16 0.59 0.48
5 " " 1.27 1.09 0.57 0.46
5-1/2 " " 1.06 0.91 0.47 0.38
6 " " 1.04 0.89 0.46 0.37
6-1/2 " " 0.53 0.45 0.24 0.18
Totals.... 17 ft 6 in 15 ft 0 in 7 ft 9 in 6 ft 3 in
The extent to which the level of high water varies from tide to
tide is shown in Fig. 7 [Footnote: Plate III.], which embraces
a period of six months, and is compiled from calculated heights
without taking account of possible wind disturbances.
The varying differences between the night and morning tides are
shown very clearly on this diagram; in some cases the night
tide is the higher one, and in others the morning tide; and while
at one time each successive tide is higher than the preceding one,
at another time the steps showing: the set-back of the tide are
very marked. During the earlier part of the year the spring-tides
at new moon were higher than those at full moon, but towards June
the condition became reversed. The influence of the position of the
sun and moon on the height of the tide is apparent throughout,
but is particularly marked during the exceptionally low spring
tides in the early part of June, when the time of new moon
practically coincides with the moon in apogee and in its most
northerly position furthest removed from the equator.
Inasmuch as the tidal waves themselves have no horizontal
motion, it is now necessary to consider by what means the
movement of water along the shores is caused. The sea is, of
course, subject to the usual law governing the flow of water,
whereby it is constantly trying to find its own level. In a
tidal wave the height of the crest is so small compared with
the length that the surface gradient from crest to trough is
practically flat, and does not lead to any appreciable
movement; but as the tidal wave approaches within a few miles
of the shore, it runs into shallow water, where its progress is
checked, but as it is being pushed on from behind it banks up
and forms a crest of sufficient height to form a more or less
steep gradient, and to induce a horizontal movement of the
particles of water throughout the whole depth in the form of a
tidal current running parallel with the shore.
The rate of this current depends upon the steepness of the
gradient, and the momentum acquired will, In some Instances,
cause the current to continue to run in the same direction for
some time after the tide has turned, i.e., after the direction
of the gradient has been reversed; so that the tide may be
making--or falling--in one direction, while the current is
running the opposite way. It will be readily seen, then, that
the flow of the current will be slack about the time of high
and low water, so that its maximum rate will be at half-ebb and
half-flood. If the tide were flowing into an enclosed or semi-
enclosed space, the current could not run after the tide
turned, and the reversal of both would be simultaneous, unless,
indeed, the current turned before the tide.
Wind waves are only movements of the surface of the water, and
do not generally extend for a greater depth below the trough of
the wave than the crest is above it, but as they may affect the
movement of the floating particles of sewage to a considerable
extent it is necessary to record the direction and strength of
the wind.
The strength of the wind is sometimes indicated wind at the
time of making any tidal observations. By reference to the
Beaufort Scale, which is a graduated classification adopted by
Admiral Beaufort about the year 1805. The following table gives
the general description, velocity, and pressure of the wind
corresponding to the tabular numbers on the scale:--
[Illustration: PLATE III
PERIOD OF SIX MONTHS.
To face page 20]
The figures indicating the pressure of the wind in the
foregoing table are low compared with those given by other
authorities. From Mutton's formula, the pressure against a
plane surface normal to the wind would be 0.97 lb per sq. foot,
with an average velocity of 15 miles per hour (22 ft per sec.),
compared with o.67 lb given by Admiral Beaufort, and for a
velocity of 50 miles per hour (73.3 ft per sec.) 10.75 lb,
compared with 7.7lb Semitone's formula, which is frequently
used, gives the pressure as 0.005V^2 (miles per hour), so that
for 15 miles per hour velocity the pressure would be 1.125 lb,
and for 50 miles it would be l2.5 lb It must not be forgotten,
however, that, although over a period of one hour the wind may
_average_ this velocity or pressure, it will vary considerably
from moment to moment, being far in excess at one time, and
practically calm at another. The velocity of the wind is
usually taken by a cup anemometer having four 9 in cups on arms
2 ft long. The factor for reducing the records varies from 2 to
3, according to the friction and lubrication, the average being
2.2.
The pressure is obtained by multiplying the Beaufort number
cubed by 0.0105; and the velocity is found by multiplying the
square root of the Beaufort number cubed by 1.87.
A tidal wave will traverse the open sea in a straight line, but
as it passes along the coast the progress of the line nearest
the shore is retarded while the centre part continues at the
same velocity, so that on plan the wave assumes a convex shape
and the branch waves reaching the shore form an acute angle
with the coast line.
CHAPTER III.
CURRENT OBSERVATIONS.
There is considerable diversity in the design of floats
employed in current observations, dependant to some extent upon
whether it is desired to ascertain the direction of the surface
drift or of a deep current, it does not by any means follow
that they run in simultaneous directions. There is also
sometimes considerable difference in the velocity of the
current at different depths--the surface current being more
susceptible to influence of wind. A good form of deep float is
seen in Fig. 8. It consists of a rod 2 in by 2 in, or 4 sq in
The lower end of which a hollow wooden box about 6 in by 6 in
is fixed, into which pebbles are placed to overcome the
buoyancy of the float and cause it to take and maintain an
upright position in the water with a length of 9in of the rod
exposed above the surface. A small hole is formed in the top of
the box for the insertion the pebbles, which is stopped up with
a cork when the float is adjusted. The length of the rod will
vary according to the depth of water, but it will generally be
found convenient to employ a float about 10 ft and to have a
spare one about 6 ft deep, but otherwise it is similar in all
respects, for use in shallow water. A cheap float for gauging
the surface drift can be made from an empty champagne bottle
weighted with stones and partly filled with water. The top 12
in of rods and the cord and neck of the bottle, as the case may
be, should be painted red, as this colour renders floats more
conspicuous when in the water and gives considerable assistance
in locating their position, especially when they are at some
distance from the observer.
A deep-sea float designed by Mr. G. P. Bidden for ascertaining
the set of the currents along the base of the ocean has
recently been used by the North Sea Fisheries Investigation
Committee. It consists of a bottle shaped like a soda-water bottle,
made of strong glass to resist the pressure of the water, and
partly filled with water, so that just sufficient air is left
in it to cause it to float. A length of copper wire heavy enough
to cause it to sink is then attached to the bottle, which is then
dropped into the sea at a defined place. When the end of the wire
touches the bottom the bottle is relieved of some of its weight
and travels along with the currents a short distance above the bed
of the sea. About 20 per cent. of the bottles were recovered, either
by being thrown up on the beach or by being fished up in trawl nets.
[Illustration: FIG. 8.--DETAIL OF WOOD TIDAL FLOAT 10 FEET
DEEP.]
A double float, weighing about 10 lb complete, was used for the
tidal observations for the Girdleness outfall sewer, Aberdeen.
The surface portion consisted of two sheet-iron cups soldered
together, making a float 9 in in diameter and 6 in deep. The
lower or submerged portion was made of zinc, cylindrical in
shape, 16 in diameter and 16 in long, perforated at intervals
with lin diameter holes and suspended by means of a brass chain
from a swivel formed on the underside of the surface float.
In gauging the currents the float is placed in the water at a
defined point and allowed to drift, its course being noted and
afterwards transferred to a plan. The time of starting should
be recorded and observations of its exact position taken
regularly at every quarter of an hour, so that the time taken
in covering any particular distance is known and the length of
travel during any quarter-hour period multiplied by four gives
the speed of the current at that time in miles per hour.
The method to be employed in ascertaining the exact position of
the float from time to time is a matter which requires careful
consideration, and is dependent upon the degree of accuracy
required according to the importance of the scheme and the
situation of neighbouring towns, frequented shores, oyster
beds, and other circumstances likely to be injuriously affected
by any possible or probable pollution by sewage.
One method is to follow the float in a small boat carrying a
marine compass which has the card balanced to remain in a
horizontal position, irrespective of the tipping and rolling of
the boat, and to observe simultaneously the bearing of two
prominent landmarks, the position of which on the plan is
known, at each of the quarter-hour periods at which the
observations are to be taken. This method only gives very
approximate results, and after checking the value of the
observations made by its use, with contemporary observations
taken by means of theodolites on the shore, the writer
abandoned the system in favour of the theodolite method, which,
however, requires a larger staff, and is therefore more
expensive. In every case it is necessary to employ a boat to
follow the float, not only so as to recover it at the end of
each day's work, but principally to assist in approximately
locating the float, which can then be found more readily when
searching through the telescope of the theodolite. The boat
should be kept about 10 ft to 20 ft from the float on the side
further removed from the observers, except when surface floats
are being used to ascertain the effect of the wind, when the
boat should be kept to leeward of the float. Although obviously
with a large boat the observations can be pursued through
rougher weather, which is an important point, still the
difficulty of maintaining a large boat propelled by mechanical
power, or sail, sufficiently near the float to assist the
observers, prevents its use, and the best result will be
obtained by employing a substantial, seaworthy rowing boat with
a broad beam. The boatmen appreciate the inclusion of a mast,
sails, and plenty of ballast in the equipment to facilitate
their return home when the day's work is done, which may happen
eight or nine miles away, with twilight fast passing into
darkness. There should be two boatmen, or a man and a strong
youth.
In working with theodolites, it is as well before starting to
select observation stations at intervals along the coast, drive
pegs in the ground so that they can easily be found afterwards,
and fix their position upon a 1/2500 ordnance map in the usual
manner. It may, however, be found in practice that after
leaving one station it is not possible to reach the next one
before the time arrives for another sight to be taken. In this
case the theodolite must be set up on magnetic north at an
intermediate position, and sights taken to at least two
landmarks, the positions of which are shown on the map, and the
point of observation subsequently plotted as near as possible
by the use of these readings. Inasmuch as the sights will be
taken from points on the edge of the shore, which is, of
course, shown on the map, it is possible, after setting up to
magnetic north, to fix the position with approximate accuracy
by a sight to one landmark only, but this should only be done
in exceptional circumstances.
The method of taking the observations with two theodolites, as
adopted by the writer, can best be explained by a reference to
Fig. 9, which represents an indented piece of the coast. The
end of the proposed sea outfall sewer, from which point the
observations would naturally start, is marked 1, the numerals
2, 3, 4, etc., indicating the positions of the float as
observed from time to time. Many intermediate observations
would be taken, but in order to render the diagram more clear,
these have not been shown. The lines of sight are marked 1A,
1B, etc. The points marked A1, A2, etc., indicate the first,
second, etc., and subsequent positions of observer A; the
points B1, B2, etc., referring to observer B. The dot-and-dash
line shows the course taken by the float, which is ascertained
after plotting the various observations recorded.
It is very desirable to have a horse and trap in waiting to
move the observers and their instruments from place to place as
required, and each observer should be provided with small flags
about 2 ft square, one white and one blue, for signalling
purposes.
The instruments are first set up at A1 and B1 respectively, and
adjusted to read on to the predetermined point 1 where the
float is to be put in Then as soon as the boatmen have reached
the vicinity of this point, the observers can, by means of the
flags, direct them which way to row so as to bring the boat to
the exact position required, and when this is done the anchor is
dropped until it is time to start, which is signalled by the observers
holding the flags straight above their heads. This is also the
signal used to indicate to the men that the day's work is
finished, and they can pick up the float and start for home.
[Illustration: FIG. 9.--PLAN OF INDENTED COAST-LINE LLUSTRATING
METHOD OF TAKING CURRENT OBSERVATIONS WITH TWO THEODOLITES.]
Directly the float is put in the water, and at every even
quarter of an hour afterwards, each observer takes a reading of
its exact position, and notes the time. As soon as the readings
are taken to the float in position 2, the observer A should
take up his instrument and drive to A2, where he must set up
ready to take reading 3 a quarter of an hour after reading 2.
It will be noticed that he might possibly have been able to
take the reading 3 from the position A1, but the angle made by
the lines of sight from the two instruments would have been too
acute for accurate work, and very probably the float would have
been hidden by the headland, so that he could not take the
reading at all. In order to be on the headland A4 at the proper
time, A must be working towards it by getting to position A3 by
the time reading 4 is due. Although the remainder of the course
of the float can be followed from B1 and A4, the instruments
would be reading too much in the same line, so that B must move
to B2 and then after reading 5 and 6 he should move to B3. As
the float returns towards the starting point, A can remain in
the position A4 while B goes to B4 and then moves back along
the shore as the float progresses.
The foregoing description is sufficient to indicate the general
method of working, but the details will of course vary
according to the configuration of the shore and the course
taken by the float. Good judgment is necessary in deciding when
to move from one station to the next, and celerity in setting
up, adjusting the instrument, and taking readings is essential.
If the boatmen can be relied upon to keep their position near
the float, very long sights can be taken with sufficient
accuracy by observing the position of the boat, long after the
float has ceased to be visible through the telescope.
The lines of sight from each station should be subsequently
plotted on the 1/2500 ordnance map; the intersection of each
two corresponding sight lines giving the position of the float
at that time. Then if a continuous line is drawn passing
through all the points of intersection it will indicate the
course taken by the float.
It is very desirable that the observers should be able to
convey information to each other by signalling with the flags
according to the Morse code, as follows. The dashes represent a
movement of the flag from a position in front of the left
shoulder to near the ground on the right side and the dots a
movement from the left shoulder to the right shoulder.
TABLE 3.
MORSE ALPHABET.
E .
A .-
R .-.
L .-..
W .--
P .--.
J .---
I ..
U ..-
F ..-.
S ...
V ...-
H ....
T -
N -.
K -.-
C -.-.
Y -.--
D -..
X -..-
B -...
M --
G --.
Q --.-
Z --..
O ---
The signal to attract attention at starting and to signify the
end of the message is .. .. .. continued until it is
acknowledged with a similar sign by the other observer; that
for a repetition is .. -- .. which is signalled when any part
of the message is not understood, otherwise after each word is
signalled the receiver waves - to indicate he understands it.
Until proficiency is attained, two copies of the alphabet
should be kept by each observer for reference, one for
dispatching a message arranged in alphabetical order and the
other far reading a message arranged as set out above. The
white flag should be used when standing against a dark
background, and the blue one when on the skyline or against a
light background.
The conditions in tidal rivers vary somewhat from those
occurring on the coast. As the crest of the tidal wave passes
the mouth of the river a branch wave is sent up the river. This
wave has first to overcome the water flowing down the river,
which is acting in opposition to it, and in so doing causes a
banking up of the water to such a height that the inclination
of the surface is reversed to an extent sufficient to cause a
tidal current to run up the river. The momentum acquired by the
water passing up-stream carries it to a higher level towards
the head of the river than at the mouth, and, similarly, in
returning, the water flowing down the river gains sufficient
impetus to scoop out the water at the mouth and form a low
water below that in the sea adjoining. Owing to a flow of
upland water down a river the ebb lasts longer than the flood
tide by a period, increasing in length as the distance from the
mouth of the river increases; and, similarly to the sea, the
current may continue to run down a river after the tide has
turned and the level of the water is rising. The momentum of
the tide running up the centre of the river is in excess of
that along the banks, so that the current changes near the
shore before it does in the middle, and, as the sea water is of
greater specific gravity than the fresh, weighing 64 lb per
cubic foot against 62-1/2 lb, it flows up the bed of the river
at the commencement of the tide, while the fresh water on the
surface is running in the opposite direction. After a time the
salt water becomes diffused in the fresh, so that the density
of the water in a river decreases as the distance from the sea
increases. The disposal of sewage discharged into a river is
due primarily to the mixing action which is taking place;
inasmuch as the tidal current which is the transporting agent
rarely flows more rapidly than from two to four miles per hour,
or, say, twelve to fifteen miles per tide. The extent to which
the suspended matter is carried back again up stream when the
current turns depends upon the quantity of upland water which
has flowed into the upper tidal part of the river during the
ebb tide, as this water occupies a certain amount of space,
according to the depth and width of the river, and thus
prevents the sea water flowing back to the position it occupied
on the previous tide, and carrying with it the matter in
suspension. The permanent seaward movement of sewage discharged
into the Thames at Barking when there is only a small quantity
of upland water is at the rate of about one mile per day,
taking thirty days to travel the thirty-one miles to the sea,
while at the mouth of the river the rate does not exceed one-
third of a mile per day.
CHAPTER IV.
SELECTION OF SITE FOR OUTFALL SEWER.
The selection of the site for the sea outfall sewer is a matter
requiring a most careful consideration of the many factors
bearing on the point, and the permanent success of any scheme
of sewage disposal depends primarily upon the skill shown in
this matter. The first step is to obtain a general idea of the
tidal conditions, and to examine the Admiralty charts of the
locality, which will show the general set of the main currents
into which it is desirable the sewage should get as quickly as
possible. The main currents may be at some considerable
distance from the shore, especially if the town is situated in
a bay, when the main current will probably be found running
across the mouth of it from headland to headland. The sea
outfall should not be in the vicinity of the bathing grounds,
the pier, or parts of the shore where visitors mostly
congregate; it should not be near oyster beds or lobster
grounds. The prosperity--in fact, the very existence--of most
seaside towns depends upon their capability of attracting
visitors, whose susceptibilities must be studied before
economic or engineering questions, and there are always
sentimental objections to sewage works, however well designed
and conducted they may be.
It is desirable that the sea outfall should be buried in the
shore for the greater part of its length, not only on account
of these sentimental feelings, but as a protection from the
force of the waves, and so that it should not interfere with
boating; and, further, where any part of the outfall between
high and low water mark is above the shore, scouring of the
beach will inevitably take place on each side of it. The
extreme end of the outfall should be below low-water mark of
equinoctial tides, as it is very objectionable to have sewage
running across the beach from the pipe to the water, and if the
foul matter is deposited at the edge of the water it will
probably be brought inland by the rising tide. Several possible
positions may present themselves for the sea outfall, and a few
trial current observations should be made in these localities
at various states of the tides and plotted on to a 1:2500
ordnance map. The results of these observations will probably
reduce the choice of sites very considerably.
Levels should be taken of the existing subsidiary sewers in the
town, or, if there are none, the proposed arrangement of
internal sewers should be sketched out with a view to their
discharging their contents at one or other of the points under
consideration. It may be that the levels of the sewers are such
that by the time they reach the shore they are below the level
of low water, when, obviously, pumping or other methods of
raising the sewage must be resorted to; if they are above low
water, but below high water, the sewage could be stored during
high water and run off at or near low water; or, if they are
above high water, the sewage could run off continuously, or at
any particular time that might be decided.
Observations of the currents should now be made from the
selected points, giving special attention to those periods
during which it is possible to discharge the sewage having
regard to the levels of the sewers. These should be made with
the greatest care and accuracy, as the final selection of the
type of scheme to be adopted will depend very largely on the
results obtained and the proper interpretation of them, by
estimating, and mentally eliminating, any disturbing
influences, such as wind, etc. Care must also be taken in
noting the height of the tide and the relative positions of the
sun, moon, and earth at the time of making the observations,
and in estimating from such information the extent to which the
tides and currents may vary at other times when those bodies
are differently situated.
It is obvious that if the levels of the sewers and other
circumstances are such that the sewage can safely be discharged
at low water, and the works are to be constructed accordingly,
it is most important to have accurate information as to the
level of the highest low water which may occur in any ordinary
circumstances. If the level of a single low water, given by a
casual observation, is adopted without consideration of the
governing conditions, it may easily be that the tide in
question is a low one, that may not be repeated for several
years, and the result would be that, instead of having a free
outlet at low water, the pipe would generally be submerged, and
its discharging capacity very greatly reduced.
The run of the currents will probably differ at each of the
points under consideration, so that if one point were selected
the best result would be obtained by discharging the sewage at
high water and at another point at low water, whereas at a
third point the results would show that to discharge there
would not be satisfactory at any stage of the tide unless the
sewage were first partially or even wholly purified. If these
results are considered in conjunction with the levels of the
sewers definite alternative schemes, each of which would work
satisfactory may be evolved, and after settling them in rough
outline, comparative approximate estimates should be prepared,
when a final scheme may be decided upon which, while giving the
most efficient result at the minimum cost, will not arouse
sentimental objections to a greater extent than is inherent to
all schemes of sewage disposal.
Having thus selected the exact position of the outfall, the
current observations from that point should be completed, so
that the engineer may be in a position to state definitely the
course which would be taken by sewage if discharged under any
conditions of time or tide. This information is not
particularly wanted by the engineer, but the scheme will have
to receive the sanction of the Local Government Board or of
Parliament, and probably considerable opposition will be raised
by interested parties, which must be met at all points and
overcome. In addition to this, it may be possible, and
necessary, when heavy rain occurs, to allow the diluted sewage
to escape into the sea at any stage of the tide; and, while it
is easy to contend that it will not then be more impure than
storm water which is permitted to be discharged into inland
streams during heavy rainfall, the aforesaid sentimentalists
may conjure up many possibilities of serious results. As far as
possible the records should indicate the course taken by floats
starting from the outfall, at high water, and at each regular
hour afterwards on the ebb tide, as well as at low water and
every hour on the flood tide. It is not, however, by any means
necessary that they should be taken in this or any particular
order, because as the height of the tide varies each day an
observation taken at high water one day is not directly
comparable with one taken an hour after high water the next
day, and while perhaps relatively the greatest amount of
information can be gleaned from a series of observations taken
at the same state of the tide, but on tides of differing
heights, still, every observation tells its own story and
serves a useful purpose.
Deep floats and surface floats should be used concurrently to
show the effect of the wind, the direction and force of which
should be noted. If it appears that with an on-shore wind
floating particles would drift to the shore, screening will be
necessary before the sewage is discharged. The floats should be
followed as long as possible, but at least until the turn of
the current--that is to say, a float put in at or near high
water should be followed until the current has turned at or
near low water, and one put in at low water should be followed
until after high water. In all references to low water the
height of the tide given is that of the preceding high water.
The time at which the current turns relative to high and low
water at any place will be found to vary with the height of the
tide, and all the information obtained on this point should be
plotted on squared paper as shown on Fig. 10, which represents
the result of observations taken near the estuary of a large
river where the conditions would be somewhat different from
those holding in the open sea. The vertical lines represent the
time before high or low water at which the current turned, and
the horizontal lines the height of the tide, but the data will,
of course, vary in different localities.
[Illustration: Hours before turn of tide. FIG 10]
It will be noticed that certain of the points thus obtained can
be joined up by a regular curve which can be utilised for
ascertaining the probable time at which the current will turn
on tides of height intermediate to those at which observations
were actually taken. For instance, from the diagram given it
can be seen that on a 20 ft tide the current will turn thirty
minutes before the tide, or on a 15 ft tide the current will
turn one hour before the tide. Some of the points lie at a
considerable distance from the regular curve, showing that the
currents on those occasions were affected by some disturbing
influence which the observer will probably be able to explain
by a reference to his notes, and therefore those particular
observations must be used with caution.
The rate of travel of the currents varies in accordance with
the time they have been running. Directly after the turn there
is scarcely any movement, but the speed increases until it
reaches a maximum about three hours later and then it decreases
until the next turn, when dead water occurs again.
Those observations which were started at the turn of the
current and continued through the whole tide should be plotted
as shown in Fig. 11, which gives the curves relating to three
different tides, but, provided a sufficiently large scale is
adopted, there is no reason why curves relating to the whole
range of the tides should not be plotted on one diagram. This
chart shows the total distance that would be covered by a float
according to the height of the tide; it also indicates the
velocity of the current from time to time. It can be used in
several ways, but as this necessitates the assumption that with
tides of the same height the flow of the currents is absolutely
identical along the coast in the vicinity of the outfall, the
diagram should be checked as far as possible by any
observations that may be taken at other states of tides of the
same heights. Suppose we require to know how far a float will
travel if started at two hours after high water on a 12 ft
tide. From Fig. 10 we see that on a tide of this height the
current turns two hours and a quarter before the tide;
therefore two hours after high water will be four hours and a
quarter after the turn of the current. If the float were
started with the current, we see from Fig. 11 that it would
have travelled three miles in four hours and a quarter; and
subtracting this from four miles, which is its full travel on a
whole tide, we see that it will only cover one mile in the two
hours and a quarter remaining before the current turns to run
back again.
Although sewage discharged into the sea rapidly becomes so
diffused as to lose its identity, still occasionally the
extraneous substances in it, such as wooden matches, banana
skins, etc., may be traced for a considerable distance; so
that, as the sewage continues to be discharged into the sea
moving past the outfall, there is formed what may be described
as a body or column of water having possibilities of sewage
contamination. If the time during which sewage is discharged is
limited to two hours, and starts, say, at the turn of the
current on a 12 ft tide, we see from Fig. 11 that the front of
this body of water will have reached a point five-eighths of a
mile away when the discharge ceases; so that there will be a
virtual column of water of a total length of five-eighths of a
mile, in which is contained all that remains of the noxious
matters, travelling through the sea along the course of the
current. We see, further, that at a distance of three miles
away this column would only take thirty minutes to pass a given
point. The extent of this column of water will vary
considerably according to the tide and the time of discharge;
for instance, on a 22 ft tide, if the discharge starts one hour
after the turn of the current and continues for two hours, as
in the previous example, it will form a column four miles long,
whereas if it started two hours after the current, and
continued for the same length of time, the column would be six
miles and a half long, but the percentage of sewage in the
water would be infinitesimal.
[Illustration: Hours after turn of current FIG. 11]
In some cases it may be essential that the sewage should be
borne past a certain point before the current turns in order to
ensure that it shall not be brought back on the return tide to
the shore near the starting point. In other words, the sewage
travelling along the line of a branch current must reach the
junction on the line of the main current by a certain time in
order to catch the connection. Assuming the period of discharge
will be two hours, and that the point which it is necessary to
clear is situated three miles and a half from the outfall, the
permissible time to discharge the sewage according to the
height of the tide can be obtained from Fig. 11. Taking the 22
ft tide first, it will be seen that if the float started with
the current it would travel twelve miles in the tide; three and
a half from twelve leaves eight and a half miles. A vertical line
dropped from the intersection of the eight miles and a half line
with the curve of the current gives the time two hours and a half
before the end, or four hours after the start of the current at which
the discharge of the sewage must cease at the outfall in order that
the rear part of the column can reach the required point before
the current turns. As on this tide high water is about fifteen
minutes after the current, the latest time for the two hours of
discharge must be from one hour and three-quarters to three
hours and three-quarters after high water. Similarly with the
12 ft tide having a total travel of four miles: three and a
half from four leaves half a mile, and a vertical line from the
half-mile intersection gives one hour and three-quarters after
the start of the current as the time for discharge to cease.
High water is two hours and a quarter after the current;
therefore the latest time for the period of discharge would be
from two hours and a half to half an hour before high water,
but, as during the first quarter of an hour the movement of the
current, though slight, would be in the opposite direction, it
would be advisable to curtail the time of discharge, and say
that it should be limited to between two hours and a quarter
and half an hour before high water. It is obvious that if
sewage is discharged about two hours after high water the
current will be nearing its maximum speed, but it will only
have about three hours to run before it turns; so that,
although the sewage may be removed with the maximum rapidity
from the vicinity of the sea outfall, it will not be carried to
any very great distance, and, of course, the greater the
distance it is carried the more it will be diffused. It must be
remembered that the foregoing data are only applicable to the
locality they relate to, although after obtaining the necessary
information similar diagrams can be made and used for other
places; but enough has been said to show that when it is
necessary to utilise the full effect of the currents the sewage
should be discharged at a varying time before high or low
water, as the case may be, according to the height of the tide.
CHAPTER V.
VOLUME OF SEWAGE.
The total quantity of sewage to be dealt with per day can be
ascertained by gauging the flow in those cases where the sewers
are already constructed, but where the scheme is an entirely
new one the quantity must be estimated. If there is a water
supply system the amount of water consumed per day, after
making due allowance for the quantity used for trade purposes
and street watering, will be a useful guide. The average amount
of water used per head per day for domestic purposes only may
be taken as follows:--
DAILY WATER SUPPLY
(Gallons per head per day.)
Dietetic purposes (cooking, drinking, &c.) 1
Cleansing purposes (washing house utensils,
clothes, &c.) 6
If water-closets are in general use, add 3
If baths are in general use, add 5
Total 15
It therefore follows that the quantity of domestic sewage to be
expected will vary from 7 to 15 gallons per head per day,
according to the extent of the sanitary conveniences installed
in the town; but with the advent of an up-to-date sewage
scheme, probably accompanied by a proper water supply, a very
large increase in the number of water-closets and baths may
confidently be anticipated, and it will rarely be advisable to
provide for a less quantity of domestic sewage than 15 gallons
per head per day for each of the resident inhabitants. The
problem is complicated in sea coast towns by the large influx
of visitors during certain short periods of the year, for whom
the sewerage system must be sufficient, and yet it must not be
so large compared with the requirements of the residential
population that it cannot be kept in an efficient state during
that part of the year when the visitors are absent. The
visitors are of two types--the daily trippers and those who
spend several days or weeks in the town. The daily tripper may
not directly contribute much sewage to the sewers, but he does
indirectly through those who cater for his wants. The resident
visitor will spend most of the day out of doors, and therefore
cause less than the average quantity of water to be used for
house-cleansing purposes, in addition to which the bulk of the
soiled linen will not be washed in the town. An allowance of 10
gallons per head per day for the resident visitor and 5 gallons
per head per day for the trippers will usually be found a
sufficient provision.
It is, of course, well known that the flow of sewage varies
from day to day as well as from hour to hour, and while there
is no necessity to consider the daily variation--calculations
being based on the flow of the maximum day--the hourly
variation plays a most important part where storage of the
sewage for any length of time is an integral part of the
scheme. There are many important factors governing this
variation, and even if the most elaborate calculations are made
they are liable to be upset at any time by the unexpected
discharge of large quantities of trade wastes. With a small
population the hourly fluctuation in the quantity of sewage
flowing into the sewers is very great, but it reduces as the
population increases, owing to the diversity of the occupations
and habits of the inhabitants. In all cases where the
residential portions of the district are straggling, and the
outfall works are situated at a long distance from the centre
of the town, the flow becomes steadier, and the inequalities
are not so prominently marked at the outlet end of the sewer.
The rate of flow increases more or less gradually to the
maximum about midday, and falls off in the afternoon in the
same gradual manner. The following table, based on numerous
gaugings, represents approximately the hourly variations in the
dry weather flow of the sewage proper from populations
numbering from 1,000 to 10,000, and is prepared after deducting
all water which may be present in the sewers resulting from the
infiltration of subsoil water through leaky joints in the
pipes, and from defective water supply fittings as ascertained
from the night gaugings. Larger towns have not been included in
the table because the hourly rates of flow are generally
complicated by the discharge of the trade wastes previously
referred to, which must be the subject of special investigation
in each case.
[TABLE NO. 4.
APPROXIMATE HOURLY VARIATION IN THE FLOW OF SEWAGE.
Percentage of Total Flow Passing Off in each Hour.
-----------+------------------------------------------------
| Population.
Hour. +-----+-----+-----+-----+-----+-----+-----+------
|1,000|2,000|3,000|4,000|5,000|6,000|8,000|10,000
-----------+-----+-----+-----+-----+-----+-----+-----+------
Midnight | 1.0 | 1.0 | 1.2 | 1.3 | 1.5 | 1.5 | 1.8 | 2.0
1.0 a.m. | 0.7 | 0.7 | 0.7 | 0.8 | 0.8 | 1.0 | 1.0 | 1.0
2.0 " | nil | nil | nil | nil | 0.2 | 0.2 | 0.3 | 0.5
3.0 " | nil | nil | nil | nil | nil | nil | nil | 0.2
4.0 " | nil | nil | nil | nil | nil | nil | nil | nil
5.0 " | nil | nil | nil | nil | nil | nil | nil | 0.2
6.0 " | 0.2 | 0.2 | 0.3 | 0.5 | 0.6 | 0.5 | 0.7 | 0.8
7.0 " | 0.5 | 0.5 | 1.0 | 1.5 | 1.6 | 1.7 | 2.0 | 2.5
8.0 " | 1.0 | 1.5 | 2.0 | 2.5 | 3.0 | 3.5 | 4.0 | 5.0
9.0 " | 3.5 | 4.5 | 4.5 | 4.8 | 5.5 | 5.8 | 6.0 | 6.5
10.0 " | 6.5 | 6.5 | 6.8 | 7.0 | 7.5 | 7.7 | 8.0 | 8.0
11.0 " |10.5 |11.0 |10.5 |10.0 | 9.6 | 9.3 | 9.0 | 8.8
Noon |11.0 |11.3 |10.8 |10.3 | 9.3 | 9.5 | 9.2 | 9.0
1.0 p.m. | 6.0 | 5.5 | 6.0 | 6.7 | 7.0 | 7.2 | 7.3 | 7.5
2.0 " | 7.0 | 7.3 | 7.0 | 7.0 | 6.5 | 6.5 | 6.2 | 6.0
3.0 " | 6.8 | 6.5 | 6.5 | 6.5 | 6.5 | 6.3 | 6.3 | 6.0
4.0 " | 7.5 | 7.5 | 7.3 | 7.0 | 6.7 | 6.5 | 6.2 | 6.7
5.0 " | 6.5 | 6.5 | 6.5 | 6.3 | 6.0 | 6.0 | 6.0 | 5.8
6.0 " | 4.5 | 4.5 | 4.7 | 4.8 | 5.0 | 5.0 | 5.0 | 5.2
7.0 " | 6.5 | 6.2 | 6.0 | 5.8 | 5.5 | 5.5 | 5.5 | 4.7
8.0 " | 6.2 | 6.0 | 5.8 | 5.5 | 5.5 | 5.3 | 5.0 | 4.8
9.0 " | 5.0 | 4.8 | 4.7 | 4.5 | 4.5 | 4.5 | 4.5 | 4.0
10.0 " | 4.8 | 4.6 | 4.2 | 4.0 | 3.8 | 3.5 | 3.0 | 3.0
11.0 " | 4.3 | 3.5 | 3.5 | 3.2 | 3.2 | 3.0 | 3.0 | 2.8
-----------+-----+-----+-----+-----+-----+-----+-----+------
Total |100.0|100.0|100.0|100.0|100.0|100.0|100.0|100.0
-----------+-----+-----+-----+-----+-----+-----+-----+------
ANALYSIS OF FLOW]
Percentage of total flow passing off during period named.
---------------------+----------------------------------------------------------------+
| Population. |
+-------+-------+-------+-------+-------+-------+-------+--------+
| 1,000 | 2,000 | 3,000 | 4,000 | 5,000 | 6,000 | 8,000 | 10,000 |
---------------------+-------+-------+-------+-------+-------+-------+-------+--------+
7.0 a.m. to 7.0 p.m | 77.3 | 78.8 | 78.6 | 78.7 | 78.5 | 78.8 | 78.7 | 75.2 |
7.0 p.m. to 7.0 a.m | 22.7 | 21.2 | 21.4 | 21.3 | 21.5 | 21.2 | 21.3 | 21.8 |
Maximum 12 hrs. | 84.0 | 83.6 | 82.6 | 81.7 | 81.0 | 80.6 | 79.7 | 78.2 |
" 10 " | 72.8 | 72.8 | 72.1 | 71.4 | 70.0 | 69.8 | 69.2 | 68.5 |
" 9 " | 66.3 | 66.6 | 66.1 | 65.6 | 64.5 | 64.8 | 64.2 | 63.3 |
" 8 " | 61.8 | 62.1 | 61.4 | 60.8 | 59.5 | 59.0 | 58.2 | 57.5 |
" 6 " | 48.8 | 49.1 | 43.1 | 47.5 | 46.8 | 46.5 | 46.0 | 45.8 |
" 3 " | 23.0 | 28.8 | 27.11| 27.3 | 26.8 | 26.5 | 26.2 | 25.8 |
" 2 " | 21.5 | 22.3 | 21.3 | 20.3 | 19.3 | 18.5 | 18.2 | 17.3 |
" 1 " | 11.0 | 11.3 | 10.8 | 10.3 | 9.8 | 9.5 | 9.2 | 9.0 |
Minimum 9 " | 3.4 | 3.9 | 5.2 | 6.6 | 7.5 | 6.9 | 8.8 | 10.0 |
" 10 " | 6.9 | 7.4 | 8.7 | 9.8 | 10.7 | 10.4 | 11.8 | 13.0 |
---------------------+-------+-------+-------+-------+-------+-------+-------+--------+
The data in the foregoing table, so far as they relate to
populations of one, five, and ten thousand respectively, are
reproduced graphically in Fig. 12.
This table and diagram relate only to the flow of sewage--that
is, water which is intentionally fouled; but unfortunately it
is almost invariably found that the flow in the sewers is
greater than is thus indicated, and due allowance must be made
accordingly. The greater the amount of extra liquid flowing in
the sewers as a permanent constant stream, the less marked will
be the hourly variations; and in one set of gaugings which came
under the writer's notice the quantity of extraneous liquid in
the sewers was so greatly in excess of the ordinary sewage flow
that, taken as a percentage of the total daily flow, the hourly
variation was almost imperceptible.
[Illustration: Fig 12 Hourly Variation in Flow of Sewage.]
Provision must be made in the scheme for the leakage from the
water fittings, and for the subsoil water, which will
inevitably find its way into the sewers. The quantity will vary
very considerably, and is difficult of estimation. If the water
is cheap, and the supply plentiful, the water authority may not
seriously attempt to curtail the leakage; but in other cases it
will be reduced to a minimum by frequent house to house
inspection; some authorities going so far as to gratuitously
fix new washers to taps when they are required. Theoretically,
there should be no infiltration of subsoil water, as in nearly
all modern sewerage schemes the pipes are tested and proved to be
watertight before the trenches are filled in; but in practice this
happy state is not obtainable. The pipes may not all be bedded as
solidly as they should be, and when the pressure of the earth comes
upon them settlement takes place and the joints are broken. Joints
may also be broken by careless filling of trenches, or by men
walking upon the pipes before they are sufficiently covered.
Some engineers specify that all sewers shall be tested and
proved to be absolutely water-tight before they are "passed"
and covered in, but make a proviso that if, after the
completion of the works, the leakage into any section exceeds
1/2 cubic foot per minute per mile of sewer, that length shall
be taken up and relaid. Even if the greatest vigilance is
exercised to obtain water-tight sewers, the numerous house
connections are each potential sources of leakage, and when the
scheme is complete there may be a large quantity of
infiltration water to be dealt with. Where there are existing
systems of old sewers the quantity of infiltration water can be
ascertained by gauging the night flow; and if it is proved to
be excessive, a careful examination of the course of the sewers
should be made with a view to locating the places where the
greater part of the leakage occurs, and then to take such steps
as may be practicable to reduce the quantity.
CHAPTER VI.
GAUGING FLOW IN SEWERS.
A method frequently adopted to gauge the flow of the sewage is
to fix a weir board with a single rectangular notch across the
sewer in a convenient manhole, which will pond up the sewage;
and then to ascertain the depth of water passing over the notch
by measurements from the surface of the water to a peg fixed
level with the bottom of the notch and at a distance of two or
three feet away on the upstream side. The extreme variation in
the flow of the sewage is so great, however, that if the notch
is of a convenient width to take the maximum flow, the hourly
variation at the time of minimum flow will affect the depth of
the sewage on the notch to such a small extent that difficulty
may be experienced in taking the readings with sufficient
accuracy to show such variations in the flow, and there will be
great probability of incorrect results being obtained by reason
of solid sewage matter lodging on the notch. When the depth on
a l2 in notch is about 6 in, a variation of only 1-16th inch in
the vertical measurement will represent a difference in the
rate of the flow of approximately 405 gallons per hour, or
about 9,700 gallons per day. When the flow is about lin deep
the same variation of 1-16th in will represent about 162
gallons per hour, or 3,900 gallons per day. Greater accuracy
will be obtained if a properly-formed gauging pond is
constructed independently of the manhole and a double
rectangular notch, similar to Fig. 13, or a triangular or V-
shaped notch, as shown in Fig. 14, used in lieu of the simpler
form.
In calculating the discharge of weirs there are several formula
to choose from, all of which will give different results,
though comparative accuracy has been claimed for each. Taking
first a single rectangular notch and reducing the formulae to
the common form:
____
Discharge per foot in width of weir = C \/ H^3
where H = depth from the surface of still water above the weir to the level of
the bottom of the notch, the value of C will be as set out in the following
table:--
TABLE No. 5.
RECTANGULAR NOTCHES.
_____
Discharge per foot in width of notch = C \/ H^3
------------------------------------------------------------------
Values of C.
--------------------------------------+---------------------------
H Measured in | Feet. | Inches.
---------------+-----------+----------+-----------+---------------
| Gallons | C. ft | Gallons | C. ft
Discharge in | per hour. | per min | per hour. | per min
---------------+-----------+----------+-----------+---------------
Authority. | | | |
Box | 79,895 | 213.6 | 1,922 | 5.13
Cotterill | 74,296 | 198.6 | 1,787 | 4.78
Francis | 74,820 | 200.0 | 1,800 | 4.81
Mo'esworth | 80,057 | 214.0 | 1,926 | 5.15
Santo Crimp | 72,949 | 195.0 | 1,755 | 4.69
---------------+-----------+----------+-----------+---------------
In the foregoing table Francis' short formula is used, which
does not take into account the end contractions and therefore
gives a slightly higher result than would otherwise be the
case, and in Cotterill's formula the notch is taken as being
half the width of the weir, or of the stream above the weir. If
a cubic foot is taken as being equal to 6-1/4 gallons instead
of 6.235 gallons, then, cubic feet per minute multiplied by
9,000 equals gallons per day. This table can be applied to
ascertain the flow through the notch shown in Fig. 13 in the
following way. Suppose it is required to find the discharge in
cubic feet per minute when the depth of water measured in the
middle of the notch is 4 in Using Santo Crimp's formula the
result will be
C\/H^3 = 4.69 \/4^3 = 4.69 x 8 = 37.52
cubic feet per foot in width of weir, but as the weir is only 6
in wide, we must divide this figure by 2, then
37.52/2 = 18.76 cubic feet, which is the discharge per minute.
+------+ +------+
| | FIG. 13 | |
| | | |
| | | |
| +------+ +------+ |
| | | |
| | | |
| | | |
| +------+ |
| |
| |
| |
| |
+----------------------------------+
Fig. 13.-ELEVATION OF DOUBLE RECTANGULAR NOTCHED GAUGING WEIR.
+------+ +------+
| \ FIG. 13 / |
| \ / |
| \ / |
| \ / |
| \ / |
| \ / |
| \ / |
| \ / |
| \ / |
| \/ |
| |
| |
| |
| |
| |
+----------------------------------+
FIG. 14.-ELEVATION OF TRIANGULAR NOTCHED GAUGING WEIR.
FIG. 15.-LONGITUDINAL SECTION, SHOWING WEIR, GAUGE-PEG, AND HOOK-GAUGE
If it is required to find the discharge in similar terms with a
depth of water of 20 in, two sets of calculations are required.
First 20 in depth on the notch 6 in wide, and then 4 in depth
on the notch, 28 in minus 6 in, or 1 ft wide.
____ _____
(1) C\/ H^3 = 4.69/2 \/ 10^3 = 2.345 x 31.62 = 74.15
____ ____
(2) C\/ H^3 = 1.0 x 4.69 \/ 4^3 = 1.0 x 4.69 x 8 = 37.52
Total in c. ft per min = 111.67
The actual discharge would be slightly in excess of this.
In addition to the circumstances already enumerated which
affect the accuracy of gaugings taken by means of a weir fixed
in a sewer there is also the fact that the sewage approaches
the weir with a velocity which varies considerably from time to
time. In order to make allowance for this, the head calculated
to produce the velocity must be added to the actual head. This
can be embodied in the formula, as, for example, Santo Crimp's
formula for discharge in cubic feet per minute, with H measured
in feet, is written
__________________
195\/(11^3 + .035V - H^2
instead of the usual form of
____
195\/ H^3, which is used
when there is no velocity to take into account. The V
represents the velocity in feet per second.
Triangular or V notches are usually formed so that the angle
between the two sides is 90 , when the breadth at any point
will always be twice the vertical height measured at the
centre. The discharge in this case varies as the square root of
the fifth power of the height instead of the third power as
with the rectangular notch. The reason for the alteration of
the power is that _approximately_ the discharge over a notch
with any given head varies as the cross-sectional area of the
body of water passing over it. The area of the 90 notch is
half that of a circumscribing rectangular notch, so that the
discharge of a V notch is approximately equal to that of a
rectangular notch having a width equal to half the width of the
V notch at water level, and as the total width is equal to
double the depth of water passing over the notch the half width
is equal to the full depth and the discharge is equal to that
of a rectangular notch having a width equal to the depth of
water flowing over the V notch from time to time, both being
measured in the same unit, therefore
____ ____ ____
C \/ H^3 becomes C x H x \/ H^3 which equals C \/ H^5.
The constant C will, however, vary from that for the
rectangular notch to give an accurate result.
TABLE No. 6.
TRIANGULAR OR V NOTCHES.
____
Discharge = C x \/ H^5.
Values of C.
--------------+-----------------------+------------------------
H Measured in | Feet. | Inches.
--------------+----------+------------+-----------+------------
Discharge in | Gallons | C. ft per | Gallons | C. ft per
| per hour | min | per hour. | min
--------------+----------+------------+-----------+------------
Alexander | 59,856 | 160 | 120.0 | 0.321
Cotterill | 57,013 | 152.4 | 114.3 | 0.306
Molesworth | 59,201 | 158.2 | 118.7 | 0.317
Thomson | 57,166 | 152.8 | 114.6 | 0.306
--------------+----------+------------+-----------+------------
Cotterill's formula for the discharge in cubic feet per minute
is
_______
16 x C x B \/ 2g H^3
when B = breadth of notch in feet and H = height of water in
feet and can be applied to any proportion of notch. When B =
2H, that is, a 90 notch, C = .595 and the formula becomes
____
152.4 \/ H^5,
and when B = 4H, that is, a notch containing an angle of 126
51' 36", C = .62 and the formula is then written
____
318 \/ H^5.
The measurements of the depth of the water above the notch
should be taken by a hook-gauge, as when a rule or gauge-slate
is used the velocity of the water causes the latter to rise as
it comes in contact with the edge of the measuring instrument
and an accurate reading is not easily obtainable, and, further,
capillary attraction causes the water to rise up the rule above
the actual surface, and thus to show a still greater depth.
When using a hook-gauge the top of the weir, as well as the
notch, should be fixed level and a peg or stake fixed as far
back as possible on the upstream side of the weir, so that the
top of the peg is level with the top of the weir, instead of
with the notch, as is the case when a rule or gauge-slate is
used. The hook-gauge consists of a square rod of, say, lin
side, with a metal hook at the bottom, as shown in Fig. 15, and
is so proportioned that the distance from the top of the hook
to the top of the rod is equal to the difference in level of
the top of the weir and the sill of the notch. In using it the
rod of the hook-gauge is held against the side of the gauge-peg
and lowered into the water until the point of the hook is
submerged. The gauge is then gently raised until the point of
the hook breaks the surface of the water, when the distance
from the top of the gauge-peg to the top of the rod of the
hook-gauge will correspond with the depth of the water flowing
over the weir.
CHAPTER VII.
RAINFALL.
The next consideration is the amount of rain-water for which
provision should be made. This depends on two factors: first,
the amount of rain which may be expected to fall; and,
secondly, the proportion of this rainfall which will reach the
sewers. The maximum rate at which the rain-water will reach the
outfall sewer will determine the size of the sewer and capacity
of the pumping plant, if any, while if the sewage is to be
stored during certain periods of the tide the capacity of the
reservoir will depend upon the total quantity of rain-water
entering it during such periods, irrespective of the rate of
flow.
Some very complete and valuable investigations of the flow of
rain-water in the Birmingham sewers were carried out between
1900 and 1904 by Mr. D. E. Lloyd-Davies, M.Inst.C. E., the
results of which are published in Vol. CLXIV., Min Proc.
Inst.C.E. He showed that the quantity reaching the sewer at any
point was proportional to the time of concentration at that
point and the percentage of impermeable area in the district.
The time of concentration was arrived at by calculating the
time which the rain-water would take to flow through the
longest line of sewers from the extreme boundaries of the
district to the point of observation, assuming the sewers to be
flowing half full; and adding to the time so obtained the
period required for the rain to get into the sewers, which
varied from one minute where the roofs were connected directly
with the sewers to three minutes where the rain had first to
flow along the road gutters. With an average velocity of 3 ft
per second the time of concentration will be thirty minutes for
each mile of sewer. The total volume of rain-water passing into
the sewers was found to bear the same relation to the total
volume of rain falling as the maximum flow in the sewers bore
to the maximum intensity of rainfall during a period equal to
the time of concentration. He stated further that while the
flow in the sewers was proportional to the aggregate rainfall
during the time of concentration, it was also directly
proportional to the impermeable area. Putting this into
figures, we see that in a district where the whole area is
impermeable, if a point is taken on the main sewers which is so
placed that rain falling at the head of the branch sewer
furthest removed takes ten minutes to reach it, then the
maximum flow of storm water past that point will be
approximately equal to the total quantity of rain falling over
the whole drainage area during a period of ten minutes, and
further, that the total quantity of rainfall reaching the
sewers will approximately equal the total quantity falling. If,
however, the impermeable area is 25 per cent. of the whole,
then the maximum flow of storm water will be 25 per cent. of
the rain falling during the time of concentration, viz., ten
minutes, and the total quantity of storm water will be 25 per
cent. of the total rainfall.
If the quantity of storm water is gauged throughout the year it
will probably be found that, on the average, only from 70 per
cent. to 80 per cent. of the rain falling on the impermeable
areas will reach the sewers instead of 100 per cent., as
suggested by Mr. Lloyd-Davies, the difference being accounted
for by the rain which is required to wet the surfaces before
any flow off can take place, in addition to the rain-water
collected in tanks for domestic use, rain required to fill up
gullies the water level of which has been lowered by
evaporation, and rain-water absorbed in the joints of the
paving.
The intensity of the rainfall decreases as the period over
which the rainfall is taken is increased. For instance, a
rainfall of lin may occur in a period of twenty minutes, being
at the rate of 3 in per hour, but if a period of one hour is
taken the fall during such lengthened time will be considerably
less than 3 in In towns where automatic rain gauges are
installed and records kept, the required data can be
abstracted, but in other cases it is necessary to estimate the
quantity of rain which may have to be dealt with.
It is impracticable to provide sewers to deal with the maximum
quantity of rain which may possibly fall either in the form of
waterspouts or abnormally heavy torrential rains, and the
amount of risk which it is desirable to run must be settled
after consideration of the details of each particular case. The
following table, based principally upon observations taken at
the Birmingham Observatory, shows the approximate rainfall
which may be taken according to the time of concentration.
TABLE No. 7.
INTENSITY OF RAINFALL DURING LIMITED PERIODS.
Equivalent rate in inches per hour
of aggregate rainfall during
Time of Concentration, period of concentration
A B C D E
5 minutes ............... 1.75 2.00 3.00 -- --
10 " ............... 1.25 1.50 2.00 -- --
15 " ............... 1.05 1.25 1.50 -- --
20 " ............... 0.95 1.05 1.30 1.20 3.00
25 " ............... 0.85 0.95 1.15 -- --
30 " ............... 0.80 0.90 1.05 1.00 2.50
35 " ............... 0.75 0.85 0.95 -- --
40 " ............... 0.70 0.80 0.90 -- --
45 " ............... 0.65 0.75 0.85 -- --
1 hour .................. 0.50 0.60 0.70 0.75 1.80
1-1/2 " .................. 0.40 0.50 0.60 -- 1.40
2 " .................. 0.30 0.40 0.50 0.50 1.10
The figures in column A will not probably be exceeded more than
once in each year, those in column B will not probably be
exceeded more than once in three years, while those in column C
will rarely be exceeded at all. Columns D and E refer to the
records tabulated by the Meteorological Office, the rainfall
given in column D being described in their publication as
"falls too numerous to require insertion," and those in column
E as "extreme falls rarely exceeded." It must, however, be
borne in mind that the Meteorological Office figures relate to
records derived from all parts of the country, and although the
falls mentioned may occur at several towns in any one year it
may be many years before the same towns are again visited by
storms of equal magnitude.
While it is convenient to consider the quantity of rainfall for
which provision is to be made in terms of the rate of fall in
inches per hour, it will be useful for the practical
application of the figures to know the actual rate of flow of
the storm water in the sewers at the point of concentration in
cubic feet per minute per acre. This information is given in
the following Table No. 8, which is prepared from the figures
given in Table No. 7, and is applicable in the same manner.
TABLE No. 8.
MAXIMUM FLOWS OF STORM WATER.
--------------------------+----------------------------------
| Maximum storm water flow in
| cubic feet per min per acre
| of impervious area.
Time of Concentration. +------+------+------+------+------
| A | B | C | D | E
--------------------------+------+------+------+------+------
5 minutes | 106 | 121 | 181 | -- | --
10 " | 75 | 91 | 121 | -- | --
15 " | 64 | 75 | 91 | -- | --
20 " | 57 | 64 | 79 | 73 | 181
25 " | 51 | 57 | 70 | -- | --
30 " | 48 | 54 | 64 | 61 | 151
35 " | 45 | 51 | 57 | -- | --
40 " | 42 | 48 | 54 | -- | --
45 " | 39 | 45 | 51 | -- | --
1 hour | 30 | 36 | 42 | 45 | 109
1-1/2 " | 24 | 30 | 36 | -- | 85
2 " | 18 | 24 | 30 | 30 | 67
--------------------------+------+------+------+------+-------
l inch of rain = 3,630 cub. feet per acre.
The amount of rainfall for which storage has to be provided is
a difficult matter to determine; it depends on the frequency
and efficiency of the overflows and the length of time during
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