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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."