THE SEWERAGE OF SEA COAST TOWNS
HENRY C. ADAMS
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
VIII. STORM WATER IN SEWERS
IX. WIND AND WINDMILLS
X. THE DESIGN OF SEA OUTFALLS
XI ACTION OF SEA WATER ON CEMENT
XIII. THE DISCHARGE OF SEA OUTFALL SEWERS
XIV. TRIGONOMETRICAL SURVEYING
XV. HYDROGRAPHICAL SURVEYING
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.
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."
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:—
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:—
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.
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.
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.
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.
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.
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.
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.
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.
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
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.
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.
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 formul 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.-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.
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 which the storm water has to be held up for tidal reasons. It is found that on the average the whole of the rain on a rainy day falls within a period of 2-1/2 hours; therefore, ignoring the relief which may be afforded by overflows, if the sewers are tide-locked for a period of 2-1/2 hours or over it would appear to be necessary to provide storage for the rainfall of a whole day; but in this case again it is permissible to run a certain amount of risk, varying with the length of time the sewers are tide-locked, because, first of all, it only rains on the average on about 160 days in the year, and, secondly, when it does rain, it may not be at the time when the sewers are tide-locked, although it is frequently found that the heaviest storms occur just at the most inconvenient time, namely, about high water. Table No. 9 shows the frequency of heavy rain recorded during a period of ten years at the Birmingham Observatory, which, being in the centre of England, may be taken as an approximate average of the country.
TABLE No. 9.
FREQUENCY OF HEAVY RAIN ———————————————————————————-
Total Daily Rainfall. Average Frequency of Rainfall
0.4 inches and over 155 times each year 0.5 " 93 " 0.6 " 68 " 0.7 " 50 " 0.8 " 33 " 0.9 " 22 " 1.0 " 17 " 1.1 " Once each year 1.2 " Once in 17 months 1.25 " " 2 years 1.3 " " 2-1/2 1.4 " " 3-1/3 1.5 " " 5 years 1.6 " " 5 years 1.7 " " 5 years 1.8 " " 10 years 1.9 " " 10 years 2.0 " " 10 years
It will be interesting and useful to consider the records for the year 1903, which was one of the wettest years on record, and to compare those taken in Birmingham with the mean of those given in "Symons' Rainfall," taken at thirty-seven different stations distributed over the rest of the country.
TABLE No. 10. RAINFALL FOR 1903.
Mean of 37 stations in Birmingham England and Wales. Daily Rainfall of 2 in and over ...... None 1 day Daily Rainfall of 1 in and over ...... 3 days 6 days Daily Rainfall of 1/2 in and over .... 17 days 25 days Number of rainy days.................. 177 days 211 days Total rainfall ...................... 33.86 in 44.89 in Amount per rainy day ................ 0.19 in 0.21 in