AUTOMATIC DOSING DEVICES
283. Types. 284. Operation. 285. Three Alternating Siphons.
286. Four or More Alternating Siphons. 287. Timed Siphons.
288. Multiple Alternating and Timed Siphons. 506–512
SEWERAGE AND SEWAGE TREATMENT
CHAPTER I
INTRODUCTION
=1. Sewerage and the Sanitary Engineer.=—Present day conceptions of
sanitation are based on the scientific discoveries which have resulted
so much in the increased comfort and safety of human life during the
past century, in the increase of our material possessions, and the
extent of our knowledge. The danger to health in the accumulation of
filth, the spreading of disease by various agents, the germ theory of
disease, and other important principles of sanitation can be counted
among the more recent scientific discoveries and pronouncements.
Experience has shown, and continues to show, that the increase of
population may be inhibited by accumulations of human waste in populous
districts. The removal of these wastes is therefore essential to the
existence of our modern cities.
The greatest need of a modern city is its water supply. Without it city
life would be impossible. The next most important need is the removal of
waste matters, particularly wastes containing human excreta or the germs
of disease. To exist without street lights, pavements, street cars,
telephones, and the many other attributes of modern city life might be
possible, although uncomfortable. To exist in a large city without
either water or sewerage would be impossible. The service rendered by
the sanitary engineer to the large municipality is indispensable. In
addition to the service necessary to the maintenance of life in large
cities, the sanitary engineer serves the smaller city, the rural
community, the isolated institution, and the private estate with
sanitary conveniences which make possible comfortable existence in them,
and which are frequently considered as of paramount necessity. Training
for service in municipal sanitation is training for a service which has
a more direct beneficial effect on humanity than any other engineering
work, or any other profession. W. P. Gerhard states:
_A Sanitary Engineer_ is an engineer who carries out those works
of civil engineering which have for their object:
(_a_) The promotion of the public and individual health;
(_b_) The remedying of insanitary conditions;
(_c_) The prevention of epidemic diseases.
A well-educated sanitary engineer should have a thorough knowledge
of general civil engineering, of architecture, and of sanitary
science. The practice of the sanitary engineer embraces water
supply, sewerage, and sewage and garbage disposal for cities and
for single buildings; the prevention of river pollution, the
improvement of polluted water supplies; street paving and street
cleaning, municipal sanitation, city improvement plans, the laying
out of cities, the preparation of sanitary surveys, the regulation
of noxious trades, disinfection, cremation, and the sanitation of
buildings.
The need of the work of the sanitary engineer in the provision of sewers
and drains is thrust upon us in our daily experience by the clogging of
sewers, the flooding of streets by heavy rains, filthy conditions in
unsewered districts, increased values of property and improved
conditions of living in sewered districts, and in many other ways. The
increasing demand for sewerage and the amount of money expended on sewer
construction is indicated by the information given in Table I.
=2. Historical.=—An ordinance passed by the Roman Senate in the name of
the Emperor about A.D. 80, states:
I desire that nobody shall conduct away any excess water without
having received my permission or that of my representatives; for
it is necessary that a part of the supply flowing from the
delivery tanks shall be utilized not only for cleaning our city,
but also for flushing the sewers.[1]
Neither the sewers mentioned nor the distributing pipes of the public
water supply were connected to individual residences. The contributions
to the sewers came from the ground and the street surface. The streets
were the receptacles of liquid and solid wastes and were often little
more than open sewers. A promenade after dark in an ancient, medieval,
or early modern city was accompanied not only by the underfoot dangers
of an uneven pavement or an encounter with a footpad, but with the
overhead danger from the emptying of slops into the streets from the
upper windows. Sewers were used for the collection of surface water; the
discharge of fecal matter into them was prohibited. The problem of the
collection of sewage remained unsolved until the Nineteenth Century.
TABLE 1
POPULATION TRIBUTARY TO SEWERAGE SYSTEMS
──────────────────────────────────────┬──────────┬──────────┬──────────
│ 1905[2] │ 1915[3] │ 1920[4]
──────────────────────────────────────┼──────────┼──────────┼──────────
Population discharging raw sewage into│ │ │
the sea or tidal estuaries │ 6,500,000│ 8,500,000│
Population discharging raw sewage into│ │ │
inland streams or lakes │20,400,000│26,400,000│
Population connected to systems where │ │ │
sewage is treated in some way │ 1,100,000│ 6,900,000│
Population connected with sewerage │ │ │
systems │28,000,000│41,800,000│46,300,000
──────────────────────────────────────┴──────────┴──────────┴──────────
The development of the London sewers was commenced early in the
Nineteenth Century. The sewerage system of Hamburg, Germany, was laid
out in 1842 by Lindley, an English engineer who with other English
engineers performed similar work in other German cities because of their
earlier experience in English communities. Berlin’s present system dates
from 1860. The construction of storm-water drains in Paris dates from
1663.[5] They were intended only as street drains but are now included
in the comprehensive system of the city. The first comprehensive
sewerage system in the United States was designed by E. S. Chesbrough
for the City of Chicago in 1855. Previous to this time sewers had been
installed in an indifferent manner and without definite plan. The
installation of a comprehensive sewerage system in Baltimore in 1915
marks the completion of installation of sewerage systems in all large
American cities.
In the early days of sewerage design it was considered unsafe to
discharge domestic wastes into the sewers as the concentration of so
much sewage was expected to create great nuisances and dangers to
health. That the fear that the concentration of large quantities of
sewage would create a nuisance was not ill founded is proven by the
conditions on the Thames at London in 1858–59. Dr. Budd states:[6]
For the first time in the history of man, the sewage of nearly
three millions of people had been brought to seethe and ferment
under a burning sun in one vast open _cloaca_ lying in their
midst.
The result we all know. Stench so foul we may well believe had
never before ascended to pollute this lower air. Never before at
least had a stink risen to the height of an historic event.... For
months together the topic almost monopolized the public prints....
‘India is in revolt and the Thames stinks’ were the two great
facts coupled together by a distinguished foreign writer, to mark
the climax of a national humiliation.[7]
The problem of sewage disposal followed the more or less successful
solutions of the problem of sewage collection. In England the British
Royal Commission on Sewage Disposal was appointed in 1857 and issued its
first report in 1865. The first studies in the United States were
started in 1887 by the establishment of an experiment station at
Lawrence, Massachusetts, where valuable work has been done. The station
is under the State Board of Health, which issued its first report
containing the results of the work at the station, in 1890.
Various methods of sewage treatment preparatory to disposal have been
devised from time to time. Some have fallen into disuse, such as the A.
B. C. (alum, blood and clay) process, and others have taken a permanent
place, such as the septic tank. The unsolved problems of sewage
collection, and the number of persons still unserved by sewerage and
sewage disposal opens a wide field to the study and construction of
sewerage works.
=3. Methods of Collection.=—The method of collection which involves the
removal of night soil from a privy vault, the pail system which involves
the collection of buckets of human excreta from closets and homes,
indoor chemical closets, and other makeshift methods of collection are
of extreme importance where no sewers exist, but they are not properly
considered as sewerage systems or sewerage works. These methods of
collection are generally confined to rural districts and to outlying
parts of urban communities. They require constant attention for their
proper conduct and little skill for their installation, the principal
requirements being to make the receptacles fly-proof.
The pneumatic system was introduced by Liernur, a Dutch engineer.[8] It
is used in parts of a few cities in Europe, but it is not capable of use
on a large scale. It consists of a system of air-tight pipes, connecting
water closets, kitchen sinks, etc., with a central pumping station at
which an air-tight tank is provided from which the air is partly
exhausted. As little water as possible is allowed to mix with the fecal
matter and other wastes in order not to overtax the system. Solid and
liquid wastes are drawn to the central station when the waste valve on
the plumbing fixture is opened.
The collection of sewage in a system of pipes through which it is
conducted by the buoyant effect and scouring velocity of water is known
as the water-carriage system. This is the only method of sewage
collection in general use in urban communities. In this system solid and
liquid wastes are so highly diluted with water as either to float or to
be suspended therein. The mixture resulting from this high dilution
follows the laws of hydraulics as applied to pure water, or water
containing suspended matter. It will flow freely through properly
designed conduits and will concentrate the sewage wastes at the point of
ultimate disposal.
=4. Methods of Disposal.=—Sewage is disposed of by dilution in water, by
treatment on land, or occasionally by discharging it into channels that
contain no diluting water. Some form of treatment to prepare sewage for
ultimate disposal is frequently necessary and will undoubtedly be
required in a comparatively short time for all sewage discharged into
watercourses. The solid matters removed by treatment may be buried,
burned, dumped into water, or used as a fertilizer.
If the volume of diluting water, or the area and character of land used
for disposal are not as they should be, a nuisance will be created. The
aim of all methods of sewage treatment has so far been to produce an
effluent which could be disposed of without nuisance and in certain
exceptional cases to protect public water supplies from pollution.
Financial returns have been sought only as a secondary consideration. A
few sewage farms and irrigation projects might be considered as
exceptions to this as the value of the water in the sewage as an
irrigant has been the primary incentive to the promotion of the farm.
It is to be remembered that since the aim of all sewage treatment is to
produce an effluent that can be disposed of without causing a nuisance,
the simplest process by which this result can be attained under the
conditions presented is the process to be adopted. No attempt is made to
_purify_ sewage completely, or on a practical scale to make drinking
water.
=5. Methods of Treatment.=—Screening and sedimentation are the primary
methods for the treatment of sewage. By these methods a portion of the
floating and settleable solids are removed, preventing the formation of
unsightly scum and putrefying sludge banks. Chemicals are sometimes
added to the sewage to form a heavy flocculent precipitate which hastens
sedimentation of the solid matters in the sewage. The process in these
methods is mechanical and the solid matters removed from the sewage must
be disposed of by other methods than dilution with the sewage effluent.
More complete methods of treatment are dependent on biologic action.
Under these methods of treatment complete stabilization of the effluent
is approached, and in the most complete treatment an effluent is
produced which is clear, sparkling, non-odorous, non-putrescible, and
sterile. Sterilization of sewage, usually with chlorine or some of its
compounds, has been used, not to reduce the amount of diluting water
necessary, but to reduce the number of pathogenic germs and to minimize
the danger of the transmission of disease.
=6. Definitions.=—Sewage and sewerage are not synonymous terms although
frequently confused. Sewage is the spent water supply of a community
containing the waste from domestic, industrial or commercial use, and
such surface and ground water as may enter the sewer.[9] Sewerage is the
name of the system of conduits and appurtenances designed to carry off
the sewage. It is also used to indicate anything pertaining to sewers.
A difference is made between sanitary sewage, storm sewage, and
industrial wastes. Sanitary sewage, sometimes called domestic sewage, is
the liquid wastes discharged from residences or institutions, and
contains water closet, laundry and kitchen wastes. Storm sewage is the
surface run-off which reaches the sewers during and immediately after a
storm. Industrial wastes are the liquid waste products discharged from
industrial plants.
A sewer is a conduit used for conveying sewage.
The names of the conduits through which sewage may flow are:
_Soil Stack._—A vertical pipe in a building through which waste water
containing fecal matter or urine is allowed to flow.
_Waste Pipe._—A vertical pipe in a building through which waste water
containing no fecal matter is allowed to flow.
_House Drain._—The approximately horizontal portion of a house drainage
system which conveys the drainage from the soil stack or waste pipe to
the point of discharge from the building.
_House Sewer._—The pipe which leads from the outside wall of the
building to the sewer in the street.
_Lateral Sewer._—The smallest branch in a sewerage system, exclusive of
the house sewers.
_Sub-main or Branch Sewer._—A sewer from which the sewage from two or
more laterals is discharged.[10]
_Main or Trunk Sewer._—A sewer into which the sewage from two or more
sub-main or branch sewers is discharged.[11]
_Intercepting Sewer._—A sewer generally laid transversely to a sewerage
system to intercept some portion or all of the sewage collected by the
system.
_Relief Sewer._—A sewer intended to carry a portion of the flow from a
district already provided with sewers of insufficient capacity and thus
preventing overtaxing the latter.[12]
_Outfall Sewer._—That portion of a main or trunk sewer below all
branches.
_Flushing Sewer._—A conduit through which water is conveyed for flushing
portions of a sewerage system.
_Force Main._—A conduit through which sewage is pumped under pressure.
CHAPTER II
WORK PRELIMINARY TO DESIGN
=7. Division of Work.=—Engineering work on sewerage can be divided into
four parts, namely: preliminary, design, construction and maintenance.
An engineer may be engaged during any one or all of these periods on the
same sewerage system, and should therefore be acquainted with his duties
during each period.
=8. Preliminary.=—The demand for sewerage normally follows the
installation or extension of the public water supply. It may be caused
by: a lack of drainage on some otherwise desirable tract of real estate;
from a public realization of unpleasant or unhealthful conditions in a
built-up district; or through the realization by the municipal
administration of the necessity for caring for the future. In whatever
way the demand may be created the engineer should take an active part in
the promotion of the work.
The engineer’s duties during the preliminary period are: to make a study
of the possible methods by which the demand for sewerage can be
satisfied; to present the results of this study in the form of a report
to the committee or organization responsible for the promotion of the
work; and so to familiarize himself with the conditions affecting the
installation of the proposed plans as to be able to answer all inquiries
concerning them. This work will require the general qualities of
character, judgment, efficiency and the understanding of men in
addressing interested persons individually and collectively on the
features of the proposed plans, and the exercise of engineering
technique in the survey and the drawing of the plans. The engineer
should assure himself that all legal requirements in the drawing of
petitions, advertising, permits, etc., have been complied with. This
requires some knowledge of national, state, and local laws. Although
none the less essential their description is not within the scope of
this book.
The engineer’s preliminary report should contain a section devoted to
the feasibility of one or more plans which may be explained in more or
less detail with a statement of the cost and advantages of each. A
conclusion should be reached as to the most desirable plan and a
recommendation made that this plan be installed. Other sections of the
report may be devoted to a history of the growing demand, a description
of the conditions necessitating sewerage, possible methods of financing,
and such other subjects as may be pertinent. The making of the
preliminary plan and the design of sewerage works are described in
subsequent chapters.
=9. Estimate of Cost.=—In making an estimate of cost the information
should be presented in a readable and easily comprehended manner. It is
necessary that the items be clearly defined and that all items be
included. The method of determining the costs of doubtful items such as
depreciation, interest charges, labor, etc., and the probability of the
fluctuation of the costs of certain items should be explained.
The engineer’s estimate may be divided somewhat as follows:
Labor.
Material.
Overhead. This may include construction plant, office expense,
supervision, bond, interest on borrowed capital, insurance,
transportation, etc. The amount of the item is seldom less than 15
per cent and is usually over 20 per cent of the contract price.
Contingencies. This allowance is usually 10 to 15 per cent of the
contract price.
Profit. This should be from 5 to 10 per cent of the sum of the
four preceding items.
The contract price is the sum of these items. To this may be added:
Engineering. 2 to 5 per cent of the contract price.
Extra Work. Zero to 15 per cent of the contract price; dependent
on the character of the work, the completeness of the preliminary
information, the completeness of the plans, etc.
Legal expense.
Purchase of land, rights of way, etc., etc.
The cost of the sewer may be stated as so much per linear foot for
different sizes of pipe, including all appurtenances such as manholes,
catch-basins, etc., or the items may be separated in great detail
somewhat as follows:
Earth excavation, per cu. yd.
Rock excavation, per cu. yd.
Backfill, per cu. yd.
Brick manholes, 3 feet by 4 feet, per foot of depth.
Vitrified sewer pipe with cement joints, in place,
... inches in diameter, 0 to 6 feet deep
6 to 8 feet deep
8 to 10 feet deep
Repaving, macadam per sq. yd.
asphalt per sq. yd.
Flush-tanks, ... gal. capacity, per tank.
Service pipes to flush-tanks, per linear foot., etc., etc.
These methods represent the two extremes of presenting cost estimates.
Each method, or modification thereof, may have its use, dependent on
circumstances.
Reliable cost data are difficult to obtain. Lists of prices of materials
and labor are published in certain engineering and trade periodicals.
The Handbook of Cost Data by H. P. Gillette contains lists of the amount
of material and labor used on certain specific jobs and types of
construction. The price of labor and materials on the local market can
be obtained from the local Chamber of Commerce, contractors and other
employers of labor, and dealers in the desired commodities. Contract
prices for sewerage work published in the construction news sections of
engineering periodicals may be a guide to the judgment of the probable
cost of proposed work, but are generally dangerous to rely upon as full
details are lacking in the description of the work. A wide experience in
the collection and use of cost data is the desirable qualification for
making estimates of cost. It is possessed by few and is not an
infallible aid to the judgment.
Having completed the design and summary of the bills of material and
labor necessary for each structure or portion of the sewerage system,
the product of the unit cost and the amount of each item plus an
allowance for overhead will equal the cost of the item. The total cost
will be the sum of the costs of each item. The items should be so
grouped that the cost of the different portions of the system are
separated in order that the effect on the total cost resulting from
different combinations of items or the omission of any one item may be
readily computed.
A method for estimating the approximate cost of sewers, devised by W. G.
Kirchoffer[13] depends upon the use of the diagram shown in Fig. 2. The
factors for local conditions are shown in Table 2. For example, let it
be required to find the cost of a 15–inch vitrified pipe sewer at a
depth of 9 feet, if the unit costs of labor and material and the
conditions are the same as shown in Table 3.
[Illustration:
FIG. 2.—Diagram for Estimating the Cost of Sewers.
Eng. News, Vol. 76, p. 781.
]
_Solution_
First: To find the factor depending on local conditions, enter the
diagram at the 10–inch diameter and continue down until the
intersection with the depth of trench at 8.2 feet is found. Now go
diagonally parallel to lines running from left to right upwards to
the intersection with the vertical line through a cost of 45 cents
per foot. The diagonal line running from left to right downwards
through this intersection corresponds to a factor of about 11.
TABLE 2
FACTORS FOR COSTS OF SEWERS TO BE USED WITH FIGURE 2
────────────────────────────────────────────────────────────────┬──────
Character of Material │Factor
────────────────────────────────────────────────────────────────┼──────
Clay, gravel and boulders, Medford │22–26
Mostly sand, deep trenches sheeted. Wages medium. Richland │
Center. │21–22
Sandy clay. Wages medium. Labor conditions good at Kiel. │15–20
Sand. _Sandy_ clay, some water. Labor conditions good. Pipe │
prices medium at Manston. │14–20
Gravelly clay, ⅒th laid in concrete at Burlington. │13–22
Sandy clay, some water, sheeting at La Farge. │17–23
Sand with water. │ 20
Gravel and boulders. High wages. │ 26
Clay soil. Good digging. │ 17
Sandy clay. Some water. │ 23
Clay 2 miles inland. Laborers boarded at sanitarium, Wales │ 35
Clay, gravel and boulders at Plymouth. │20–27
Sand, clay and good digging at Lake Mills. │16–19
Red clay. Machine work at North Milwaukee. │20–24
Good digging. Wages medium at West Salem. │17–19
Sandy soil, bracing only required. No water. Wages and pipe │
medium. │ 14
Red sticky clay. │ 24
Good digging in any soil. Work scarce. │ 15
Red clay. No bracing. │ 20
Work inland from railroad. Boarding laborers _and_ other │
expenses. │ 35
────────────────────────────────────────────────────────────────┴──────
Second: To find the cost of 15–inch pipe at a depth of 9.0 feet,
enter the diagram at a diameter of 15 inches and continue down
until the intersection with a depth of trench at 9 feet is found.
Now go diagonally parallel to lines running from left to right
upwards to the intersection with the diagonal line running from
left to right downwards corresponding to the factor of 11 found
above. The vertical line passing through this point shows the cost
to be 67 cents per foot.
TABLE 3
COST OF SEWER CONSTRUCTION AT ATLANTIC, IOWA
(From Gillette’s Handbook of Cost Data)
Material: Clay, not difficult to spade and requiring little or no
bracing and practically no pumping. All hand work except backfill which
was done by team and scraper. Depth of trench averaged 8.2 feet; width
30 inches. Diameter of pipe 10 inches.
───────────────────────────────────────────────────────────┬─────┬─────
Item │Wage,│Cost,
│Cents│Cents
│ per │ per
│Hour │Foot.
───────────────────────────────────────────────────────────┼─────┼─────
Pipe. │ │0.20
Hauling team and driver. │ 30│ .003
Hauling. Man helping. │ 17│ .001
Cement and sand. │ │ .006
Pipe layers. │ 22│ .014
Pipe layer’s helper. │ 17│ .014
Trenching. Top men. │ 17│ .027
Trenching. Bottom men. │ 17│ .130
Trenching. Scaffold men. │ 17│ .002
Trenching. Bracing men. │ 17│ .002
Backfilling. Shovel. │ 17│ .010
Backfilling. Team and scraper. │ 30│ .008
Backfilling. Man and scraper. │ 17│ .005
Water boy. │ 10│ .006
Foreman. │ 30│ .022
───────────────────────────────────────────────────────────┼─────┼─────
Total. │ │ .450
───────────────────────────────────────────────────────────┴─────┴─────
METHODS OF FINANCING
The construction of sewerage works may be paid for by the issue of
municipal bonds, by special assessment, by funds available from the
general taxes, or by private enterprise.
=10. Bond Issues.=—A municipal bond is a promise by the municipality to
pay the face value of the bond to the holder at a certain specified
time, with interest at a stipulated rate during the interim. The
security on the bond is the taxable property in the municipality. The
legal restrictions thrown around municipal bond issues, the value of the
taxable property in the municipality, all of which may be used as
security for municipal bonds, and the fact that a municipality can be
sued in case of default, make municipal bonds desirable and provide a
good market for their sale. The funds available from a municipal bond
issue are limited by the amount that the legal limit is in excess of the
outstanding issues. The legal limit varies in different states from
about 5 to 15 per cent of the assessed value of the property in the
municipality. In some cases the amount available from municipal bonds
has been increased by forming a municipality within a municipality such
as a sanitary district, a park district, a drainage district, etc.,
which comprises a large portion or all of an existing municipal
corporation. This case is well illustrated in some parts of the City of
Chicago where the municipal taxing powers are shared by the City
government, the Sanitary District, and Park Commissioners. The right to
create a new municipal corporation must be granted by the state
legislature. Knowledge of fixed bonds, serial bonds, life of bonds,
sinking funds, etc. is an important part of an engineer’s education.[14]
Bond issues must usually be presented to the voters for approval at an
election. If approved, and other legal procedure has been followed, the
bonds may be bought by some of the many bonding houses, or by private
individuals, and the money is immediately available for construction.
The bonds are redeemed by general taxation spread over the period of the
issue.
=11. Special Assessment.=—A special assessment is levied against
property benefited directly by the structure being paid for. Special
assessments are used for the payment for the construction of lateral
sewers which are a direct benefit to separate districts but are without
general benefit to the city. In case the construction of an outfall
sewer or the erection of a treatment plant, which may be of some general
benefit, is necessary to care for a separate district, a part of the
expense may be borne by funds available from general taxation. The legal
procedure for the raising of funds by special assessment and the purpose
to which the funds so raised may be applied are stipulated in great
detail in different states and their directions must be followed
implicitly. Illinois procedure, which is similar to that in some other
states, is as follows: a meeting of the interested property owners is
called by a committee or board of the municipal government, as the
result of a petition by interested persons or through the independent
action of the Board. At this preliminary meeting or public hearing
arguments for and against the proposed improvement are heard. The
engineer is present at this meeting to answer questions and to advise
concerning the engineering features of the plan. If approval is given by
the Board the plan and specifications are prepared complete in every
detail and incorporated in an ordinance which is presented to the
legislative branch of the city government for passage. If the project is
adopted it is taken to the county court. An assessment roll is prepared
by a commissioner appointed by the court. This roll shows the amount to
be assessed against each piece of property benefited. A hearing is then
held in the county court at which the owner of any assessed property may
voice objections to the continuation of the project. The project may be
thrown out of court for many different reasons, such as the misspelling
of a street name, an error in an elevation, an error in the description
of a pavement, but most important of all is definite proof that the
benefit is not equal to the assessment. The many minor irregularities
which may nullify the procedure in a special assessment differ in
different states and in different courts in the same state, but in
general no court can approve an assessment greater than the benefits
given. After the project has passed through the county court and the
assessment roll has been approved, bonds may be issued for the payment
of the contractor. Special assessment bonds are liens against the
property assessed and have not the same security as a general municipal
bond. For this reason a city which has reached its legal limit of
municipal bond issues can still pay for work by special assessment.
The funds available from special assessments are limited only by the
benefit to the property assessed. The amount of the benefit is difficult
to fix and may lead to much controversy. It should not exceed the amount
demanded for similar work in other localities, unless unusual and
well-understood reasons can be given.
=12. General Taxation.=—In paying for public improvements by general
taxation the money is taken from the general municipal funds which have
been apportioned for that purpose by the legislative department of the
municipal government. This method of raising funds for sewerage
construction is seldom used unless the political situation is
unfavorable to the success of a bond issue or special assessment and the
need for the improvement is great. It is usually difficult to
appropriate sufficient funds for new construction as the general tax is
apportioned to support only the operating expenses of the city, and
statutory provisions limit the amount of tax which can be levied.
=13. Private Capital.=—Private capital has been used for financing
sewerage works in some cases because of the aversion of the public in
some cities to the payment of a tax for the negative service performed
by a sewer. Sewers are buried, unseen, and frequently forgotten, but
knowledge of their necessity has spread and the number of privately
owned sewerage works is diminishing because of the better service which
can be provided by the municipality.
Franchises are granted to private companies for the construction of
sewers only after the city has exhausted other methods for the raising
of capital. The return on the private capital invested is received from
a rental paid by the city, or paid directly by the users of the system,
an initial payment usually being demanded for connection to the system.
To be successful the enterprise must be popular and must fill a great
need. This method of financing sewerage works is seldom employed as
favorable conditions are not common.
PRELIMINARY WORK
=14. Preparing for Design.=—Methods for the design of sewerage systems
are given in Chapter V. Before the design is made certain information is
essential. A survey must be made from which the preliminary map can be
prepared as described in Art. 42. Other necessary information which is
the basis of subsequent estimates of the quantity of sewage to be cared
for must be obtained by a study of rates of water consumption and the
density and growth of population, the measurement of the discharge from
existing sewers, and the compilation of rainfall and run-off data. If no
rainfall data are available estimates must be made from the nearest
available data. Observations of rainfall or run-off for periods of less
than 10 to 20 years are likely to be misleading. Methods for gathering
and using this information are explained in subsequent chapters.
Underground surveys are desirable along the lines of the proposed sewers
to learn of obstructions, difficult excavation and other conditions
which may be met. All such data are seldom gathered except for sewerage
systems involving the expenditure of a large amount of money. For
construction in small towns or small extensions to an existing system
the funds are usually insufficient for extensive preliminary
investigation. The saving in this respect is paid unknowingly to the
contractor as compensation for the risk in bidding without complete
information.
=15. Underground Surveys.=—These may be more or less extensive dependent
on the character of the district in which construction is to take place.
In built-up districts the survey should be more thorough than in
sparsely settled districts where only the character of the excavated
material is of interest and no obstructions are to be met.
Underground surveys furnish to the engineer and to prospective bidders
on contract work information on which the design and estimate of cost
and the contractor’s bid may be based and without which no intelligent
work can be done. By removing much of the uncertainty of the conditions
to be met in the construction of the sewer, the design can be made more
economical and the contractor’s bid should be markedly lower,
sufficiently so to repay more than the expense of the survey. The
information to be obtained consists of the location of the ground-water
level, and the location and sizes of water, gas, and sewer pipes,
telephone and electric conduits, street-car tracks, steam pipes, and all
other structures which may in any way interfere with subsurface
construction. These structures should be located by reference to some
permanent point on the surface. The elevation of the top of the pipes,
except sewers, rather than the depth of cover should be recorded, as the
depth of cover is subject to change. The elevation of sewers should be
given to the invert rather than to the top of the pipe.
A portion of the map of the subsurface conditions at Washington, D. C.,
is shown in Fig. 3. Many of the dimensions and notations are not shown
to avoid confusion on this small reproduction.[15] Colors are generally
used instead of different forms of cross hatching to show the different
classes of pipe and structures. In addition to a record of the
underground structures the character of the ground and the pavement
should be recorded. A comprehensive underground survey is seldom
available nor does time usually permit its being made preliminary to the
design of a sewerage system. The character of the material through which
the sewer is to pass should be determined in all cases.
[Illustration:
FIG. 3.—Record Map of Underground Structures, Washington, D. C.
Eng. Record, Vol. 74, p. 263.
The various subsurface lines are differentiated by colors as follows:
_A_—Sewers, vermilion. _B_—Water mains, blue. _C_—Potomac Electric
Power Co., carmine. _D_—Washington Railway and Electric Co.,
carmine. _E_—Capital Traction Co., violet. _F_—Chesapeake and
Potomac Telephone Co., green. _G_—Washington Gas Light Co., green.
_H_—Western Union Telegraph Co., orange. _I_—Postal Telegraph Co.,
orange. _K_—Private vaults, black. _L_—City Electric Co., yellow.
]
[Illustration:
FIG. 4.
Punch Drill.
]
Underground pipes and structures are located by excavations, which may
be quite extensive in some cases. Their position is fixed by
measurements referred to manholes and other underground structures which
are somewhat permanent in position. A city engineer should grasp every
opportunity to record underground structures when excavations are made
in the streets. The character of the material through which the sewer is
to pass is determined by borings.
=16. Borings.=—Methods used for the investigation of subsurface
conditions preliminary to sewer construction are: punch drilling, boring
with earth auger, jet boring, wash boring, percussion drilling, abrasive
drilling, and hydraulic drilling. The last three methods named are used
only for unusually deep borings or in rock.
Punch drills are of two sorts. The simplest punch drill consists of an
iron rod ⅞ of an inch to 1 inch in diameter, in sections about 4 feet
long. One section is sharpened at one end and threaded at the other so
that the next section can be screwed into it without increasing the
diameter of the rod, as shown in Fig. 4. The drill is driven by a sledge
striking upon a piece of wood held at the top of the drill to prevent
injury to the threads. The drill should be turned as it is driven to
prevent sticking. It is pulled out by a hook and lever as shown in Fig.
5. It is useful in soft ground for soundings up to 8 to 12 feet in
depth. Another form of punch drill described by A. C. Veatch[16]
consists of a cylinder of steel or iron, one to two feet long split
along one side and slightly spread. The lower portion is very slightly
expanded and tempered into a cutting edge. In use it is attached to a
rope or wooden poles and lifted and dropped in the hole by means of a
rope given a few turns about a windlass or drum. By this process the
material is forced up into the bit, slightly springs it, and so is held.
When the bit is filled it is raised to the surface and emptied. Much
deeper holes can be made with this than with the sharpened solid rod.
[Illustration:
FIG. 5.—Lever for Pulling Punch Drill.
]
[Illustration:
FIG. 6.—Earth Augers.
]
Types of earth augers about 1½-inches in diameter are shown in Fig. 6.
They are screwed on to the end of a section of the pipe or rod and as
the hole is deepened successive lengths of pipe or rod are added. The
device is operated by two men. It is pulled by straight lifting or with
the assistance of a link and lever similar to that shown in Fig. 5. The
device is suitable for soft earth or sand free from stones, and can be
used for holes 15 to 25 feet in depth. For deeper holes a block and
tackle should be used for lifting the auger from the hole. It is not
suitable for holes deeper than about 35 feet.
In the jetting method water is led into the hole through a ¾-inch or
1–inch pipe, and forced downward through the drill bit or nozzle against
the bottom of the hole. The complete equipment is shown in Fig. 7.[17]
It is not always necessary to case the hole as shown in the figure as
the muddy water and the vibration of the pipe puddle the sides so that
they will stand alone. The jet pipe may be churned in the hole by a rope
passing over a block and a revolving drum. In suitable soft materials
such as clay, sand, or gravel, holes can be bored to a depth of 100 feet
and samples collected of the material removed. An objection to the
method is the difficulty of obtaining sufficient water.
[Illustration:
FIG. 7.—Jetting Outfit.
U. S. Geological Survey, Water Supply Paper, No. 257
1. Simple Jetting Outfit. 2. Jetting Process. 3. Common Jetting Drill.
4_a_ and 4_b_. Expansion Bit or Paddy. 5. Drive Shoe.
]
Methods of drilling in rock up to depths of 20 feet are described in
Chapter XI under Rock Drilling. For deeper holes percussion, abrasive,
or hydraulic methods as used for deep well drilling must be employed.
CHAPTER III
QUANTITY OF SEWAGE
=17. Dry weather Flow.=—Estimates of the quantity of sewage flow to be
expected are ordinarily based on the population, the character of the
district, the rate of water consumption, and the probable ground-water
flow. Future conditions are estimated and provided for, as the sewers
should have sufficient capacity to care for the sewage delivered to them
during their period of usefulness.
=18. Methods for Predicting Population.=—Methods for the prediction of
future population are given in the following paragraphs.
The method of _graphical extension_. This is the quickest and most
simple of all. In this method a curve is plotted on rectangular
coordinates to any convenient scale, with population as ordinates and
years as abscissas. The curve is extended into the future by judgment of
its general tendency. An example is given of the determination of the
population of Urbana, Illinois, in 1950. Table 4 contains the population
statistics which have been plotted on line A in Fig. 8 and extended to
1950. The probable population in 1950 is shown by this line to be about
21,000.
The method of _geometrical progression_. In this method the rate of
increase during the past few years or decades is assumed to be constant
and this rate is applied to the present population to forecast the
population in the future. For example the rate of increase of population
in Urbana for the past 7 decades has varied widely, but indications are
that for the next few decades it will be about 20 per cent. Applying
this rate from 1920 to 1950 the population in 1950 is shown to be about
17,800. It is evident that this method may lead to serious error as
insufficient information is given in the table to make possible the
selection of the proper rate of increase.
TABLE 4
POPULATION STUDIES
────┬────────────────────────────
│ Urbana, Illinois
────┼──────────┬────────┬────────
Year│Population│Absolute│Per Cent
│ │Increase│Increase
│ │for Each│for Each
│ │ Decade │ Decade
────┼──────────┼────────┼────────
1850│ 210│ │
1860│ 2,038│ 1828│ 85.6
1870│ 2,277│ 239│ 10.5
1880│ 2,942│ 665│ 22.6
1890│ 3,511│ 569│ 16.2
1900│ 5,728│ 2217│ 38.7
1910│ 8,245│ 2517│ 30.5
1920│ 10,230│ 1985│ 19.4
────┴──────────┴────────┴────────
────┬───────────────────────────────────────────────────────────────
│ Population of
────┼───────┬────────┬─────────┬────────┬──────┬───────────┬────────
Year│Decatur│Danville│Champaign│Kankakee│Peoria│Bloomington│ Ann,
│ │ │ │ │ │ │ Arbor
│ │ │ │ │ │ │Michigan
│ │ │ │ │ │ │
────┼───────┼────────┼─────────┼────────┼──────┼───────────┼────────
1850│ │ 736│ │ │ 5,095│ 1,594│
1860│ 3,839│ 1,632│ 1,727│ 2,984│14,045│ 7,075│ 5,097
1870│ 7,161│ 4,751│ 4,625│ 5,189│22,849│ 14,590│ 7,368
1880│ 9,547│ 7,733│ 5,103│ 5,651│29,259│ 17,180│ 8,061
1890│ 16,841│ 11,491│ 5,839│ 9,025│41,024│ 20,484│ 9,431
1900│ 20,754│ 16,354│ 9,098│ 13,595│56,100│ 23,286│ 14,509
1910│ 31,140│ 27,871│ 12,421│ 13,986│66,950│ 25,786│ 14,817
1920│ 43,818│ 33,750│ 15,873│ 16,721│76,121│ 28,638│ 19,516
────┴───────┴────────┴─────────┴────────┴──────┴───────────┴────────
[Illustration:
FIG. 8.—Diagram Showing Methods for Estimating Future Population.
]
The method of utilizing a _decreasing rate of increase_. This method
attempts to correct the error in the assumption of a constant rate of
increase. After a certain period of growth, as the age of a city
increases its rate of increase diminishes. In applying this knowledge to
a prediction of the future population of a city the population curve is
plotted, as in the graphical method and a straight line representing a
constant rate or increase is drawn tangent to the curve at its end. The
curve is then extended at a flatter rate in accordance with the rate of
change of a similar nearby larger city. This method has not been applied
to any of the cities included in Table 4, as none has reached that
limiting period where the rate of increase has begun to diminish.
The method of utilizing an _arithmetical rate of increase_. This method
allows for the error of the geometrical progression which tends to give
too large results for old and slow-growing cities. This method generally
gives results that are too low. The absolute increase in the population
during the past decade or other period is assumed to continue throughout
the period of prediction. Applying this method to the same case, the
increase in the population during the past decade was 2,000. Adding
three times this amount to the population in 1920, the population of
Urbana in 1950 will be about 16,000.
The method involving the _graphical comparison with other cities_ with
similar characteristics. In this method population curves of a number of
cities larger than Urbana but having similar characteristics, are
plotted with years as abscissas and population as ordinates, with the
present population of Urbana as the origin of coordinates. The
population curve for Urbana is first plotted. It will lie entirely in
the third quadrant as shown by the heavy full line in Fig. 8. The
population curves of some larger cities are then plotted in such a
manner that each curve passes through the origin at the time their
population was the same as that of the present population of Urbana.
These curves lie in the first and third quadrants. The population curve
of the city in question is then extended to conform with the curves of
older cities in the most probable manner as dictated by judgment. Such a
series of plots has been made in Fig. 8. The results indicate that the
population of Urbana in 1950 will be about 25,500.
The last method described will give the most probable result as it is
the most rational. For quick approximations the geometrical progression
is used. The arithmetical progression is useful only as an approximate
estimate for old cities.
=19. Extent of Prediction.=—The period for which a sewerage system
should be designed is such that each generation bears its share of the
cost of the system. It is unfair to the present generation to build and
pay for an extensive system that will not be utilized for 25 years. It
is likewise unfair to the next generation to construct a system
sufficient to comply with present needs only, and to postpone the
payment for it by a long term bond issue. An ideal solution would be to
plan a system which would satisfy present and future needs and to
construct only those portions which would be useful during the period of
the bond issue. Unfortunately this solution is not practical, because,
1st, it is less expensive to construct portions of the system such as
the outfall, the treatment plant, etc., to care for conditions in
advance of present needs, and 2nd, the life of practically all portions
of a sewerage system is greater than the legal or customary time limit
on bond issues.
A compromise between the practical and the ideal is reached by the
design of a complete system to fulfill all probable demands, and the
construction of such portions as are needed now in accordance with this
plan. The payment should be made by bond issues with as long life as is
financially or legally practical, but which should not exceed the life
of the improvement.
The prediction of the population should therefore be made such that a
comprehensive system can be designed with intelligence. Practice has
seldom called for predictions more than 50 years in the future.
=20. Sources of Information on Population.=—The United States decennial
census furnishes the most complete information on population.
Unfortunately it becomes somewhat old towards the end of a decade. More
recent information can be obtained from local sources. Practically every
community takes an annual school census the accuracy of which is fairly
reliable. The general tendencies of the population to change can be
learned by a study of the post office records showing the amount of mail
matter handled at various periods. Local chambers of commerce and
newspapers attempt to keep records of population, but they are often
inaccurate. Another source of information is the gross receipts of
public service companies, such as street railways, water, gas,
electricity, telephone, etc. The population can be assumed to have
increased almost directly as their receipts, with proper allowance for
change in rates, character of management, and other factors.
=21. Density of Population.=—So far the study of population has been
confined to the entire city. It is frequently necessary to predict the
population of a district or small section of a city. A direct census may
be taken, or more frequently its population is determined by estimating
its density based on a comparison with similar districts of known
density, and multiplying this density by the area of the district. In
determining the density, statistics of the population of the entire city
will be helpful but are insufficient for such a problem. A special
census of the area involved would be conclusive but is generally
considered too expensive. A count of the number of buildings in the
district can be made quickly, and the density determined by
approximating the number of persons per building. Statistics of the
population of various districts together with a description of the
character of the district are given in Table 5.
[Illustration:
FIG. 9.—Density, Area, and Population, Cincinnati, Ohio. 1850 to 1950.
]
TABLE 5
DENSITIES OF POPULATION
────────────┬────────────────────────────────────────┬────────┬────────
City │ Character of District │ Area, │Density
│ │ Acres │per Acre
────────────┼────────────────────────────────────────┼────────┼────────
Philadelphia│Thomas Run. Residential. Mostly pairs of│ │
│ two and three-story houses. 1204 acres│ │
│ settled. │ 1,840│ 59
│Pine Street. Residential. Mostly solid │ │
│ four to six-story houses. 156 acres │ │
│ settled. │ 160│ 97
│Shunk Street. Residential. Mostly pairs │ │
│ of two and three-story houses. 539 │ │
│ acres settled. │ 539│ 119
│Lombard Street. Tenements and hotels, │ │
│ 145 acres settled. │ 147│ 113
│York Street. Residential and │ │
│ manufacturing. 354 acres settled. │ 358│ 94
│ │ │
New York │Residential. Three-story dwellings with │ │
City │ 18–foot frontage, and four-story flats│ │
│ with 20–foot frontage. │ │ 100
│Residential. Five-story flats. │ │520–670
│Residential. Six-story flats. │ │800–1000
│Residential. Six-story apartments. High │ │
│ class. │ │ 300
│ │ │
Chicago │1st Ward. Retail and commercial. The │ │
│ “Loop”. │ 1,440│ 20.5
│2d Ward. Commercial and low-class │ │
│ residential solidly built up. │ 800│ 53.5
│3d Ward. Low-class residential. │ 960│ 48.1
│5th Ward. Industrial. Some low-class │ │
│ residences. Not solidly built up. │ 2,240│ 25.51
│6th Ward. Residential. Four and │ │
│ five-story apartments. A few detached │ │
│ residences. │ 1,600│ 47.0
│7th Ward. Same as Ward 6. Not solidly │ │
│ built up. Contains a large park. │ 4,160│ 21.7
│8th Ward. Industrial. Sparsely settled. │ 13,624│ 4.8
│9th Ward. Industrial and low-class │ │
│ residential. Solidly built up. │ 640│ 70.0
│10th Ward. Same as Ward 9. │ 640│ 80.8
│13th Ward. Low-class residential. │ │
│ Solidly built with three and │ │
│ four-story flats. │ 6,100│ 36.7
│16th Ward. Middle-class residential. │ │
│ Some industries. Well built up. │ 800│ 81.5
│19th Ward. Industrial and commercial. │ │
│ Some low-class residences. │ 640│ 90.7
│20th Ward. Low-class residential. Some │ │
│ industries. Entirely built up. │ 800│ 77.1
│21st Ward. Industrial. Entirely built │ │
│ up. │ 960│ 49.9
│23d Ward. Industrial and residential. │ 800│ 55.4
│24th Ward. Residential apartment houses │ │
│ and middle-class residences. │ 1,120│ 46.8
│25th Ward. Residential. High-class │ │
│ apartments. Wealthy homes. Contains a │ │
│ large park. │ 4,160│ 24.0
│26th Ward. Residential. Middle-class │ │
│ homes and apartments. Fairly well │ │
│ built up. │ 4,640│ 16.1
│27th Ward. Residential. Sparsely │ │
│ settled. │ 20,480│ 5.5
│29th Ward. Low-class residential. │ │
│ Two-story frame houses. “Back of the │ │
│ Yards”. │ 6,400│ 12.8
│30th Ward. The Stock Yards. │ 1,280│ 40.1
│32d Ward. Scattered residences. │ 8,480│ 8.3
│33d Ward. Scattered residences. │ 12,944│ 5.5
│35th Ward. Scattered residences. │ 4,960│ 12.0
│ │ │
General │The most crowded conditions with │ │
average │ five-story and higher, contiguous │ │
│ buildings in poor class districts. │ │750–1000
│Five and six-story contiguous flat │ │
│ buildings. │ │500–750
│Six-story high-class apartments. │ │300–500
│Three and four-story dwellings, business│ │
│ blocks and industrial establishments. │ │
│ Closely built up. │ │100–300
│Separate residences, 50 to 75–foot │ │
│ fronts, commercial districts, │ │
│ moderately well built up. │ │ 50–100
│Sparsely settled districts and scattered│ │
│ frame dwellings for individual │ │
│ families. │ │ 0–50
────────────┴────────────────────────────────────────┴────────┴────────
The density of population in Cincinnati from 1850 to 1913 with
predictions to 1950 is given in Fig. 9.[18] This shows the densities for
the entire city and is illustrative of the manner in which future
conditions were predicted for the design of an intercepting sewer. The
data given in Table 5 are of value in estimating the densities of
population in various districts. The Committee on City Plan of the Board
of Estimate and Apportionment of New York City obtained some valuable
information on this point, especially in Manhattan. Three-story
dwellings with 18–foot frontage, or four-story flats with 20–foot
frontage, presumably contiguous, were found to hold 100 persons to the
acre. Five-story flats held 520 to 670 persons per acre. Six-story flats
held 800 to 1,000 persons per acre, and high-class six-story apartments
held less than 300 per acre.
=22. Changes in Area.=—In order to determine the probable extent of a
proposed sewerage system it is important to estimate the changes in the
area of a city as well as the changes in the population. With the same
population and an increased area the quantity of sewage will be
increased because of the larger amount of ground water which will enter
the sewers. Predictions of the area of a city are less accurate than
predictions of population because the factors affecting changes cannot
be so easily predicted. An area curve plotted against time would be
helpful in guiding the judgment, but its extension into the future based
on past occurrences would be futile. A knowledge of the city, its
political tendencies, possibilities of extension, and other factors must
be weighed and judged. The engineer, if he is ignorant of the city for
which he is making provision, is dependent upon the testimony of real
estate men, business men and others acquainted with the local situation.
=23. Relation between Population and Sewage Flow.=—The amount of sewage
discharged into a sewerage system is generally equal to the amount of
water supplied to a community, exclusive of ground water. The entire
public water supply does not reach the sewers, but the losses due to
leakage, lawn sprinkling, manufacturing processes, etc., are made up by
additions from private water supplies, surface drainage, etc. The
estimated quantity of water used but which did not reach the sewers in
Cincinnati is shown in Table 6. The amount shown represents 38 per cent
of the total consumption. Unless direct observations have been made on
existing sewers or other factors are known which will affect the
relation between water supply and sewage, the average sewage flow
exclusive of ground water, should be taken as the average rate of water
consumption. Experience has shown that water consumption increases after
the installation of sewers.
TABLE 6
ESTIMATED QUANTITY OF WATER USED BUT NOT DISCHARGED INTO THE SEWERS IN
CINCINNATI
Expressed in gallons per capita per day, and based on a total
consumption of 125 to 150 gallons per capita per day.
──────────────────────────────────────────────────────────────┬────────
Steam railroads. │6 to 7
Street sprinklers. │6 to 7
Consumers not sewered. │9 to 10½
Manufacturing and mechanical. │6 to 7
Lawn sprinklers. │3 to 3½
Leakage. │18 to 21
──────────────────────────────────────────────────────────────┴────────
The public water supply is generally installed before the sewerage
system. By collecting statistics on the rate of supply of water a fair
prediction can be made of the quantity of sewage which must be cared
for. The rate of water supply varies widely in different cities. It is
controlled by many factors such as meters, cost and availability of
water, quality of water, climate, population, etc. In American cities a
rough average of consumption is 100 gallons per capita per day. Other
factors being equal the rate of consumption after meters have been
installed will be about one-half the rate before the meters were
installed. Low cost, good quantity and good quality will increase the
rate of consumption, and the rate will increase slowly with increasing
population. Statistics of rates of water consumption are given in Table
7.
=24. Character of District.=—The various sections of a city are
classified as commercial, industrial, or residential. The residential
districts can be subdivided into sparsely populated, moderately
populated, crowded, wealthy, poor, etc. Commercial districts may be
either retail stores, office buildings, or wholesale houses. Industrial
districts may be either large factories, foundries, etc., or they may be
made up of small industries housed in loft buildings.
In cities of less than 30,000 population the refinement of such
subdivisions is generally unnecessary in the study of sewage flow, all
districts being considered the same. The data given in Tables 8 and 9
indicate the difference to be found in different districts of large
cities. The Milwaukee data are presented in a form available for
estimates on different bases. These data are shown in Table 10.
TABLE 7
RATES OF WATER CONSUMPTION
From Journals of American and New England Water Works Associations
───────────────────────────────────┬───────────┬───────────┬───────────
City │Population │ Per Cent │Consumption,
│ in │ Metered │ Gal. per
│ Thousands │ │Capita per
│ │ │ Day
───────────────────────────────────┼───────────┼───────────┼───────────
Tacoma, Wash. │ 100 │ 11.6│ 460
Buffalo, N. Y. │ 450 │ 4.9│ 310
Cheyenne, Wyo. │ 13 │ │ 270
Erie, Pa. │ 72 │ 3.0│ 198
Philadelphia, Pa. │ 1611 │ 4.6│ 180
St. Catherines, Ont. │ 17 │ 3.2│ 160
Port Arthur, Ont. │ 18 │ 14.7│ 145
Ogdensburg, N. Y. │ 18 │ 0.2│ 140
Los Angeles, Cal. │ 516 │ 77.9│ 140
Wilmington, Del. │ 92 │ 43.7│ 125
Lancaster Pa. │ 60 │ 34.6│ 120
Richmond, Va. │ 120 │ 75.2│ 115
St. Louis, Mo. │ 730 │ 6.7│ 110
Springfield, Mass. │ 100 │ 94.4│ 110
Keokuk, Ia. │ 14 │ 64.5│ 105
Jefferson City, Mo. │ 13.5│ 34.4│ 100
Muncie, Ind. │ 30 │ 23.8│ 95
Burlington, Ia. │ 24 │ 4.5│ 90
Council Bluffs, Ia. │ 32 │ 75.5│ 80
San Diego, Cal. │ 85 │ 100 │ 80
Monroe, Wis. │ 3 │ 100 │ 80
Yazoo City, Miss. │ 7 │ 84.1│ 75
Oak Park, Illinois. │ 26 │ 100 │ 70
Portsmouth, Va. │ 75 │ 8.1│ 65
New Orleans, La. │ 360 │ 99.7│ 60
Rockford, Ill. │ 53 │ 93.0│ 55
Fort Dodge, Ia. │ 20 │ 96.0│ 50
Manchester, Vt. │ 1.5│ 69.0│ 45
Woonsocket, R. I. │ 47.5│ 95.6│ 35
───────────────────────────────────┴───────────┴───────────┴───────────
Attempts have been made to express the rate of sewage flow in different
units other than in gallons per capita per day. A unit in terms of
gallons per square foot of floor area tributary has been suggested for
commercial and industrial districts. It has not been generally adopted.
The rates of flow in New York City as reported in this unit by W. S.
McGrane are given in Table 11.
The most successful way to predict the flow from commercial or
industrial districts is to study the character of the district’s
activities and to base the prediction on the quantity of water demanded
by the commerce and industry of the district affected.
=25. Fluctuations in Rate of Sewage Flow.=—The rate of flow of sewage
from any district varies with the season of the year, the day of the
week, and the hour of the day. The maximum and minimum rates of sewage
flow are the controlling factors in the design of sewers. The sewers
must be of sufficient capacity to carry the maximum load which may be
put upon them, and they must be on such a grade that deposits will not
occur during periods of minimum flow. The maximum and minimum rates of
flow are usually expressed as percentages of the average rate of flow.
TABLE 8
SEWAGE FLOW FROM DIFFERENT CLASSES OF DISTRICTS
Arranged from data by Kenneth Allen in Municipal Engineer’s Journal,
Feb., 1918.
──────────────────────────────────────────────────────┬───────┬───────
District │Gallons│Gallons
│ per │ per
│Capita │ Acre
│per Day│per Day
──────────────────────────────────────────────────────┼───────┼───────
Buffalo, N. Y. From Report of International Joint │ │
Commission on the Pollution of Boundary Waters: │ │
Industrial: Metal and automobile plants. Maximum. │ │ 13,000
Industrial: Meat packing, chemical and soap. │ │ 16,000
Commercial: Hotels, stores and office buildings. │ │ 60,000
Domestic: Average. │ 80 │
Domestic: Apartment houses. │ 147 │
Domestic: First-class dwellings. │ 129 │
Domestic: Middle-class dwellings. │ 81 │
Domestic: Lowest-class dwellings. │ 35.5│
│ │
Cincinnati, Ohio. 1913 Report on Sewerage Plan: │ │
Industrial, in addition to residential and ground │ │
water. │ │ 9,000
Commercial, in addition to residential and ground │ │
water. │ │ 40,000
Domestic. │ 135 │
│ │
Detroit, Mich.: │ │
Domestic. │ 228 │
Industrial, in addition to residential and ground │ │
water. │ │ 12,000
Commercial, in addition to residential and ground │ │
water. │ │ 50,000
│ │
Milwaukee, Wis. 1915 Report of Sewerage Commission: │ │
Industrial, maximum. │ 81 │ 16,600
Industrial, average. │ 31 │ 8,300
Commercial, maximum. │ │ 60,500
Commercial, average. │ │ 37,400
Wholesale commercial, maximum. │ │ 20,000
Wholesale commercial, average. │ │ 9,650
──────────────────────────────────────────────────────┴───────┴───────
TABLE 9
OBSERVED WATER CONSUMPTION IN DIFFERENT CLASSES OF DISTRICTS IN NEW YORK CITY
From data by Kenneth Allen in Municipal Engineers Journal, for 1918
─────────────┬─────────────┬──────────┬─────────────┬───────────┬─────────────
Hotels │ Daily Cons. │Tenements │ Daily Cons. │Office and │ Daily Cons.
│ Gals. per │ │ Gals. per │ Loft │ Gals. per
│1000 Sq. Ft. │ │1000 Sq. Ft. │ Buildings │1000 Sq. Ft.
│ Floor Area │ │ Floor Area │ │ Floor Area
─────────────┼────────┬────┼──────────┼────────┬────┼───────────┼────────┬────
Building │Max.[19]│Avg.│ Location │Max.[19]│Avg.│ Building │Max.[19]│Avg.
─────────────┼────────┼────┼──────────┼────────┼────┼───────────┼────────┼────
Hotel │ │ │78th–79th │ │ │McGraw │ │
Biltmore. │ │ │ St. and │ │ │ Bldg. │ │
│ 470 │368 │ B’way. │ 256 │192 │ │ 309 │206
Hotel │ │ │410 E. │ │ │N. Y. │ │
McAlpin. │ │ │ 65th St.│ │ │ Telephone│ │
│ 753 │694 │ │ 350 │295 │ Bldg. │ │194
Hotel Plaza. │ │ │30th St. │ │ │Met. Life │ │
│ │ │ and │ │ │ Bldg. │ │
│ │ │ Madison │ │ │ │ │
│ 630 │578 │ Ave │ 306 │188 │ │ │256
Hotel Waldorf│ │ │27 Lewis │ │ │42d St. │ │
Astoria. │ 618 │482 │ St. │ 307 │250 │ Bldg │ │271
Hotel Astor. │ │ │258 │ │ │Municipal │ │
│ │ │ Delancey│ │ │ Bldg. │ │
│ 732 │492 │ St. │ 267 │226 │ │ │118
Hotel │ │ │ │ │ │Equitable │ │
Vanderbilt.│ 604 │545 │ │ │ │ Bldg. │ 366 │268
─────────────┼────────┼────┼──────────┼────────┼────┼───────────┼────────┼────
Average │ 634 │526 │ Average │ 297 │230 │ Average │ 338 │219
─────────────┴────────┴────┴──────────┴────────┴────┴───────────┴────────┴────
TABLE 10
SEWAGE FLOW FROM DIFFERENT CLASSES OF DISTRICTS BASED ON 1915 REPORT OF
MILWAUKEE SEWERAGE COMMISSION
────────────────────────────────────────────────────────────────┬──────
Ratio of maximum to average rate for department store district. │ 1.755
Ratio of maximum to average rate for hotel district. │ 1.65
Ratio of maximum to average rate for office building district. │ 1.51
Ratio of maximum to average rate for wholesale commercial │
district. │ 2.1
│
│——————│——————
Average and maximum gallons per thousand square feet of │ │
floor area: │ Avg. │ Max.
│——————│——————
For department store district. │ 232│ 407
For office building district. │ 541│ 891
For wholesale commercial district. │ 164│ 344
For all districts except wholesale commercial. │ 381│ 618
│ │
Average and maximum gallons per day: │ │
For all districts except wholesale commercial. │17,700│29,800
For wholesale commercial district. │ 9,650│20,000
─────────────────────────────────────────────────────────┴──────┴──────
TABLE 11
RATES OF CONSUMPTION PREDICTED FOR DIFFERENT DISTRICTS IN NEW YORK CITY
────────────┬───────────┬──────┬────────┬────────┬─────────
│ Net Bldg. │ │Observed│Observed│
│Area in Sq.│ Avg. │Cons. in│Cons. in│Predicted
District │ Ft. per │Number│ g.p.d. │ g.p.d. │ Mean
│ Acre for │ of │per 1000│per 1000│ Cons.
│ Ultimate │Floors│Sq. Ft. │Sq. Ft. │
│Consumption│ │ Max. │ Avg. │
────────────┼───────────┼──────┼────────┼────────┼─────────
Hotel and │ 24,800│ 15│ 634│ 526│ 500
midtown. │ │ │ │ │
Midtown and │ 24,800│ 15│ 338│ 219│ 300
financial.│ │ │ │ │
East and │ │ │ │ │
West of │ 24,800│ 10│ 297│ 230│ 300
midtown. │ │ │ │ │
Apartment, │ │ │ │ │
59th to │ 20,400│ 7│ │ 230│ 300
155th Sts.│ │ │ │ │
Manhattan │ │ │ │ │
north of │ 20,400│ 5│ │ 230│ 300
155th St. │ │ │ │ │
────────────┴───────────┴──────┴────────┴────────┴─────────
────────────┬─────────┬─────────┬─────────┬────────┬────────
│Predicted│Predicted│Predicted│Measured│Measured
│ Mean in │ Dry │Max. Dry │Avg. Dry│Max. Dry
District │ Million │ Weather │ Weather │Weather │Weather
│Gals. per│ Flow, │ Flow, │ Flow, │ Flow,
│Acre per │ c.f.s. │ c.f.s. │ c.f.s. │ c.f.s.
│ Day │per Acre │per Acre │per Acre│per Acre
────────────┼─────────┼─────────┼─────────┼────────┼────────
Hotel and │ .20 │ .29│ .34│ 1.04 │ .146
midtown. │ │ │ │ │
Midtown and │ .12 │ .18│ .23│ .078│ .110
financial.│ │ │ │ │
East and │ │ │ │ │
West of │ .074│ .12│ .15│ .057│ .097
midtown. │ │ │ │ │
Apartment, │ │ │ │ │
59th to │ .043│ .06│ .09│ │
155th Sts.│ │ │ │ │
Manhattan │ │ │ │ │
north of │ .031│ .05│ .08│ │
155th St. │ │ │ │ │
────────────┴─────────┴─────────┴─────────┴────────┴────────
Midtown district consists of department stores, large railroad
terminals, industrial and loft buildings, and sky-scraper office
buildings.
It is difficult to set any definite figure for the percentage which the
maximum rate of flow is of the average. Fluctuations above and below the
average are greater the smaller the tributary population. This relation
can be expressed empirically as
_M_ = 500⁄_P_^⅕,
in which _M_ represents the per cent which the maximum flow is of the
average, and _P_ represents the tributary population in thousands. The
expression should not be used for populations below 1,000 nor above
1,000,000. Having determined the expected average flow of sewage by a
study of the population, water consumption, etc., the maximum quantity
of sewage is determined by multiplying the average flow by the per cent
which the maximum is of the average. In this connection W. G. Harmon[20]
offers the relation
_M_ = 1 + 14⁄(4 + √(_P_)),
which was used in the design of the Ten Mile Creek intercepting sewer at
Toledo, Ohio. For rough estimates and for comparative purposes the ratio
of the average to the minimum flow can be taken the same as the ratio of
the maximum to the average flow, unless direct gaugings or other
information show it to be otherwise.
[Illustration:
Fig. 10.—Daily and Hourly Variations of Sewage Flow.
]
1. Toledo, O.; Manufacturing average.
2. Toledo, O.; Manufacturing, Monday.
3. Toledo, O.; Manufacturing, Sunday.
4. Toledo, O.; Residential, average.
5. Toledo, O.; Residential, Monday.
6. Toledo, O.; Residential, Sunday.
7. Cincinnati, O., Industrial, average.
8. Cincinnati, O.; Residential, average.
9. Cincinnati, O.; Commercial, average.
10. Average of 7 cities.
The fluctuations of flow in commercial and industrial districts are so
different from those in residential districts that the formulas given
should not be used in the design of sewers other than those draining
residential areas. It is reasonable to suppose that fluctuations in
rates of flow from industrial districts are dependent upon the character
of the tributary industries. A study of these industries will give
valuable light on the maximum and minimum rates at which sewage will be
delivered to the sewers.
Hourly, daily, and seasonal fluctuations in rates of sewage flow are of
interest in the design of pumping stations to give knowledge of the
rates at which the pumps must operate at various periods. The
fluctuations in rates of sewage flow during various hours and days in
different cities and districts are shown in Fig. 10. Fluctuations in
rate of flow of sewage lag behind fluctuations in rate of water
consumption, the time being dependent on the distance through which the
wave of change must travel in the sewer.
=26. Effect of Ground Water.=—Sewers are seldom laid with water-tight
joints. Since they usually lie below the ground water level it is
inevitable that a certain amount of ground water will enter. Various
units have been suggested for the expression of the inflow of ground
water in an attempt to include all of the many factors. Some of these
units are: gallons per acre drained by the sewer per day, gallons per
mile of pipe per day, gallons per inch diameter per mile of pipe per
day, etc. Since the ground water enters pipe sewers at the joints, the
longer the joints the greater the probability of the entrance of ground
water. The last unit is therefore the most logical but the accuracy of
the result is scarcely worthy of such refinement and the unit usually
adopted is gallons per mile of pipe per day.
No definite figure can be given for the amount of ground water to be
expected in sewers since the character of the soil and the ground water
pressure must be considered. Relatively normal infiltration may be found
from 5,000 to 80,000 gallons per mile of pipe per day. The minimum is
seldom reached in wet ground and the maximum is frequently exceeded.
Table 12 shows the amount of ground water measured in various sewers as
given by Brooks.[21]
=27. Résumé of Method for Determination of Quantity of Dry weather
Sewage.=—The steps in the determination of the quantity of sewage are:
determine the period in the future for which the sewers are to be
designed; estimate the population and tributary area at the end of this
period; estimate the rate of water consumption and assume the sewage
flow to equal the water consumption; determine the maximum and minimum
rates of sewage flow; and finally, estimate the maximum rate of ground
water seepage and add it to the maximum rate of sewage flow to give the
total quantity of sewage to be carried by the proposed sewers.
TABLE 12
DATA ON THE INFILTRATION OF GROUND WATER INTO SEWERS
Abstracted from paper by J. N. Brooks in Transactions Am. Society of Civil
Engineers, Vol. 76, p. 1909.
───────────┬─────┬──────┬─────┬───────┬──────┬─────┬──────────────────────
Place │ │Diam- │ │ │ │ │
│ │ eter │ │ Wet │ Avg. │ │
│ │ or │ │Trench,│ Head │Char-│
│ │Dimen-│ │ Per │ of │acter│
│ │sions │ │Cent of│Ground│ of │
│ │ in │Mate-│ Total │Water,│Sub- │
│Shape│Inches│rial │Length │ Fee │grade│ Gallons per 24 Hours
───────────┼─────┼──────┼─────┼───────┼──────┼─────┼─────┬──────┬─────────
│ │ │ │ │ │ │ │ Per │
│ │ │ │ │ │ │ │ Inch │
│ │ │ │ │ │ │ │Diam- │
│ │ │ │ │ │ │ │ eter │
│ │ │ │ │ │ │ Per │ Per │
│ │ │ │ │ │ │Foot │ Mile │
│ │ │ │ │ │ │ of │ of │Per Mile
│ │ │ │ │ │ │Joint│ Pipe │ of Pipe
───────────┼─────┼──────┼─────┼───────┼──────┼─────┼─────┼──────┼─────────
Boston, │ │ 8 to │ │ │ │ │ │ │
Mass. │Circ.│ 36 │V.P. │ │ │ │ 2.6│ 1,818│ 40,000
East │ │ │ │ │ │ │ │ │
Orange, │ │ │ │ │ │ │ │ │
N. J. │ │ │ │ │ 10│ Q. │ │ │ 22,400
East │ │ │ │ │ │ │ │ │
Orange, │ │ 8 to │ │ │ │ │ │ │
N. J. │ │ 24 │V.P. │ │ │ │ 0.8│ 540│ 8,650
Joint trunk│ │ │ │ │ │ │ │ │
sewer, │ │ │ │ │ │ │ │ │
New │ │ │ │ │ │G. & │ │ │
Jersey │ │ │ │ │ │ Q. │ │ │ 25,000
Rogers │ │ │ │ │ │ │ │ │
Park, │ │ │ │ │ │ │ │ │
Ill. │ │ 6 │ │ │ │ │ 0.3│ 207│ 1,240
Altoona, │ │ │ │ │ │ │ │ │
Pa. │ │ 30 │ │ │ │ │ 5.0│ 2,890│ 86,592
Concord, │ │ │ │ │ │ │ │ │
Mass. │ │ │ │ 18│ 8│ │ │ │ 43,000
Malden, │ │ │ │ │ │ │ │ │
Mass. │Circ.│ │V.P. │ 60│ │ │ │ │ 50,000
Westboro, │ │ │ │ │ │ │ │ │
Mass. │ │ 15 │V.P. │ 100│ │ │ │88,100│1,320,300
Fond du │ │ │ │ │ │ │ │ │
Lac, Wis.│Circ.│ 24 │V.P. │ 100│ 5│ C. │ 1.5│ 1,010│ 24,370
East │ │ │ │ │ │ │ │ │
Orange, │ │10 to │ │ │ │ │ │ │
N. J. │Circ.│ 24 │V.P. │ 100│ │ │ 4.7│ 2,540│ 43,250
Ocean │ │ │ │ │ │ │ │ │
Grove, N.│ │ 4 to │ │ │ │ │ │ │
J. │Circ.│ 12 │V.P. │ 100│ 3│S.C. │ 2.7│ 1,890│ 15,126
Ocean │ │ │ │ │ │ │ │ │
Grove, N.│ │ 4 to │ │ │ │ │ │ │
J. │Circ.│ 12 │V.P. │ 100│ 4│S.C. │ 7.9│ 5,480│ 43,764
East │ │ │ │ │ │ │ │ │
Orange, │ │ 24 × │ │ │ │ │ │ │
N. J. │Rect.│ 36 │Brick│ 100│ │ │ │ │ 570,000
Westboro, │ │ │ │ │ │ │ │ │
Mass. │ │ │Brick│ │ │ │ │ │ 415,850
Altoona, │ │ 33 × │B. & │ │ │ │ │ │
Pa. │Rect.│ 44 │ C. │ │ │ │ │ 5,390│ 264,000
Columbus, │ │ 42 × │Con- │ │ │ │ │ │
Ohio. │H.S. │ 42 │crete│ │ │ │ │ 120│ 6,340
Bronx │ │ │ │ │ │ │ │ │
Valley, │ │44 to │Con- │ │ │ │ │ │
N. Y. │Circ.│ 72 │crete│ │ │ G. │ │ 123│ 7,266
Cincinnati,│ Estimated in design. Data not │ │ │ │
Ohio. │ from Brooks │ │ │ │ 67,500
Milwaukee, │ Residential districts, gals. per acre per │ │ 1460 to
Wis. │ day. Not taken from Brooks │ │ 2200
───────────┴─────────────────────────────────────────────┴──────┴─────────
Abbreviations: H.S. = horseshoe shaped; B. & C = Brick and concrete; V.P.
= vitrified pipe; G. = gravel; Q. = quicksand; S. C. = sand clay; C. =
clay.
QUANTITY OF STORM WATER
=28. The Rational Method.=—The water which falls during a storm must be
removed rapidly in order to prevent the flooding of streets and
basements, and other damages. The quantity of water to be cared for is
dependent upon: the rate of rainfall, the character and slope of the
surface, and the area to be drained. All methods for the determination
of storm-water run-off, whether rational or empirical, depend upon these
factors.
The so-called Rational Method can be expressed algebraically, as,
_Q_ = _AIR_,
in which _Q_ = rate of run-off in cubic feet per second;
_A_ = area to be drained expressed in acres;
_I_ = percentage imperviousness of the area;
_R_ = maximum average rate of rainfall over the entire
drainage area, expressed in inches per hour, which
may occur during the time of concentration.
The area to be drained is determined by a survey. A discussion of _R_
and _I_ follows in the next two sections. An example of the use of the
Rational Method is given on page 95.
=29. Rate of Rainfall.=—Rainfall observations have been made over a long
period of time by United States Weather Bureau observers and others.
Continuous records are available in a few places in this country showing
rainfall observations covering more than a century. Such records have
been the bases for a number of empirical formulas for expressing the
probable maximum rate of rainfall in inches per hour, having given the
duration of the storm. Table 13 is a collection of these formulas with a
statement as to the conditions under which each formula is applicable.
The formula most suitable to the problem in hand should be selected for
its solution.[22]
TABLE 13
RAINFALL FORMULAS
────────────┬─────────────────────────┬────────────────────────────────
Name of │ Conditions for which │ Formula
Originator │ Formula is Suitable │
────────────┼─────────────────────────┼────────────────────────────────
E. S. Dorr │ │_i_ = 150⁄(_t_ + 30)
A. N. Talbot│Maximum storms in Eastern│_i_ = 360⁄(_t_ + 30)
│ United States │
A. N. Talbot│Ordinary storms in │_i_ = 105⁄(_t_ + 15)
│ Eastern United States │
Emil │Heavy rainfall near New │_i_ = 120⁄(_t_ + 20), etc.
Kuichling │ York City │
L. J. Le │For San Francisco. See T.│
Conte │ A. S. C. E. v. 54, p. │_i_ = 7⁄_t_^½
│ 198 │
Sherman │Maximum for Boston, Mass.│_i_ = 25.12⁄_t_^{.687}
Sherman │Extraordinary for Boston,│_i_ = 18⁄_t_ ^½
│ Mass. │
Webster │Ordinary for │_i_ = 12⁄_t_^{0.6}
│ Philadelphia, Pa. │
│Ordinary storms for │
Hendrick │ Baltimore. Eng. & │_i_ = 105⁄(_t_ + 10)
│ Cont., Aug. 9. 1911 │
J. de │Ordinary storms for │_i_ = 163⁄(_t_ + 27)
Bruyn-Kops│ Savannah, Ga. │
C. D. Hill │For Chicago, Ill. │_i_ = 120⁄(_t_ + 15)
Metcalf and │Louisville, Ky. Am. Sew. │_i_ = 14⁄_t_^½
Eddy │ Prac., Vol I. │
W. W. Horner│St. Louis, Mo. Eng. News,│_i_ = 56⁄(_t_ + 5)^{.85}
│ Sept. 29, 1910 │
R. A. │For Spokane, Wash. Eng. │_i_ = 23.92⁄(_t_ + 2.15) + 0.154
Brackenbuy│ Record, Aug. 10, 1912 │
Metcalf and │New Orleans │_i_ = 19⁄_t_^½
Eddy │ │
Metcalf and │For Denver, Colo. │_i_ = 84⁄(_t_ + 4)
Eddy │ │
│Central Park, N. Y. │
Kenneth │ 51–Year Record. Eng. │_i_ = 400⁄(2_t_ + 40)[23]
Allen │ News-Record, April 7, │
│ 1921, p. 588 │
────────────┴─────────────────────────┴────────────────────────────────
=30. Time of Concentration.=—By the time of concentration is meant the
longest time without unreasonable delay that will be required for a drop
of water[24] to flow from the upper limit of a drainage area to the
outlet. Assuming a rainfall to start suddenly and to continue at a
constant rate and to be evenly distributed over a drainage area of 100
per cent imperviousness and even slope towards one point, the rate of
run-off would increase constantly until the drop of water from the upper
limit of the area reached the outlet, after which the rate of run-off
would remain constant. In nature the rate of rainfall is not constant.
The shorter the duration of a storm the greater the intensity of
rainfall. Therefore the maximum run-off during a storm will occur at the
moment when the upper limit of the area has commenced to contribute.
From that time on the rate of run-off will decrease.
The time of concentration can be measured fairly well by observing the
moment of the commencement of a rainfall, and the time of maximum
run-off from an area on which the rain is falling. A prediction of the
time of concentration is more or less guess work. As the result of
measurements some engineers assume the time of concentration on a city
block built up with impervious roofs and walks, and on a moderate slope,
is about 5 to 10 minutes. This is used as a basis for the judgment of
the time of concentration on other areas. For relatively large drainage
areas such a method cannot be used. The procedure is to measure the
length of flow through the drainage channels of the area, to assume the
velocity of the flood crest through these channels and thus to determine
the time of concentration. Table 14 shows the flood crest velocities in
various streams of the Ohio River Basin under flood conditions. The
velocity over the surface of the ground may be approximated by the use
of the formula[25]
_V_ = 2,000_I_√(_S_),
in which _V_ = the velocity of flow over the surface of the ground in
feet per minute;
_I_ = the percentage imperviousness of the ground;
_S_ = the slope of the ground.
For areas up to 100 acres where natural drainage channels are not
existent this formula will give more satisfactory results than guesses
based on the time of concentration of certain known areas.
Having determined the time of concentration, the rate of rainfall _R_ to
be used in the Rational Method is found by substitution in some one of
the rainfall formulas given in Table 13.
TABLE 14
FLOOD CREST VELOCITIES IN OHIO RIVER BASIN IN MARCH, 1913
From Table 12. U. S. G. S., Water Supply Paper. No. 334
───────────┬───────────────┬────────┬────────┬───────────────┬─────────┬───────────┬────────
River │ Stations │ │Distance│ Distance of │Velocity │ Velocity │
│ │Distance│to Mouth│ Lower Station │ between │ from │ Time
│ │between │ of │ below │Stations,│Pittsburgh,│between
│ │Stations│ River, │Starting-point,│Miles per│ Miles per │Stations
│ │in Miles│ Miles │ Miles │ Hour │ Hour │in Hours
───────────┼───────────────┼────────┼────────┼───────────────┼─────────┼───────────┼────────
Ohio │Pittsburgh, │ │ │ │ │ │
│ Pa., to │ │ │ │ │ │
│ Wheeling, W. │ │ │ │ │ │
│ Va. │ 90│ 967│ 90│ 9.0│ 9.0│ 10.0
Ohio │Wheeling, W. │ │ │ │ │ │
│ Va., to │ │ │ │ │ │
│ Marietta, │ │ │ │ │ │
│ Ohio │ 82│ 877│ 172│ 5.9│ 7.2│ 14
Ohio │Marietta, Ohio,│ │ │ │ │ │
│ to │ │ │ │ │ │
│ Parkersburg, │ │ │ │ │ │
│ W. Va. │ 12│ 795│ 184│ 0.9│ 4.8│ 14
Ohio │Parkersburg to │ │ │ │ │ │
│ Point │ │ │ │ │ │
│ Pleasant, W. │ │ │ │ │ │
│ Va. │ 80│ 783│ 264│ 6.7│ 5.3│ 12
Ohio │Point Pleasant │ │ │ │ │ │
│ to │ │ │ │ │ │
│ Huntington, │ │ │ │ │ │
│ W. Va. │ 44│ 703│ 308│ 11.0│ 5.7│ 4
Ohio │Huntington to │ │ │ │ │ │
│ Catlettsburg,│ │ │ │ │ │
│ W. Va. │ 9│ 659│ 317│ 0.8│ 4.1│ 11
Ohio │Catlettsburg, │ │ │ │ │ │
│ W. Va., to │ │ │ │ │ │
│ Portsmouth, │ │ │ │ │ │
│ Ohio │ 38│ 650│ 355│ │ 5.0│
Ohio │Portsmouth │ │ │ │ │ │
│ Ohio, to │ │ │ │ │ │
│ Maysville, │ │ │ │ │ │
│ Ky. │ 52│ 612│ 407│ 5.2│ 5.0│ 10
Ohio │Maysville, Ky.,│ │ │ │ │ │
│ to │ │ │ │ │ │
│ Cincinnati, │ │ │ │ │ │
│ Ohio │ 61│ 560│ 468│ 6.8│ 5.2│ 9
Ohio │Cincinnati, │ │ │ │ │ │
│ Ohio, to │ │ │ │ │ │
│ Louisville, │ │ │ │ │ │
│ Ky. │ 136│ 499│ 604│ 11.4│ 5.9│ 12
Ohio │Louisville, │ │ │ │ │ │
│ Ky., to │ │ │ │ │ │
│ Evansville, │ │ │ │ │ │
│ Ind. │ 183│ 363│ 787│ 1.9│ 5.3│ 96
Ohio │Evansville, │ │ │ │ │ │
│ Ind., to Mt. │ │ │ │ │ │
│ Vernon Ind. │ 36│ 180│ 823│ 9.0│ 5.3│ 4
Ohio │Mt. Vernon, │ │ │ │ │ │
│ Ind., to │ │ │ │ │ │
│ Paducah, Ky.│ 101│ 144│ 924│ 2.1│ 4.6│ 48
Ohio │Paducah, Ky. to│ │ │ │ │ │
│ Cairo, Ill. │ 43│ 43│ 967│ 2.9│ 4.2│ 15
Monongahela│Fairmont, W. │ │ │ │ │ │
│ Va., to Lock │ │ │ │ │ │
│ No. 2 Pa. │ │ │ │ │ │
│ (Upper) │ 107│ 119│ 107│ 6.7│ │ 16
Little │Creston, W. │ │ │ │ │ │
Kanawha │ Va., to Dam. │ │ │ │ │ │
│ No. 4 W. Va. │ │ │ │ │ │
│ (Upper) │ 16│ 48│ 16│ 16.0│ │ 1
New │Radford, W. │ │ │ │ │ │
│ Va., to │ │ │ │ │ │
│ Hinton, W. │ │ │ │ │ │
│ Va. │ 78│ 139│ 78│ 3.0│ │ 26
Kanawha │Kanawha Falls, │ │ │ │ │ │
│ W. Va. to │ │ │ │ │ │
│ Charleston, │ │ │ │ │ │
│ W. Va. │ 37│ 95│ 37│ 2.6│ │ 14
Scioto │Columbus, Ohio,│ │ │ │ │ │
│ to │ │ │ │ │ │
│ Chillicothe, │ │ │ │ │ │
│ Ohio │ 52│ 110│ 52│ 4.7│ │ 11
Miami │Dayton, Ohio, │ │ │ │ │ │
│ to Hamilton, │ │ │ │ │ │
│ Ohio │ 44│ 77│ 44│ 14.7│ │ 3
Kentucky │Highbridge, │ │ │ │ │ │
│ Ky., to │ │ │ │ │ │
│ Frankfort, │ │ │ │ │ │
│ Ky. │ 52│ 117│ 52│ 5.2│ │ 10
Cumberland │Celina, Tenn. │ │ │ │ │ │
│ to Nashville,│ │ │ │ │ │
│ Tenn. │ 190│ 383│ 190│ 2.9│ │ 64.5
Tennessee │Knoxville to │ │ │ │ │ │
│ Chattanooga, │ │ │ │ │ │
│ Tenn. │ 183│ 635│ 183│ 3.2│ │ 57
───────────┴───────────────┴────────┴────────┴───────────────┴─────────┴───────────┴────────
NOTE.—The velocities shown are the velocities of the crest of the flood wave and are not the
average velocity of the flow of the river. The velocity of the crest of the flood wave
should be used in determining the time of concentration. The flood crest velocity is slower
then that of the river because of the storage in the river basin.
=31. Character of Surface.=—The proportion of total rainfall which will
reach the sewers depends on the relative porosity, or imperviousness,
and the slope of the surface. Absolutely impervious surfaces such as
asphalt pavements or roofs of buildings will give nearly 100 per cent
run-off regardless of the slope, after the surfaces have become
thoroughly wet. For unpaved streets, lawns, and gardens the steeper the
slope the greater the per cent of run-off. When the ground is already
water soaked or is frozen the per cent of run-off is high, and in the
event of a warm rain on snow covered or frozen ground, the run-off may
be greater than the rainfall. The run-off during the flood of March,
1913, at Columbus, Ohio, was over 100 per cent of the rainfall. Table
15[26] shows the relative imperviousness of various types of surfaces
when dry and on low slopes. The estimates for relative imperviousness
used in the design of the Cincinnati intercepter are given in Table 16.
TABLE 15
VALUES OF RELATIVE IMPERVIOUSNESS
Roof surfaces assumed to be water-tight 0.70– 0.95
Asphalt pavements in good order .85– .90
Stone, brick, and wood-block pavements with tightly cemented
joints .75– .85
The same with open or uncemented joints .50– .70
Inferior block pavements with open joints .40– .50
Macadamized roadways .25– .60
Gravel roadways and walks .15– .30
Unpaved surfaces, railroad yards, and vacant lots .10– .30
Parks, gardens, lawns, and meadows, depending on surface
slope and character of subsoil .05– .25
Wooded areas or forest land, depending on surface slope and
character of subsoil .01– .20
Most densely populated or built up portion of a city .70– .90
TABLE 16
COEFFICIENTS OF IMPERVIOUSNESS USED IN THE DESIGN OF THE CINCINNATI SEWERS
──────────────┬─────────────────────────────┬──────────────────┬───────────
Character of │ │ │Residential,
Improvement │ │ │291.1 A. 20
│ │ │ per Acre,
│ │ │ Middle
│ │ │ Class,
│ │ │ Detached
│ │ │Dwellings,
│ │ │Yellow and
│ │Combined Tenement │ Blue Clay
│ │ and Industrial. │ Overlying
│Typical Commercial Area, 30.4│ 35.6 A., 55 per │ Beds of
│A. None Undeveloped. Sand and│ Acre. Clay, Sand │ Shale and
│ Gravel │ and Gravel │ Sandstone
──────────────┼──────┬─────┬─────┬──────────┼──────┬─────┬─────┼─────┬─────
│ Area │ │ │Equivalent│ Area │ │ │ Per │
│ in │ Per │ │Imp. Area,│ in │ Per │ │Cent │
│1000’s│Cent │ I, │ 1000’s │1000’s│Cent │ I, │ of │ I,
│Square│Total│Esti-│ Square │Square│Total│Esti-│Total│Esti-
│ Feet │Area │mated│ Feet │ Feet │Area │mated│Area │mated
──────────────┼──────┼─────┼─────┼──────────┼──────┼─────┼─────┼─────┼─────
Roofs: │ │ │ │ │ │ │ │ │
Public and │ │ │ │ │ │ │ │ │
commercial│ 881.2│ 66.5│ 0.90│ 793.0│ 66.8│ 4.3│ 0.40│ 4.8│ 0.40
Residences │ │ │ │ │ 289.2│ 18.6│ .90│ 13.1│ .90
Barns and │ │ │ │ │ │ │ │ │
sheds │ │ │ │ │ 79.2│ 5.1│ .75│ 1.4│ .75
│ │ │ │ │ │ │ │ │
Interior │ │ │ │ │ │ │ │ │
Walks: │ │ │ │ │ │ │ │ │
Brick │ 7.5│ 0.6│ .40│ 3.0│ 35.6│ 2.3│ .40│ 0.6│ .40
Cement │ 10.0│ 0.7│ .75│ 7.5│ 22.6│ 1.5│ .75│ 2.6│ .75
│ │ │ │ │ │ │ │ │
Street Walks: │ │ │ │ │ │ │ │ │
Brick │ 6.1│ 0.5│ .40│ 2.4│ 48.2│ 3.1│ .40│ 1.0│ .40
Cement │ 139.3│ 10.5│ .75│ 104.5│ 78.1│ 5.0│ .75│ 3.4│ .75
│ │ │ │ │ │ │ │ │
Street │ │ │ │ │ │ │ │ │
Pavements: │ │ │ │ │ │ │ │ │
Asphalt, │ │ │ │ │ │ │ │ │
brick, │ │ │ │ │ │ │ │ │
wood block│ 145.5│ 11.0│ .85│ 123.7│ │ │ │ 5.0│ .85
Granite │ │ │ │ │ │ │ │ │
block │ 111.4│ 8.4│ .75│ 83.6│ │ │ │ 1.0│ .75
Macadam and │ │ │ │ │ │ │ │ │
cobble │ 23.2│ 1.8│ .40│ 9.3│ 238.6│ 15.4│ .40│ 4.8│ .40
Granite and │ │ │ │ │ │ │ │ │
poor │ │ │ │ │ │ │ │ │
macadam │ │ │ │ │ │ │ │ 0.4│ .20
│ │ │ │ │ │ │ │ │
Unimproved │ │ │ │ │ │ │ │ │
yards and │ │ │ │ │ │ │ │ │
lawns: │ │ │ │ │ 692.4│ 44.7│ .15│ │
Tributary to│ │ │ │ │ │ │ │ │
paved │ │ │ │ │ │ │ │ │
gutters │ │ │ │ │ │ │ │ 57.1│ .15
Not │ │ │ │ │ │ │ │ │
tributary │ │ │ │ │ │ │ │ │
to paved │ │ │ │ │ │ │ │ │
gutters │ │ │ │ │ │ │ │ 7.9│ .10
──────────────┼──────┼─────┼─────┼──────────┼──────┼─────┼─────┼─────┼─────
Total │1324.2│100.0│ │ 1127.0│1550.7│100.0│ │100.0│
──────────────┼──────┴─────┴─────┴──────────┼──────┴─────┴─────┼─────┴─────
Impervious │ │ │
coefficient │ │ │
for the │ │ │
district │ 85.1 │ 44.4 │ 35.9
──────────────┴─────────────────────────────┴──────────────────┴───────────
C. E. Gregory[27] states that _I_, in the expression _Q_ = _AIR_ is a
function of the time of concentration or the duration of the storm. If
_t_ represents the time of concentration and _T_ represents the duration
of the storm, then when _T_ is less than _t_
_I_ = 0.175_t_^⅓,
but when _T_ is greater than _t_,
_I_ = 0.175⁄_t_(_T_^{4/3} − (_T_ − _t_)^{4/3}).
Gregory condenses Kuichling’s rules with regard to the per cent run-off,
as follows:
1. The per cent of rainfall discharged from any given drainage
area is nearly constant for heavy rains lasting equal periods of
time.
2. This per cent varies directly with the area of impervious
surface.
3. This per cent increases rapidly and directly or uniformly with
the duration of the maximum intensity of the rainfall until a
period is reached which is equal to the time required for the
concentration of the drainage waters from the entire area at the
point of observation, but if the rainfall continues at the same
intensity for a longer period this per cent will continue to
increase at a much smaller rate.
4. This per cent becomes larger when a moderate rain has
immediately preceded a heavy shower on a partially permeable
territory.
Gregory’s formulas have not been generally accepted and are not widely
used in practice. Marston stated:[28]
All that engineers are at present, warranted in doing is to make
some deduction from 100 per cent run-off ... the deduction ...
being at present left to the engineer in view of his general
knowledge and his familiarity with local conditions.
Burger states[29] in the same connection:
In its application there will usually be as many results
(differing widely from each other) as the number of men using it.
In spite of these objections the Rational Method is in more favor with
engineers than any other method.
=32. Empirical Formulas.=—The difficulty of determining run-off with
accuracy has led to the production by engineers of many empirical
formulas for their own use. Some of these formulas have attracted wide
attention and have been used extensively, in some cases under conditions
to which they are not applicable. In general these formulas are
expressions for the run-off in terms of the area drained, the relative
imperviousness, the slope of the land, and the rate of rainfall.
The Burkli-Ziegler formula, devised by a Swiss engineer for Swiss
conditions and introduced into the United States by Rudolph Hering, was
one of the earliest of the empirical formulas to attract attention in
this country. It has been used extensively in the form
_Q_ = _CiA_∜(_S_⁄_A_),
in which_Q_ = the run-off in cubic feet per second;
_i_ = the maximum rate of rainfall in inches per hour over
the entire area. This is determined only by
experience in the particular locality, and is usually
taken at from 1 to 3 inches per hour;
_S_ = the slope of the ground surface in feet per thousand,
_A_ = the area in acres;
_C_ = an expression for the character of the ground surface,
or relative imperviousness. In this form of the
expression _C_ is recommended as 0.7.
The McMath formula was developed for St. Louis conditions and was first
published in Transactions of the American Society of Civil Engineers,
Vol. 16, 1887, p. 183. Using the same notation as above, the formula is,
_Q_ = _CiA_⁵√(_S_⁄_A_),
McMath recommended the use of _C_ equal to 0.75, _i_ as 2.75 inches per
hour, and _S_ equal to 15. The formula has been extended for use with
all values of _C_, _i_, _S_, and _A_ ordinarily met in sewerage
practice. Fig. 11 is presented as an aid to the rapid solution of the
formula.
[Illustration:
FIG. 11.—Diagram for the Solution of McMath’s Formula,
_Q_ = _Aci_⁵√_S_⁄_A_.
]
Other formulas have been devised which are more applicable to drainage
areas of more than 1,000 acres.[30] Such areas are met in the design of
sewers to enclose existing stream channels draining large areas.
Kuichling’s formulas, published in 1901 in the report of the New York
State Barge Canal, were devised for areas greater than 100 square miles.
The following modification of these formulas for ordinary storms on
smaller areas was published for the first time in American Sewerage
Practice, Volume I, by Metcalf and Eddy:
_Q_ = 25,000⁄(_A_ + 125) + 15.
[Illustration:
FIG. 12.—Comparison of Empirical Run-off Formulas.
]
It is to be noted that the only factor taken into consideration is the
area of the watershed. It is obvious that other factors such as the rate
of rainfall, slope, imperviousness, etc., will have a marked effect on
the run-off.
There are other run-off formulas devised for particular conditions, some
of which are of as general applicability as those quoted. Two formulas
which are frequently quoted are: Fanning’s, _Q_ = 200_M_^⅝ and Talbot’s
_Q_ = 500_M_^¼, in which _M_ is the area of the watershed in square
miles. A comprehensive treatment of the subject is given in American
Sewerage Practice, Vol. I, by Metcalf and Eddy.
A comparison of the results obtained by the application of a few
formulas to the same conditions is shown graphically in Fig. 12. It is
to be noted that the divergence between the smallest and largest results
is over 100 per cent. As these formulas are not all applicable to the
same conditions, the differences shown are due partially to an extension
of some of them beyond the limits for which they were prepared.
=33. Extent and Intensity of Storms.=—In the design of storm sewers it
is necessary to decide how heavy a storm must be provided for. The very
heaviest storms occur infrequently. To build a sewer capable of caring
for all storms would involve a prohibitive expense over the investment
necessary to care for the ordinary heavy storms encountered annually or
once in a decade. This extra investment would lie idle for a long period
entailing a considerable interest charge for which no return is easily
seen. The alternative is to construct only for such heavy storms as are
of ordinary occurrence and to allow the sewers to overflow on
exceptional occasions. The result will be a more frequent use of the
sewerage system to its capacity, a saving in the cost of the system, and
an occasional flooding of the district in excessive storms. The amount
of damage caused by inundations must be balanced against the extra cost
of a sewerage system to avoid the damage. A municipality which does not
provide adequate storm drainage is liable, under certain circumstances,
for damages occasioned by this neglect. It is not liable if no drainage
exists, nor is it liable if the storm is of such unusual character as to
be classed legally as an act of God.
Kuichling’s studies of the probabilities of the occurrence of heavy
storms are published in Transactions of the American Society of Civil
Engineers, Vol. 54, 1905, p. 192. Information on the extent of rain
storms is given by Francis in Vol. 7, 1878, p. 224, of the same
publication. Kuichling expresses the intensity of storms which will
occur,
once in 10 years as _i_ = 105⁄(_t_ + 20),
once in 15 years as _i_ = 120⁄(_t_ + 20),
in which _i_ is the intensity of rainfall in inches per hour and _t_ is
the duration of the storm in minutes.
CHAPTER IV
THE HYDRAULICS OF SEWERS
=34. Principles.=—The hydraulics of sewers deals with the application of
the laws of hydraulics to the flow of water through conduits and open
channels. In so far as its hydraulic properties are concerned the
characteristics of sewage are so similar to those of water that the same
physical laws are applicable to both. In general it is assumed that the
energy lost due to friction between the liquid and the sides of the
channel varies as some function of the velocity, usually the square, and
that the total energy passing any section of the stream differs from the
energy passing any other section only by the loss of energy due to
friction.
The general expression for the flow of sewage would then be,
_h_ = (_f_)_V_^n,
in which _h_ is the head or energy lost between any two sections, and
_V_ is the average velocity of flow between these sections. It is to be
noted in this general expression that the quantity and rate of flow past
all sections is assumed to be constant. This condition is known as
_steady flow_. Problems are encountered in sewerage design which involve
conditions of unsteady flow, and methods of solution of them have been
developed based on modifications of this general expression. The average
velocity of flow is computed by dividing the rate (quantity) of flow
past any section by the cross-sectional area of the stream at that
section. This does not represent the true velocity at any particular
point in the stream, as the velocity near the center is faster than that
near the sides of the channel. The distribution of velocities in a
closed circular channel is somewhat in the form of a paraboloid
superimposed on a cylinder.
The laws of flow are expressed as formulas the constants of which have
been determined by experiment. It has been found that these constants
depend on the character of the material forming the channel and the
hydraulic radius. The _hydraulic radius_ is defined as the ratio of the
cross-sectional area of the stream to the length of the wetted
perimeter, or line of contact between the liquid and the channel,
exclusive of the horizontal line between the air and the liquid.
=35. Formulas.=—The loss of head due to friction caused by flow through
circular pipes flowing full as expressed by Darcy is,
_h_ = _f_(_l_⁄_d_) (_V_^2⁄2_g_),
in which _h_ is the head lost due to friction in the distance _l_, _V_
is the velocity of flow, _g_ is the acceleration due to gravity, and _f_
is a factor dependent on _d_ and the material of which the pipe is made.
A formula for _f_ expressed by Darcy as the result of experiments on
cast-iron pipe is,
_f_ = 0.0199 + 0.00166⁄_d_,
in which _d_ is the diameter in feet. In using the formula with this
factor the units used must be feet and seconds.
Another form of the same expression is known as the Chezy formula. It is
an algebraic transformation of the Darcy formula, but in the form shown
here, by the use of the hydraulic radius, it is made applicable to any
shape of conduit either full or partly full. The Chezy formula is,
_V_ = _C_√(_RS_),
in which _R_ is the hydraulic radius, _S_ the slope ratio of the
hydraulic gradient, and _C_ a factor similar to _f_ in the Darcy
formula.
Kutter’s formula was derived by the Swiss engineers, Ganguillet and
Kutter, as the result of a series of experimental observations. It was
introduced into the United States by Rudolph Hering and its derivation
is given in Hering and Trautwine’s translation of “The Flow of Water in
Open Channels by Ganguillet and Kutter.” In English units it is,
_V_ = {(1.81/_n_ + 41.67 + .0028/_S_)/(1 + (_n_/√_R_)(41.67 +
(.0028/_S_)))}√(_RS_),
in which _n_ is a factor expressing the character of the surface of the
conduit and the other notation is as in the Chezy formula. _V_ is the
velocity in feet per second, _S_ is the slope ratio, and _R_ the
hydraulic radius in feet. The values of _n_ to be used in all cases are
not agreed upon, but in general the values shown below are used in
practice.
VALUES OF _n_ IN KUTTER’S FORMULA
_n_ CHARACTER OF THE MATERIALS
0.009 Well-planed timber.
0.010 Neat cement or very smooth pipe.
0.012 Unplaned timber. Best concrete.
Smooth masonry or brickwork, or concrete sewers under ordinary
0.013 conditions.
0.015 Vitrified pipe or ordinary brickwork.
0.017 Rubble masonry or rough brickwork.
0.020 } Smooth earth.
0.035
0.030 } Rough channels overgrown with grass.
0.050
Kutter’s formula is of general application to all classes of material
and to all shapes of conduits. It is the most generally used formula in
sewerage design.
The cumbersomeness of Kutter’s formula is caused somewhat by the attempt
to allow for the effect of the low slopes of the Mississippi River
experiments on the coefficients. The correctness of these experiments
has not been well established and the slopes are so flat that the
omission of the term 0.0028⁄_S_ will have no appreciable effect on the
value of _V_ ordinarily used in sewer design. The difference between the
value of _V_ determined by the omission of this term and the value of
_V_ found by including it is less than 1 per cent for all slopes greater
than 1 in 1,000 for 8 inch pipe (_R_ = 0.167 feet). As the diameter of
the pipe or the hydraulic radius of the channel increases up to a
diameter of 13.02 feet (_R_ = 3.28 feet), the difference becomes less
and at this value of _R_ there is no difference whether the slope is
included or not. For larger pipes the difference increases slowly. For a
16 foot pipe (_R_ = 4 feet) on a slope of 1 in 1,000 the difference is
less than 0.2 per cent, and on a slope of 1 in 10,000 the difference is
approximately 1 per cent. Flatter slopes than these are seldom used in
sewer design, except for very large sewers where careful determinations
of the hydraulic slope are necessary. It is therefore safe in sewer
design to use Kutter’s formula in the modified form shown below in which
the term (.0028)⁄_S_ has been omitted.
_V_ = (1.81 + 41.67_n_)_R_√_S_/_n_(√_R_ + 41.67_n_).
Bazin’s formula is
_V_ = √(_RS_)/√(α + β/_d_)
in which α and β are constants for different classes of material. For
cast-iron pipe α is 0.00007726 and β is 0.00000647. This formula is
seldom used in sewerage design.
Exponential formulas have been developed as the result of experiments
which have demonstrated that _V_ does not vary as the one-half power of
_R_ and _S_ but that the relation should be expressed as,
_V_ = _CR_^{_p_}_S_^{_q_},
in which _p_ and _q_ are constants and _C_ is a factor dependent on the
character of the material. The various formulas coming under this
classification have been given the names of the experimenters proposing
them. Examples of these formulas are: Flamant’s, in English units, for
new cast-iron pipe, which is,
_V_ = 232_R_^{.715}_S_^{.572},
and Lampé’s for the same material which is,
_V_ = 203.3_R_^{.694}_S_^{.555}.
These formulas are useful only for the material to which they apply, but
they can be used for conduits of any shape. A. V. Saph and E. W. Schoder
have shown[31] that the general formula for all materials lies between
the limits,
_V_ = (93 to 142)_S_^{.50 to .55}_R_^{.63 to .69}.
Hazen and Williams’ formula is in the form,
_V_ = 1.31_CR_^{.63}_S_^{.54},
in which _C_ is a factor dependent on the character of the material of
the conduit. The values of _C_ as given by Hazen and Williams are,
_C_ CHARACTER OF MATERIAL
95 Steel pipe under future conditions. (Riveted steel.)
Cast iron under ordinary future conditions and brick
100 sewers in good condition.
110 New riveted steel, and cement pipe.
120 Smooth wood or masonry conduits under ordinary conditions.
Masonry conduits after some time and for very smooth pipes
such as glass, brass, lead, etc., when old, and for new
130 cast-iron pipe under ordinary conditions.
This formula is of as general application as Kutter’s formula and is
easier of solution, but being more recently in the field and because of
the ease of the solution of Kutter’s formula by diagrams it is not in
such general use. Exponential formulas are used more in waterworks than
in sewerage practice.
Manning’s formula is in the form,
_V_ = 1.486⁄_n__R_^⅔_S_^½
in which _n_ is the same as for Kutter’s formula. Charts for the
solution of Manning’s formula are given in Eng. News-Record, Vol. 85,
1920, p. 837.
=36. Solution of Formulas.=—The solution of even the simplest of these
formulas, such as Flamant’s, is laborious because of the exponents
involved. Darcy’s and Kutter’s formulas are even more cumbersome because
of the character of the coefficient. The labor involved in the solution
of these formulas has resulted in the development of a number of
diagrams and other short cuts. Since each formula involves three or more
variables it cannot be represented by a single straight line on
rectangular coordinate paper. The simplest form of diagram for the
solution of three or more variables is the nomograph, an example of
which is shown in Fig. 13 for the solution of Flamant’s formula. A
straight-edge placed on any two points of the scales of two different
vertical lines will cross the other line at a point on the scale
corresponding to its correct value in the formula. Such a diagram is in
common use for the solution of problems for the flow of water in
cast-iron pipe.
[Illustration:
FIG. 13.—Diagram for the Solution of Flamant’s Formula for the Flow of
Water in Cast-iron Pipe.
]
Fig. 14 has been prepared to simplify the solution of Hazen and
Williams’ formula. The scales of slope for different classes of material
are shown on vertical lines to the left of the slope line. For use these
scales must be projected horizontally on the slope line. The scales for
other factors are shown on independent reference lines.
For example let it be required to find the loss of head in a 12
inch pipe carrying 1 cubic foot per second when the coefficient of
roughness is 100. A straight-edge placed at 1.0 cubic feet per
second on the quantity scale, and 12 inches on the diameter scale
crosses the slope line at .00092 opposite the slope scale for _c_
= 100. It crosses the velocity line at 1.31 feet per second.
Kutter’s formula is the most commonly used for sewer design and has been
generally accepted as a standard in spite of its cumbersomeness. Fig. 15
is a graphical solution of Kutter’s formula for small pipes, and Fig. 16
for larger pipes. The diagrams are drawn on the nomographic principle
and give solutions for a wide range of materials, but they are specially
prepared for the solution of problems in which _n_ = .015. In their
preparation the effect of the slope on the coefficient has been
neglected. Fig. 17 is drawn on ordinary rectangular coordinate paper and
can be used only for the solution of problems in which _n_ = .015. Both
diagrams are given for practice in the use of the different types.
[Illustration:
FIG. 14.—Diagram for the Solution of Hazen and Williams’ Formula.
]
[Illustration:
FIG. 15.—Diagram for the Solution of Kutter’s Formula.
For values of _n_ between 0.010 and 0.020. Specially arranged for _n_
= 0.015. Values of Q from 0.1 to 10 second-feet.
]
[Illustration:
FIG. 16.—Diagram for the Solution of Kutter’s Formula.
For values of _n_ between 0.010 and 0.020. Specially arranged for _n_
= 0.015. Values of Q from 10 to 1,000 second-feet.
]
[Illustration:
FIG. 17.—Diagram for the Solution of Kutter’s Formula.
]
[Illustration:
FIG. 18.—Conversion Factors for Kutter’s Formula.
]
In Figs. 15 and 16 the diameter scales are varied for different values
of the roughness coefficient _n_. The velocity scale is shown _only for
a value of n = .015_. The velocity for other values of _n_ can be
determined by the method given in the following paragraphs.
37. =Use of Diagrams.=—There are five factors in Kutter’s formula: _n_,
_Q_, _V_, _d_ (or _R_), and _S_. If any three of these are given the
other two can be determined, except when the three given are _Q_, _V_,
and _d_. These three are related in the form _Q_ = _AV_, which is
independent of slope or the character of the material. There are only
nine different combinations possible with these five factors, which will
be met in the solution of Kutter’s formula. The solution of the problems
by means of the diagrams is simple when the data given include _n_
= .015. For other given values of _n_ the solution is more complicated.
Results of the solution of types of each of the nine problems are given
in Table 17 and the explanatory text below.
_If n is given and is equal to .015_, the solution is simple.
For example in Table 17 _case 1, example 1_; to be solved on Fig.
15. Place a straight-edge at 1.0 on the _Q_ line and at 6 inches
on the diameter line for _n_ = .015. The slope and the velocity
will be found at the intersection of the straight-edge with these
respective scales.
All problems in which _n_ is given as .015 and the solution for which
falls within the limits of Fig. 15 or 16 should be solved by placing a
straight-edge on the two known scales and reading the two unknown
results at the intersection of the straight-edge and the remaining
scales.
For example in _case 1_, _example 2_ find the intersection of the
horizontal line representing _Q_ = 100 with the sloping diameter
line representing _d_ = 48 inches. The vertical slope line passing
through this point represents _S_ = .0065 and the sloping velocity
line passing through this point represents 8.5 feet per second.
In general problems in which _n_ = .015, can be solved on Fig. 17 by
finding the intersection of the two lines representing the given data,
and reading the values of the remaining variables represented by the
other two lines passing through this point.
TABLE 17
SOLUTIONS OF PROBLEMS BY KUTTER’S FORMULA
─────┬───────┬────────────────────────────┬────────────────────────────
Case │Example│ Given │ Found
─────┼───────┼─────┬─────┬────┬────┬──────┼─────┬─────┬────┬────┬──────
│ │ _n_ │ _Q_ │_V_ │_d_ │ _S_ │ _n_ │ _Q_ │_V_ │_d_ │ _S_
─────┼───────┼─────┼─────┼────┼────┼──────┼─────┼─────┼────┼────┼──────
1 │ 1 │0.015│ 1.0│ 2.5│ 6│ │ │ │5.0 │ │0.0575
1 │ 2 │ .015│100.0│ │ │ │ │ │8.5 │ │.0065
1 │ 3 │ .020│ 1.0│ │ 6│ │ │ │5.0 │ │.13
1 │ 4 │ .020│100.0│ │ 48│ │ │ │8.5 │ │.0125
2 │ 1 │ .015│ 5.0│ │ │0.0003│ │ │1.2 │28 │
2 │ 2 │ .010│ 5.0│ │ │.0003 │ │ │1.7 │23.5│
3 │ 1 │ .015│ │ │ 18│.002 │ │ 4.0│2.25│ │
3 │ 2 │ .018│ │ │ 18│.0008 │ │ 2.0│1.1 │ │
4 │ 1 │ .015│ 2.0│ 2.5│ │ │ │ │ │12 │.00475
4 │ 2 │ .011│ 2.0│ 2.5│ │ │ │ │ │12 │.0022
5 │ 1 │ .015│ │ 5.0│ 36│ │ │ 35.0│ │ │.0038
6 │ 1 │ .018│ │ 5.0│ │.001 │ │185.0│ │80 │
7 │ 1 │ │ 3.0│ │ 18│.002 │0.019│ │1.7 │ │
7 │ 2 │ │ 50.0│ │ 36│.005 │ .012│ │7.0 │ │
8 │ 1 │ │ 6.0│ 2.5│ │.003 │ .018│ │ │21 │
9 │ 1 │ │ │ 4.2│ 66│.00059│ .011│100.0│ │ │
─────┴───────┴─────┴─────┴────┴────┴──────┴─────┴─────┴────┴────┴──────
_If n is given and is not equal to .015_ the solution is not so simple.
In Fig. 15 and 16 the diagram is so drawn that the _position_ of the
diameter scales for all values of _n_ is fixed on the vertical
“diameter” line. The _scales_ of diameter change for each value of _n_.
These scales of diameter are shown for each value of _n_ from .010
to .020 on vertical lines to the left of the “diameter” line. For use,
the proper diameter scale for any given value of _n_ must be projected
horizontally upon the vertical “diameter” line. The velocity can be
determined on Fig. 15 and 16, _only when the diameter has been
determined_ and then _only when the diameter scale for n equal .015 is
used, since the only scale shown for velocity is for n = .015._
For example, in _Case 1_, _Example 3_ there are given _n_ = .020,
_Q_, and _d_. Find the intersection of the vertical line for _n_ =
.020 with the sloping diameter line for _d_ = 6 inches. Project
the intersection horizontally to the right to the vertical
“diameter” line. Place a straight-edge at this point and at _Q_ =
1.0 on the quantity scale. The required value of _S_ is read at
the intersection of the straight-edge and the slope scale and is
equal to 0.13. The intersection of the straight-edge in this
position with the velocity scale is not the required value of the
velocity since the velocity scale is made out for _n_ = .015 and
not .020. It is necessary to change the position of the
straight-edge so that it may lie on _Q_ equal 1.0 and on _d_ equal
6 inches for _n_ equal .015. The value of _V_ is shown in this
position as 5 feet per second.
The reverse process for Fig. 15 and 16 is illustrated _by Case 4_,
_Example 2_ in which _n_ = .011 and _Q_ and _V_ are also given.
When _Q_ and _V_ are given the value of _d_ is fixed independent
of all other factors. Therefore the value of _d_ can be read from
the scale with _n_ = .015 and is found to be 12 inches. Now find
the value of _d_ = 12 inches on the scale for _n_ = .011 and
project on to the “diameter” line. Place the straight-edge at this
point and at _Q_ = 2. The required slope is read as .0022.
Fig. 17 is prepared for the solution of problems in which _n_ = .015
only. For problems in which _n_ has some other value it is necessary to
transform the data to equivalent conditions in which _n_ = .015. This is
done by means of the conversion factors shown in Fig. 18. The given
slope or velocity is multiplied by the proper factor to convert from or
to the value of _n_ = .015.
For example in _Case 1_, _Example 4_ there are given _n_ = .020,
_Q_, and _d_. With _Q_ and _d_ given the value of _V_ can be read
from Fig. 17 without conversion. The corresponding value of _S_
for _n_ = .015 is .0065. It is now necessary to use the
transformation diagram Fig. 18. The hydraulic radius of the given
pipe is one foot. On Fig. 18 at the intersection of the slope line
for _R_ = 1.0 foot and _n_ = .020 the value of the factor is read
as 1.92. Since the given _n_ is for rougher material than that
represented by _n_ = .015 the required slope must be greater than
for _n_ = .015 to give the same velocity. It is therefore
necessary to multiply .0065 × 1.92 and the required slope is
.0125.
In _Case 6_, _Example 1_ there are given _n_ = .018, _d_, and _S_.
The remaining factors are to be solved by Fig. 17. Solve first as
though _n_ = .015 in order to find an approximate value of _d_ or
_R_. In this case it is evident that _d_ is greater than 57
inches. The value of _R_ is therefore about 1.25. Referring to
Fig. 18 the conversion factor for the slope for _n_ = .018 is
about 1.52. Since the given slope for _n_ = .018 is .001, for an
equal velocity and for _n_ = .015 the slope should be less.
Therefore in reading Fig. 17 it is necessary to use a slope of
.001⁄1.52 = .00066. The diameter is found to be about 80 inches.
Since this is nearer to the correct diameter the value of the
conversion factor must be corrected for this approximation. The
hydraulic radius for an 80 inch pipe is 1.67 feet, and the
conversion factor from Fig. 18 is about 1.48. The slope for _n_ =
.015 should be therefore .001⁄1.48 = .000675 and from Fig. 17 the
required diameter and quantity are read as 80 inches and 185
second-feet, respectively.
_If n is not given_ but must be solved for, the solution on Fig. 15 and
16 is relatively simple. The desired value of _n_ is read at the
intersection of the sloping diameter line representing the known
diameter and the horizontal projection of the intersection of the
straight-edge with the vertical “diameter” line.
For example in _Case 7_, _Example 1_ there are given _Q_, _d_, and
_S_. Lay the straight-edge on the given values of _Q_ = 3 and _S_
= .002. At the point where the straight-edge crosses the vertical
“diameter” line project a horizontal line to the sloping diameter
line for _d_ = 18 inches. The vertical line passing through this
point represents a value of _n_ = .019. In order to find the value
of _V_ lay the straight-edge on _Q_ = 3 and _d_ = 18 inches for
_n_ = .015. The value of _V_ is read as 1.7.
A slightly different condition is illustrated in the solution of
_Case 8_, _Example 1_ in which _Q_, _V_ and _S_ are given.
Determine first the value of _d_ as though _n_ = .015. Then
proceed to determine _n_ as in the preceding examples.
The solution for an unknown value of _n_ on Fig. 17 is not so simple. It
must be determined by working backwards from the conversion factor.
For example in _Case 7_, _Example 2_ there are given _Q_, _d_, and
_S_. The value of _V_ is read directly as though _n_ = .015 as 7
feet per second. The value of _S_ read for _n_ = .015 is .0075.
But the given slope is .005. Since the given slope is flatter than
that for _n_ = .015 the conversion factor is less than unity and
is therefore .005⁄.0075 = 0.67. With this value of the conversion
factor and the value of _R_ given as 0.75 the value of _n_ is read
from Fig. 18 as slightly greater than .012.
=38. Flow in Circular Pipes Partly Full.=—The preceding examples have
involved the flow in circular pipes completely filled. The same methods
of solution can be used for pipes flowing partly full except that the
hydraulic radius of the wetted section is used instead of the diameter
of the pipe. Diagrams are used to save labor in finding the hydraulic
radius and the other hydraulic elements of conduits flowing partly full.
The hydraulic elements of a conduit for any depth of flow are: (_a_) The
hydraulic radius, (_b_) the area, (_c_) the velocity of flow, and (_d_)
the quantity or rate of discharge. The velocity and quantity when partly
full as expressed in terms of the velocity and quantity when full as
calculated by Kutter’s formula will vary slightly with different
diameters, slopes and coefficients of roughness. The other elements are
constant for all conditions for the same type of cross-section. The
hydraulic elements for all depths of a circular section for two
different diameters and slopes are shown in Fig. 19. The differences
between the velocity and quantity under the different conditions are
shown to be slight, and in practice allowance is seldom made for this
discrepancy.
In the solution of a problem involving part full flow in a circular
conduit the method followed is to solve the problem as though it were
for full flow conditions and then to convert to partial flow conditions
by means of Fig. 19, or to convert from partial flow conditions to full
flow conditions and solve as in the preceding section.
For example let it be required to determine the quantity of flow
in a 12–inch diameter pipe with _n_ = .015 when on a slope of .005
and the depth of flow is 3 inches. First find the quantity for
full flow. From Fig. 15 this is 2.0 cubic feet per second. The
depth of flow of 3 inches is one-fourth or 0.25 of the full depth
of 12 inches. From Fig. 19, running horizontally on the 0.25 depth
line to meet the quantity curve, the proportionate quantity at
this depth is found to be on the 0.13 vertical line, and the
quantity of flow is therefore 2 × 0.13 = 0.26 cubic feet per
second.
[Illustration:
FIG. 19.—Hydraulic Elements of Circular Sections.
]
_d_ = 12′ 0″ _s_ = .0004 _n_ = .015
_d_ = 1′ 0″ _s_ = .01 _n_ = .013
Another problem, involving the reversal of this process is illustrated
by the following example:
Let it be required to determine the diameter and full capacity of
a vitrified pipe sewer on a grade of 0.002 if the velocity of flow
is 3.0 feet per second when the sewer is discharging at 30 per
cent of its full capacity, the depth of flow being 12 inches. From
Fig. 19 the depth of flow when the sewer is carrying 30 per cent
of its full capacity is 0.38 of its full depth. Since the partial
depth is 12 inches the full diameter is 12⁄.038 = 31.6 inches. The
velocity of flow at 38 per cent depth is 86 per cent of the full
velocity. Since the velocity given is 3.0 feet per second, the
full velocity is 3.0⁄.86 = 3.5 feet per second. With a full
velocity of 3.5 feet per second and a diameter of 31.6 inches from
Fig. 16 the full capacity of the sewer is 18 cubic feet per
second.
=39. Sections Other than Circular.=—The ordinary shape used for small
sewers is circular. The difficulty of constructing large sewers in a
circular shape, special conditions of construction such as small head
room, soft foundations, etc., or widely fluctuating conditions of flow
have led to the development of other shapes. For conduits flowing full
at all times a circular section will carry more water with the same loss
of head than any other section under the same conditions. In any section
the smaller the flow the slower the velocity, an undesirable condition.
The ideal section for fluctuating flows would be one that would give the
same velocity of flow for all quantities. Such a section is yet to be
developed. Sections have been developed that will give relatively higher
velocities for small quantities of flow than are given by a circular
section. The best known of these sections is the egg shape, the
proportions and hydraulic elements of which are shown in Fig. 20. Other
shapes that have the same property, but which were not developed for the
same purpose are the rectangular, the U-shape, and the section with a
cunette. The egg-shaped section has been more widely used than any other
special section. It is, however, more difficult and expensive to build
under certain conditions, and has a smaller capacity when full than a
circular sewer of the same area of cross-section. Various sections are
illustrated in Fig. 22 and 23.
The U-shaped section is suitable where the cover is small, or close
under obstructions where a flat top is desirable and the fluctuations of
flow are so great as to make advantageous a special shape to increase
the velocity of low flows. The proportions of a U-shaped section are
shown in Fig. 23 (6). Other sections used for the same purpose are the
semicircular and special forms of the rectangular section.
The proportions and the hydraulic elements of the square-shaped section
are shown in Fig. 21. This is useful under low heads where a flat roof
is required to carry heavy loads, and the fluctuations of flow are not
large.
Sections with cunettes have not been standardized. A cunette is a small
channel in the bottom of a sewer to concentrate the low flows, as shown
in Fig. 22 (7). A cunette can be used in any shape of sewer.
[Illustration:
FIG. 20.—Hydraulic Elements of an Egg-shaped Section.
_d_ = 6′ 0″ _s_ = .00065 _n_ = .015
]
[Illustration:
FIG. 21.—Hydraulic Elements of a Square Section.
_d_ = 10′ 0″ _s_ = .0004 _n_ = .015
]
Sections developed mainly because of the greater ease of construction
under certain conditions are the basket handle, the gothic, the
catenary, and the horse shoe. Some of these shapes are shown in Fig. 22
and 23. They are suitable for large sewers on soft foundations, where it
is desirable to build the sewer in three portions, such as invert, side
walls, and arch. They are also suitable for construction in tunnels
where the shape of the sewer conforms to the shape of the timbering, or
in open cut work where the shape of the forms are easier to support.
Problems of flow in all sections can be solved by determining the
hydraulic radius involved, and substituting directly in the desired
formula, or by the use of one of the diagrams after converting to the
equivalent circular diameter. The determination of the hydraulic radius
of these special sections is laborious, and hence other less difficult
methods are followed. Problems are more commonly solved by converting
the given data into an equivalent circular sewer, solving for the
elements of this circular sewer and then reconverting into the original
terms, or by working in the other direction. The hydraulic elements of
various sections when full are given in Table 18.
TABLE 18
HYDRAULIC ELEMENTS OF SEWER SECTIONS. SEWERS FLOWING FULL.
───────────────┬─────────────┬─────────────┬─────────────┬──────────────
Section │Area in Terms│ Hydraulic │ Vert. Dia. │ Source
│ Vertical │ Radius in │_D_ in Terms │
│ Diameter │ terms of │ of Dia. _d_ │
│Squared _D_^2│Vertical Dia.│of Equivalent│
│ │ _D_ │ Circular │
│ │ │ Section │
───────────────┼─────────────┼─────────────┼─────────────┼──────────────
Circular │ 0.7854│ 0.250 │1.000 │
Egg │ 0.5150│ .1931│1.295 │Eng. Record,
│ │ │ │ Vol. 72: 608
Ovoid │ 0.5650│ .2070│1.208 │Eng. Record,
│ │ │ │ Vol. 72: 608
Semi-elliptical│ 0.8176│ .2487│1.041 │Eng. News,
│ │ │ │ Vol. 71: 552
Catenary │ 0.6625│ .2237│1.1175 │Eng. Record,
│ │ │ │ Vol. 72: 608
Horseshoe │ 0.8472│ .2536│0.985 │Eng. Record,
│ │ │ │ Vol. 72: 608
Basket handle │ 0.8313│ .2553│0.979 │Eng. Record,
│ │ │ │ Vol. 72: 608
Rectangular │ 1.3125│ .2865│0.7968 │Hydraulic
│ │ │ │ Dgms. and
│ │ │ │ Tbls.
│ │ │ │ Garrett
Square (3 sides│ 1.0000│ .333 │0.7500 │Eng. Record,
wet) │ │ │ │ Vol. 72: 608
Square (4 sides│ 1.0000│ .250 │1.0000 │Eng. Record,
wet) │ │ │ │ Vol. 72: 608
───────────────┴─────────────┴─────────────┴─────────────┴──────────────
[Illustration:
1. Standard Egg-shaped Section, North Shore Intercepter, Chicago,
Illinois.
]
[Illustration: