Transcriber’s Note:

The cover image was created by the transcriber and is placed in the public domain.

Fig. 1.—Construction of Peck’s Run Sewer, Baltimore, Maryland.
Frontispiece.

SEWERAGE
AND
SEWAGE TREATMENT

BY

HAROLD E. BABBITT, M.S.

Assistant Professor, Municipal and Sanitary Engineering, University of Illinois; Associate Member American Society of Civil Engineers

NEW YORK

JOHN WILEY & SONS, Inc.

London: CHAPMAN & HALL, Limited

1922

Copyright, 1922, by

HAROLD E. BABBITT, M.S.

PRESS OF

BRAUNWORTH & CO.

BOOK MANUFACTURERS

BROOKLYN, N. Y.

PREFACE

This book is a development of class-room and lecture notes prepared by the author for use in his classes at the University of Illinois. He has found such notes necessary, since among the many books dealing with sewerage and sewage treatment he has found none suitable as a text-book designed to cover the entire subject. The need for a single book of the character described has been expressed by engineers in practice, and by students and teachers for use in the class-room. This book has been prepared to meet both these needs. It is hoped that the searching questions propounded by students in using the original notes, and the suggestions and criticisms of engineers and teachers who have read the manuscript, have resulted in a text which can be readily understood.

The ground covered includes an exposition of the principles and methods for the designing, construction and maintenance of sewerage works, and also of the treatment of sewage. In covering so wide a field the author has deemed it necessary to include some chapters which might equally well appear in works on other branches of engineering, such as the chapter on Pumps and Pumping Stations. Special stress has been laid on the fundamentals of the subject rather than the details of practice, although illustrations have been drawn freely from practical work. The quotation of expert opinions which may be in controversy, or the citation of examples of different methods of accomplishing the same thing, has been avoided when possible in order to simplify explanations and to avoid confusing the beginner.

The work is to some extent a compilation of notes and quotations which have been collected by the author during years of study and teaching the subject. Credit has been given wherever due, and at the same time references have pointed out the original sources whenever possible. These references, which have been supplemented by brief bibliographies at the end of certain chapters, will be useful to the student and engineer interested in further study. Occasionally the original reference has been lost or the phraseology of a quotation has been so altered by class-room use, as to make it impossible to trace the original source, so that in some few instances full credit may be lacking.

The author is indebted to many of his friends for their criticisms and suggestions in the preparation of the manuscript; but he desires particularly to acknowledge the assistance of Professor A. N. Talbot, Professor of Municipal and Sanitary Engineering at the University of Illinois, and of Professor M. L. Enger, Professor of Mechanics and Hydraulics at the University of Illinois, in the entire work; also that of Mr. T. D. Pitts, Principal Assistant Engineer of the Baltimore Sewerage Commission during the construction of the Baltimore sewers, for his suggestions on the first half of the book; and to Mr. Paul Hansen, consulting engineer, of Chicago, and to Mr. Langdon Pearse, Sanitary Engineer of the Sanitary District of Chicago, for their help on the section covering the treatment of sewage; and to Professor Edward Bartow, Professor of Chemistry at the University of Iowa, for his review of the chapter on Activated Sludge; in general his thanks are due to all others who have furnished suggestions, illustrations, or quotations, acknowledgments of which have been included in the text.

H. E. B.

Urbana, Illinois, 1922.

TABLE OF CONTENTS

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.

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.

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.

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.

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.

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.

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.

Fig. 5.—Lever for Pulling Punch Drill.

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.

Fig. 7.—Jetting Outfit.
U. S. Geological Survey, Water Supply Paper, No. 257
1. Simple Jetting Outfit. 2. Jetting Process. 3. Common Jetting Drill. 4a and 4b. 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.

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.

Fig. 9.—Density, Area, and Population, Cincinnati, Ohio. 1850 to 1950.

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.

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.

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.

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.

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.

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]]

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 = 2,000I√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.

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.

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 = 0.175t^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

in whichQ = 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,

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.

Fig. 11.—Diagram for the Solution of McMath’s Formula,

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.

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 = 200M^⅝ and Talbot’s Q = 500M^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)Vⁿ,

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 = fl
d V²
2g,

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,

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.

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.

Bazin’s formula is

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^pS^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 = 232R^.715S^.572,

and Lampé’s for the same material which is,

V = 203.3R^.694S^.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 = 1.31CR^.63S^.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,

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
nR^⅔S^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.

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.

Fig. 14.—Diagram for the Solution of Hazen and Williams’ Formula.

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.

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.

Fig. 17.—Diagram for the Solution of Kutter’s Formula.