Water-Resources Engineering - Parte 1

WATER-RESOURCES ENGINEERING RAY K. LINSLEY FRANZINI JOSEPH B. DAVID L. FREYBERG GEORGE TCHOBANOGLOUS FOURTH EDITION

Me Graw Hill Education

WATER-RESOURCES ENGINEERING

McGraw-Hill Series in Water Resources and Environmental Engineering Consulting Editors Paul H. King Rolf Eliassen, Emeritus Bailey and Ollis: Bioch emical Engineering Fundamenta ls Bishop: Marin e Pollutio n an d It s Con trol Bouwer: Groundwater Hydrology Canter: Enviro nmental Imp act Asses smen t Chanlett: Enviro nmenta l Prote ctio n Chow, Maidment, and Mays: Ap pli ed Hy dr olo gy Davis and Cronwell: Introdu ction to Enviro nmen tal Engineering Eckenfelder: Indu strial Wate r Pollution Con tro l

~

Linsley, Franzini, Freyberg, Tchobanoglous: Water-Resources Engineering Mays and Tung: Hy dr os ys tem s Engineering and Man agem ent Metcalf & Eddy, Inc.: Wastewater Engineering: Collection and Pumping of Wastewater Metcalf & Eddy, Inc.: Wastewater Engineering: Treatment

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PREFACE

This is the fourth edition of this book. During the preparation of this edition two new coauthors were brought aboard: Dr. David L. Freyberg and Dr. George Tchobanoglous. Shortly before the manuscript for this edition was completed the senior author, Dr. Ray K. Linsley, passed away after a lengthy illness. Dr. Linsley was a leader in the field of hydrology and was an authority on water-resources planning. He is the senior au thor of the widely used textbook Hydrology for Engineers. He will be missed greatly by his many friends and colleagues. This edition has been updated to conform with changing technology. Its goal is the same as that of the first edition—to give the student an up-to-date background for the planning and design of systems to manage water resources. World population continues to grow, placing greater pressure on available water supplies for human use, industrial production, and sanitation and for the growing of food and fiber. Floods result in property damage and loss of life and curtail the production of industrial and agricultural products. Pollution of both surface and groundwater reduces the available supply of potable water for many uses. Efficient water management today is necessary to ensure the availability of adequate water supplies in the future. Management in this sense includes more

than engineering activities. Economic, social, political, and environmental con siderations are an important part of the decision-making process. Planning in the true sense of the word is a complex process in which competing uses for water must be considered in the light of physical, economic, and environmental con straints. Water-resources engineering draws on the student’s background in science, the humanities, social studies, and design. A course in water-resources engineering should present relevant material in a unified framework, emphasizing

XIV

PREFACE

why things are done along with how they are done. That is what this book was designed to do. This edition of the book is set up in the same format as previous editions. The first five chapters deal with the subjects of hydrology, the determination of where water can be found, and how the available amounts can be estimated. Legal aspects, often critical constraints on water management, are discussed in Chapter

6. Physical works—dams, canals, pipelines, hydraulic machines, and so on, which are utilized in water management—are considered in Chapters 7 through 12. Cost effectiveness, an important consideration in planning water projects, is reviewed in Chapter 13 along with relevant principles of engineering economy applicable to water-resources planning. Specific purposes of water management with special attention to ways in which planning differs among the various purposes are presented in Chapters 14 through 20. The planning procedure for single and multi-purpose projects is summarized in Chapter 21. We feel that students learn best by working problems. There are many new problems in this edition, and nearly all of the problems retained from the previous edition have been revised with new data. About 40 percent of the problems are in SI metric units. Dr. Frey berg’s expertise is in water-resources engineering, particularly in the fields of grou ndw ater an d surface-water hydrology. He was responsible for Cha pter 4 and the solutions manual, and prepared the prdblems and solutions for all chapters except Chapters 15 and 19, which were written by Dr. Tchobanoglous, who also prepared those chapters for the third edition of this book. Dr. Tchobanoglous’s expertise is in the fields of water quality and water and wastewater treatment. The authors wish to express their special appreciation to Professor Eugene L. Grant, who prepared Chapter 13 for the first edition. The list of persons who contributed to previous editions is long and we thank them all, including the reviewers who provided us and our publisher with many useful suggestions. Joseph B. Franzini David L. Freyberg George Tchobanoglous

COMMENTS ON UNITS

Those working in the field of water-resources engineering must be versed in the English system of units as well as the International System of Units (SI). Though conversion to the SI metric system is gradually taking place in the United States, the English system of units is still widely used. In contrast, the use of the SI metric system is almost universal throughout the rest of the world. In this edition most units are expressed in the English system with corresponding SI units given in parentheses. Many abbreviations are used in the English system. The student should become familiar with them. Some of the abbreviations a re more widely used than others. A list of abbreviations for English units is as follows:

Abbreviation

Representation

Correct Form of English Units

cfs cfs/ft

\ cubic feet per second \ cubic feet per second per foot1

ft3/sec (ft3/sec)/ft

cfs/sq mi cu ft cu yd fps sped gpd/acre spd gpd/ft2 gpm mgd mph pcf psf psi sfd second-foot sq ft

cubic feet per second per square mile cubic feet cubic yards feet per second gallons per capita per day gallons per day per acre gallons per day gallons per day per square foot gallons per minute million gallons per day miles per hour pounds per cubic feet pounds per square foot pounds per square inch second-foot-day, equals one cfs flowing for one day cubic foot per second square foot

(ft3/sec)/mi2 ft3 yd3 ft/sec gal/capitaday gal/dayac gal/day gal/dayft2 gal/min Mgal/day mi/hr lb/ft3 lb/ft2 lb/in2 ft3 day/sec ft3/sec ft2 xv

xvi

COMMENTS ON UNITS

In this edition of the book a few of the English Units are expressed in terms of the abbreviations cfs, gpm, and psi, for example. Often, however, the correct dimensional form shown in the right-hand column of the preceding list is used in the literature.

CHAPTER 1

INTRODUCTION

The management and control of our water resources requires the conception, planning, and execution of designs to make use of the water or avoid damage from too much water. For most of the twentieth century this has been viewed as the work of civil engineers. It is becoming apparent that engineering structures are not always the preferred solution. In some cases a nonstructural solution is superior. This means that more alternatives must be considered in the planning phase and may require the service of other disciplines—economies, social and political science, biology, and geology. Each problem involves a unique set of physical conditions and constraints, which can be resolved by the careful c oordina tion of the various disciplines. 1.1

Fields of Water -Resourc es Enginee ring

Water is controlled and regulated to serve a wide variety of purposes. Flood mitigation, storm drainage, sewerage, and highway culvert design are applications of water-resources engineering to the control of water so that it will not cause excessive damage to property, inconvenience to the public, or loss of life. Municipal water supply, irrigation, hydroelectric-power development, and navigation im provements are examples of the utilization of water for beneficial purposes. Pollution threatens the utility of water for municipal and irrigation uses and seriously despoils the aesthetic value of rivers—hence pollution control or waterquality management has become an important phase of water-resources engineer ing. Finally, the potential of nonstructural measures such as zoning to avoid flood 1

* T '

2

WATER-RESOURCES ENGINEERING

damage and the preservation of natural beauty are factors the water-resources engineer must consider. There has been a tendency toward specialization within these applications in the water-resources field, but actually the problems en countered and the solutions to these problems have much in common. Table 1.1 summarizes the problems that may be encountered within the nine main functional fields of water-resources engineering.

TABLE 1.1

Problems of water-resources engineering Conser vation C o n t ro l of ex ce ss w a t e r Flood

Storm drain

Bridges,

required

miti gation

age

culverts

How much water is needed?

—

Studies and facilities

How much water* can be expected? Minimum flow* Annual yield* Flood peaks Flood volume Groundwater*

-

-

—

—

-

-

X

X

X

X

Sewer age

Water

X

X X

Irriga tion

supply

--

X X

X

X X

—

X

—

X

X

X

X

—

X

—

X

X

X

X

—

X

X

X

X

X

X

X

X

Sediment What structural problems exist? I Geology / Dams Spillways Gates Sluiceways Intakes X Channel works Levees Pipelines Canals Locks Pumps Turbines Purification

X

X

—

— -

X

—

—

X

X —

—

X

X

X X

—

—

X

Is the project economic?

X

—

—

—

—

—

X

—

—

X

—

—

—

X

—

X

X

X

X X

X X

X

X

X XX X

X

X

X

XXX X

X

X

X

—

X X

—

—

X X

X X

X

—

X

X

Does project affect wild life or nat ural beauty?

—

X X

X

X

—

X

—

-

X

—

X

-r -

X

—

X

—

X X

—

X

—

—

X —

X X X

XX

X

—

XX

XX

X X

X

X

X

—

X

X

X

What kind of water is it? Chemical Bacteriological

-

Pollution control

X

-

—

Navi

X

-X

(quality)

gation

X

Who may use the water?

-

Hydro power

X X

-

X

—

C o n se r v a t i o n ( qu a n t it y)

X

X

X

X

—

X

X X

—

X

XXX —

—

—

X

XX

X

X

X

X —

X

X

X

X

—

X X

X

X

X .

X X

* Available water must be expressed in terms of the probability that it will be available in any year.

X

X

INTRODUCTION

1.2

3

Quality o f Water

V. jome risk of oversimplification, the job of the water-resources engineer may be -graced to a number of basic questions. Since the water-resources project is for l&e control or use of water, the first questions naturally deal with the quantities iSÍ ’* ater. Where utilization is proposed, the first question is usually How much This is probably the most difficult of all the design problems to «war¿T needed? accurately because it involves social and economic aspects as well as sacineering. On the basis of an economic analysis, a decision must also be made OTaeerning the span of years for which the proposed project will serve. Table 1.2 summarizes 1980 water use in the United States in relation to gross mater supply-precipitation. In discussing water use it is important to distinguish between diversion (withdrawal), or water taken into a system, and consumption, mater that is evaporated or combined in a product and is no longer available for use. Almost all project designs depend on the answer to the question How much +axer can be expected?Peak rates of flow are usually the basis of design of projects l s

to control water, whilefor volume flow during longer toperiods of time are is of interest in excess designing projects use ofofwater. The answers this question found through the application of hydrology , the study of the occurrence and distribution of the natural waters of the earth. Since the* future ca nnot be accurately

TABLE 1.2 Water balance of the coterminous United States* Component

109 bgd

106 AF/yr

*n./yr

lO’ irrVyr

Precipitation Evapotranspiration

4200 2800

4704 3136

29.7 19.8

5786 3857

Diversions for Irrigation Publicuse Industry!

152 42 256

170 47 287

1.1 0.3 1.8

209 58 353

450

504

3.2

620

Consumption Irrigation Publicuse Industry

84 10 6

94 11 7

0.60 0.07 0.04

116 13 9

Total consumption Outflow to ocean

100 1300

112 1456

0.71 9.2

138 1791

___ ___

Total diversionsf

• Adapted from W. B. Solley, E. B. Chase, and W. B. Mann, IV, Estimated Use of Water In the United States 1980, U.S. Geol. Surv. Circ.1001, 1983. + Approximately 87% of the water withdrawn by industry in the United States is used for the cooling of thermoelectric power plants. Í Twenty percent of the diverted water comes from groundwater. The remaining $0% is from surface water. Reclaimed water accounts for less than 0.2%.

4

WATER-RESOURCES ENGINEERING

forecast, hydrology involves assessment of probability. The principles of hydrology are outlined in Chaps. 2 to 5. The water flowing in a stream is not necessarily available for use by every person or group desiring it. The right to use water has considerable value, especially in regions where water is scarce. Like other things of value, water rights are protected by law, and a legal answer to the question Who may use this water? may be required before the quantities of available water can be evaluated. Diversion of natural streamflow may cause property damage and alterations in natural flow conditions are governed by legal restrictions that should be investi gated before completion of the project plan. 1.3

Water Qua lity

In addition to being adequate in quantity, water must often withstand certain tests of quality. Problems of water quality are encountered in planning water-supply and irrigation projects and in the disposal of wastewater. Polluted streams create problems for fish and wildlife, are unsuited for recreation, and are often unsightly and sometimes odorous. Chemical and bacteriologic tests are employed to de termine the amount and character of impurities in water. Plant and human physiologists must evaluate the effect of these impurities on crops or human consumers and set standards of acceptable quality. The engineer must then provide the necessary facilities for removing impurities from the water by physical, chemical, or biologic methods. Hydrologic studies are necessary to evaluate the effectiveness of the wastewater management plan. Governmental agencies having the authority to regulate the disposal of wastes are required to safeguard our waters against pollution.

1.4

Hydra ulic Structures

Structural design^oLfacilities for water-resources projects utilizes the techniques of civil engineering. The shape and dimensions of the structure are often dictated by the hydraulic characteristics it must possess and hence are determined by application of the principles of fluid mechanics. Many hydraulic structures are relatively massive as compared with buildings and bridges, and the structural design involves much less fine detail. However, hydraulic structures frequently involve complex curved and warped surfaces and sometimes intricate detail for gates, valves, control systems, etc. Almost all the conventional engineering mater ials are employed in hydraulic structures. Earth, mass and reinforced concrete, timber, clay tile, asphaltic compounds, and most of the common metals are found in such structures. Largely because of topographic controls, it is not always possible to select the most satisfactory location for a hydraulic structure from the structural viewpoint. Hence, geologic investigations are an important part of the preliminary planning. These investigations should be aimed at selecting the best of the otherwise suitable sites, predicting the structural problems that will result from

INTRODUCTION

5

the particular conditions at the site, and locating sources of native material suitable for use in the proposed structure.

1.5

Econo mics in Water-Resour ces Engin eering

Little skill is required to design a structure for some purpose if unlimited funds are available. The special ability of the engineer is reflected in the planning of projects that serve their intended purpose at a cost com mensurate with the benefits (value engineering). An economic analysis to determine the best of several alternatives is required in planning most projects. It must usually be demonstrated that the project cost is sufficiently less than the expected benefits to warrant the required investment. In many cases the estimated benefits serve also as a basis for determining a schedule of payments by the beneficiaries who will repay the project cost to the construction agency. Precipitation and streamflow vary widely from year to year. It is usually uneconomic to design a project to provide protection against the worst possible flood or to assure an adequate water supply during the most severe drought that could conceivably occur. Instead the project design is gaged against a scale of probability so that the probability of-the project failing to serve its purpose is small but still positive. Economic analysis (Chap. 13) is dependent on hydrologic analysis of the pr obability of occurrence of extreme floods or d rou ghts (Chap. 5).

1.6

Social Aspects o f Water-Resou rces Engin eering

Most water projects are planned for and financed by some governmental unit—a municipal water-supply or sewerage system, a state highway department, or a federal irrigation or flood-mitigation project—or by a public utility. Many such projects become controversial political issues and are debated at length by people whose understanding of the basic engineering aspects of the problem is limited. It is a clear responsibility of an engineer who has the necessary facts concerning such a project to take a firm position in the public interest if the final decision is not to be made on political and emotional grounds. It is particularly important that the engineer carefully analyze the facts and present a sound case in simple terms and avoid championing a “pet” project that is of limited benefit to the public. Throughout any negotiations concerning a publicly financed project, the engineer should adhere carefully to the code of ethics of the professional society that represents the civil engineering profession in his or her country. Failure to do so prejudices the case and the entire profession in the eyes of the public. 1.7

Planning o f Water-Re sources Projects

Planning is an important step in the development of a water-resources project. The planning of a project (Fig. 1.1) generally involves a political incentive or recognition of the need for a project. This is followed by the conception of

6

WATER-RESOURCES ENGINEERING

FIGURE 1.1 Steps in planning a water-resources project.

alternative technically feasible solutions that would satisfy the need. The alterna tive proposals are subjected to an economy study that analyzes their benefits and costs and thus determines their economic feasibility. Evaluation of social and environmental impacts is also an important step in planning. Finally, financial feasibility (can the project be paid for?) and political practicality (is the project acceptable to the public?) play an important role in the choice of alternatives. A detailed discussion of planning for water-resources development is presented in Chap. 21.

1.8

History o f Water -Resources Enginee ring

The importance of water to human life justifies the supposition that some ancient man conceived the idea of diverting streamflow from a natural channel to an artificial one in order to convey water to some point where it was needed for crops or humans. The Old World contains numerous evidences of water projects of considerable magnitude. The earliest large-scale drainage and irrigation works are attributed to Menes, founder of the first Egyptian dynasty, about 3200 b . c . These works were followed by many varied projects in the Mediterranean and Near East area, including dams, canals, aqueducts, and sewer systems. Some 381 mi of aqueducts were constructed to bring water to the city of Rome. An irrigation project in Szechwan Province of China dating from about 250 b .c . is still in use. Even in the New World, projects of considerable scope antedate the coming of Europeans. Ruins of elaborate and extensive irrigation projects constructed about a . d . 1100 by Hohokam Indians in what is now Arizona and similar Aztec works in Mexico indicate flourishing irrigation economies. These early works were not designed and built by engineers in the modern sense of the word. The ancient builders were master craftsmen and technicians (the Greek architekton , or archtechnician) who employed amazing intuitive judg ment in planning and executing their works. Rules of thumb developed through experience guided the leading builders, but these trade secrets were not necessarily conveyed to other men. The great thinkers of the Greek era contributed much to science, but since manual labor was considered demeaning, the application of their knowledge in practical pursuits was retarded. Many erroneous concepts and gaps in understanding delayed the development of engineering as it is known today. It was not until the time of Leonardo da Vinci (about a .d . 1500) that the idea that precipitation was the source of streamflow received any real support and many years later before it was def initely proved. The limita tions of available construc tion materials also influenced early engineering works. Since no materials suitable for

INTRODUCTION

7

large pressure pipes were available to the Romans, their aqueducts were designed as massive structures to carry water under atmospheric pressure at all times. The first effort at organized engineering knowledge was the founding in 1760 >f ihe École des Ponts et Chaussées in Paris. As late as 1850, however, engineering designs were based mainly on rules of thumb developed through experience and tempered with liberal factors of safety. Since that date, utilization of theory has increased rapidly untildesigns. today aAvast amount of lag careful computation is an integral part of most project considerable seems to exist between research and application. The answers to many professional problems are available in laboratory records and even published papers, but they have not yet been extensively employed by practicing engineers. 1.9

The Future o f Water-Resou rces Engineer ing

Laymen, unfamiliar with engineering problems, often view the enormous activity in flood mitigation, irrigation, and other phases of water-resources engineering with the thought that opportunities for further work must be negligible. Actually modern civilization is far more dependent on water than were the civilizations of the past. Modern medical science together with modern sanitary engineering has reduced death rates and increased life expectancy. Modern standards of personal cleanliness require vastly more water than was used a century ago. The increasing population requires expanded acreage for agriculture, much of which must come through land drainage or irrigation. Increasing urban populations require more attention to storm drainage, water supply, and sewerage. Industrial progress finds increasing uses for water in process industries and for electric-power production. The emphasis of water-resources engineering shifts more or less continuously. The major work in this field during the early years of the United States was the construction canals forbuttransport. Other modes of transportation have made the canal bpatof obsolete, these new means of transport have introduced new problems^ of drainage for highways, railroads, and airports. The development of civilization has increased the importance of waterresources engineering, and there is no prospect of a decline of activity in this field in the foreseeable future. In fact, the increasing pressure for water is forcing the development of marginal projects that might not have been considered only a few years ago. If a project of marginal value is to be successful, it must be planned with more care and thought than was required for the more obvious projects of the past. More accurate hydrologic methods must be employed in estimating available water. More efficient methods and better construction material must be utilized to reduce costs so that difficult projects may become economically feasible. The water-resources engineers of the future will find themselves deeply involved with new technology and new concepts. Reclamation of wastewater, weather modification, land management to improve water yield, and new water saving techniques in all areas of water use are topics of increasing interest and research. An expanding world population is changing ecologic patterns in many ways, and water planning must include evaluation of ways to minimize undesirable

8

WATER-RESOURCES ENGINEERING

ecologic conseqences. Concern for the preservation of the natural environment will be increasingly important in water planning of the future. The conflict between preserving our ecosystem and meeting the “needs” of people for water management must certainly lead to new approaches in water management and quite possibly to new definitions ofneed. It will not be sufficient to attack water problems of the future by simply copying methods of the past.

BIBLIOGRAPHY Biswas, Asit K.: “A History of Hydrology,” North Holland Publishing Company, Amsterdam, 1970. Chow, Ven Te (Ed.): “Handbook of Applied Hydrology,” McGraw-Hill, New York, 1964. Kelly, D.: Estimated Use of Water in the United States, U.S. Geol. Surv. Circ. 876, 1983. Langbein, W. B., and W. G. Hoy t: “ Wate r Facts for the N atio n’s Futu re, ” Ronald, New York, 195 9. Maass, Arthur, M. M. Hufschmidt, Robert Dorfman, H. A. Thomas, S. A. Marglin, and G. M. Fair: “Design of Water-Resource Systems,” Harvard, Cambridge, Mass., 1962. Merdinger, Charles J.: Civil Engineering through the Ages, Trans. ASCE , Vol. CT, pp. 1-27, 1953. “The Nation’s Water Resources,” U.S. Water Resources Council, Washington D.C., 1968. Rouse, Hunter, and S. Ince: “History of Hydraulics,” Institute of Hydraulic Research, University of Iowa City, Iowa, 1957. and David K. Todd: “The Water Encyclopedia,” 2d ed., Lewis van derIowa, Leeden, Frits Fred L. Troise, Publishers, Boca Raton, Fla. 1989. “Water Policies for the Future,” Report of the U.S. National Water Commission, Washington D.C., 1973. ' White, Gilbert F.: “Strategies of American Water Management,” University of Michigan Press, Ann Arbor, Mich., 1969.

CHAPTER

2

DESCRIPTIVE HYDROLOGY 1

2.1

The Hydrologic Cycle

The wor ld’s supply of fresh wate r is quite small comp ared to the enormous volumes of salt water in the oceans. Fortunately the freshwater supply is renewed by the hydrologic cycle, which is an immense solar distillation system. Water evaporated from the oceans is transported over the continents by moving air masses. When this moisture-bearing air is cooled to its dewpoint temperature, the vapor con denses into water droplets forming fog or cloud. The cooling occurs when the moist air is lifted to higher elevations. Since air pressure decreases with elevation (Table A-3), the air expands as it is lifted and cooled in accordance with the Ideal Gas Law const p V /T =

(2.1)

Lifting occurs in three ways. Orographic lifting occurs when the air is forced up over the underlying terrane. Frontal lifting occurs when the air mass is pushed up by a cooler air mass. The boundary between the two air masses is called a frontal surface. Finally, the moist air may be heated from below as it passes over a warmer

1 “Hy drology is the science tha t treats of the waters of the Earth, their occurrence, circulati on, and distribution, their chemical and physical properties, and their reaction with their environment, including their relation to living things.” (From “Scientific Hydrology,” U.S. Federal Council for Science and Technology, June 1962.)

9

10

WATER-RESOURCES ENGINEERING

FIGURE 2.1 Schematic diagram of the hydrologic cycle.

surface, causing convective lifting, which may result in a convective thunderstorm. Often two or more of these mechanisms may take place together. About two-thirds of the precipitation that reaches the land surface is returned to the atmosphere by evaporation from water surfaces, soil, and vegetation and through plant transpiration. The remaining third of the precipitation returns ultimately to the ocean through surface or underground channels. The large percentage of precipitation that is evaporated has often led to the belief that increasing this evaporation by construction of reservoirs or planting of trees will increase the moisture available in the atmosphere for precipitation. Actually only a small portion of the moisture (usually much less than 10 percent) that passes over any given poin t on the ea rth ’s surface is pre cipitate d.1 Hence, moisture evaporated from the land surfaces is a minor part of the total atmospheric moisture.12 The hydrologic cycle is depicted diagramfnatically in Fig. 2.1. No simple figure can do justice to the complexities of the cycle ass it occurs in nature. The science of hydrolog y is devoted to a study of the rate of exchange of water between phases of the cycle and in particular to the variations in this rate with time and

1G. S. Benton, R. T. Blackburn, and V. O. Snead, The Role of the Atmosphere in the Hydrologic Cycle, Trans. Am. Geophys. Union , Vol. 31, pp. 61-73, February 1950. 2 F. A. Huff and G. E. Stout, A Preliminary Study of Atmospheric-moistur e-precipitation Relationships over Illinois, Bull. Am. Meteorol. Soc ., Vol. 32, pp. 295-297, 1951.

DESCRIPTIVE HYDROLOGY

11

place. This information provides the da ta necessary for the hydraulic design of physical works to control and utilize natural water. 2.2

The River Bas in

A river basin (catchm ent)1 is the area tri butary to a given point on a stream and is separated from adjacent basins by a divide, or ridge, that can be traced on topographic maps. All surface water srcinating in the area enclosed by the divide is discharged through the lowest point in the divide through which the main stream of the catchment passes, it is commonly assumed that the movement of groundwater conforms to the surface divides, but this assumption is not always correct, and large quantities of water may be transported from one catchment to another as groundwater. PRECIPITATION 2.3

Types of Precipitation

Precipitation includes all water that falls from the atmosphere to the earth’s surface. Precipitation occurs in a variety of forms that are of interest to the meteorologist, but the hydrologist is interested in distinguishing only between liquid precipitation (rainfall) and frozen precipitation (snow, hail, sleet, and freezing rain). Rainfall runs off to the streams soon after it reaches the ground and is the cause of most floods. Froz en precipita tion may r emain where it falls for a long time before it melts. Melting snow is rarely the cause of major floods although, in combination with rainfall, it may contribute to major floods such as that on the upper Mississippi River in 1969. Mountain snowpacks are often important sources of water for irrigation and other purposes. The snowfields serve as vast reservoirs that store water precipitation until spring thaws release it near the time it is required for irrigation. ^ 2.4

Fo g Drip and Dew •

Fog consists of water droplets so small that their fall velocities are negligible. Fog particles that contact vegetation may adhere, coalesce with other droplets, and eventually form a drop large enough to fall to the ground. Fog drip is an important source of water for native vegetation during the rainless summers of the Pacific Coast of North America. On clear nights the loss of heat by radiation from the soil causes cooling of the ground surface and of the air immediately above it. Condensation of the water vapor present in the air results in a deposit of dew. The small quantities of dew

1The words river basin, drainage basin, watershed, and catchment are used interchangeably. A subbasin is a tributary basin of a larger drainage basin.

12

WATER-RESOURCES ENGINEERING

FIGURE 2.2 Standard 8-in. nonrecording precipitation gage. ( U.S . National Weather Service)

and fog drip deposited in any day do not contribute to streamflow or groundwater. They do, however, offer a source of water that may be exploited locally. Research in Israel1 has shown that br oad-lea ved crops such as cabbage may be efficient dew collectors that can be grown in an arid region with little or no irrigation.

2.5

Precipitation Mea surem ent—

Amount of precipitation is expressed as the depth in inches or millimeters that falls on a level surface. This may be measured as the depth of water deposited in an open, straight-sided container. The standard gage1 2 used in the United States (Fig. 2.2) consists of a funnel 8 in. (20.32 cm) in diameter discharging into a tube 2.53 in. (6.43 cm) in diameter. The area of the inner tube is 0.1 that of the funnel, and a stick graduated in inches and tenths can be used to measure precipitation to the nearest 0.01 in. (0.25 mm). Precipitation in excess of 2 in. (50 mm) overtops the inner tube and collects in the overflow can. By removing the funnel and inner

1D. Ashbel, Frequency and Distribution of Dew in Palestine, 1949.

Geogr. Rev., Vol. 39, pp. 291-297, April

2 Worldwide, a variety of different types of gages are used. Practically, there is little difference in accuracy in measuring rain, but smaller gages are not suitable for snowfall.

DESCRIPTIVE HYDROLOGY

13

tube from the gage, the 8-in.-diameter overflow can may be used to collect snowfall, which is melted and measured in the inner tube. Large storage gages are used in remote areas to catch and store precipitation for periods of 30 days or more. If snowfall is expected, an initial charge of calcium chloride brine is placed in the gage to melt the snow and to prevent the freezing of the liquid in the gage. A thin film of oil is used to prevent evaporation from the gage between observations. Wind sets up air currents around precipitation gages that usually cause the gages to catch less prec ipita tion th an they sh ould.1 The low fall velocity of snowflakes makes this effect even more marked for snowfall than for rain. The deficiency in catch may vary from 0 to 50 percent or more depending on the type of gage, wind velocity, and local terrane. The U.S. National Weather Service1 2 uses an Alter shield consisting of a series of metal slats pivoted about a circular ring near the top of the gage and joined by a chain at the bottom. The tops of the slats are about 2 in. (5 cm) above the top of the gage. The flexible construction is intended to permit wind to move the slats and minimize the accumulation of snow on the shield. In order to determine rates of rainfall over short periods of time, recording rain gages are used. The weighing rain gage has a bucket supported by a spring or lever balance. Movement of the bucket is transmitted to a pen that traces a record of the increasing weight of the bucket and its contents on a clock-driven chart or punched paper tape. The tipping-bucket gage consists of a pair of buckets pivoted under a funnel in such a way that when one bucket receives 0.01 in. (0.25 mm) of precipitation, it tips, discharging its contents into a reservoir and bringing the other bucket under the funnel. A recording mechanism indicates the time of occurrence of each tip. The tipping-bucket gage is well adapted to the measurement of rainfall intensity for short periods, but the more rugged construc tion of the weighing-type gage and its ability to record snowfall as well as rain make Subsequent it preferabletofor purposes.of radar in World War II it was found that themany development microwave ra da r (1 to 20 bm wavelength) would indicate the presence of rain3 within its scanning area. The amount of reflected energy is dependent on the raindrop size and the distance from the transmitter. Drop size is roughly correlated with rain intensity, and the image on the radar screen (isoecho map) can be interpreted as an approximate indication of rainfall intensity. A calibration may also be determined from actual rain-gage measurements in the area scanned by the radar. Radar offers a means of obtaining information on a real rainfall distribution, which would be only roughly defined by the usual network of rain gages.

1C. C. Warnick, Experiments with Windshields for Precipitation Gages, Union, Vol. 34, pp. 379-388, June 1953.

Trans. Am. Geophys.

2 The U. S. Weather Bureau was changed to the National Weather Service in 1970. 3 L. J. Battan, “ Rada r O bserva tion of the A tmosp here,” University of Chicago Press, Chicago, 1973.

14 2.6

WATER-RESOLJRCF.S ENGINEERING

Computation o f Average Precipitation

Large differences in precipitation are observed within short distances in mountain ous terrane or during showery precipitation in level country. The average density of rain gages in the United States is about one per 250 mi2 (700 km2), and the data so obtained represent only a scattered sample of precipitation over large areas. It issimplest sometimes necessary to estimate thecompute averagethe precipitation a given area. The method of doing this is to arithmetic over average of the recorded precipitation values at stations in or near the area. If the precipitation is nonuniform and the stations unevenly distributed within the area, the arithmetic average may be incorrect. To overcome this error, the precipitation at each station may be weighted in proportion to the area the station is assumed to represent. A common method of determining weighting factors is the Thiessen network (Fig. 2.3). A Thiessen network is constructed by connecting adjacent Stations on a map by straight lines and erecting perpendicular bisectors to each connecting line. The polygon formed by the perpendicular bisectors around a station encloses an area that is everywhere closer to that station than to any other station. This area is assumed to be best represented by the precipitation at the enclosed station. This is often a reasonable assumption but may not always be correct. To compute the average rainfall, the area represented by each station is expressed as a percentage of the total area. The average rainfall is the sum of the individual station amounts, each multiplied by its percentage of area. An alternative method is shown in Fig. 2.3. If the stations are uniformly distributed in the area, the Thiessen areas will be equal and the computed average rainfall will equal the arithmetic average. The basis for the Thiessen method is the assumption that a station best represents the area that is closest to it. If precipitation is controlled by topography or results from intense convection, this assumption may not be valid. An isohyetal map (Fig. 2.4) showing contours of equal precipitation may be drawn to conform to other pertinent information in , addition to the precipitation data and thus present a more accurate picture of the rainfall distribution. Since precipitation

FIGURE 2.3 Thiessen network.

15

DESCRIPTIVE HYDROLOGY

Isohyets

Area between Average isohyets. precipitation, m i2 in.

Product m i2

in .

3 .0 19

3.45

66

106

3.75

398

102

4.25

434

60

4 .7 5

285

150

5.25

788

3 .5 4 .0 4 .5 5 .0 5 .5 84

5 .7 5

483

6 .0 47

6.20

291

6 .5 Total

568

—

2745

FIGURE 2.4 \ e isohyetal map.

usually increases with elevation, the isohyets may be made to conform approximately with the contours of elevation. To compute average precipitation from an isohyetal map, the areas enclosed between successive isohyets are measured and multiplied by the average precipitation between the isohyets. The sum of these products divided by the total area is the average precipitation. If the isohyets are interpolated linearly between stations, the computed average precipitation will not differ appreciably from that computed with a Thiessen network. 2.7

Snow

The measurement of snowfall has been discussed in Sec. 2.5. Snow on the ground is measured in terms of its depth (in inches or centimeters). Shallow depths are measured with any convenient scale, while large depths are measured on a snow stake , a graduated post permanently installed at the desired site. Because of variations in snow density, a depth measurement is not sufficient to tell how much water is contained in the snow pack. The water equivalent, or depth of water that would result from melting a column of snow, is measured by forcing a small tube into the snow, withdrawing it, and weighing the tube to determine the weight of the snow core removed. There are a number of types of snow samplers, but the most common type is the Mt. Rose pattern with an internal diameter of 1.485 in. (3.772 cm) so th at each ounce of snow in the core represents 1 in. (25 mm) of water equivalent. The specific gravity of each freshly fallen snow depth. is usually 0.1.gravity Thus, its water equivalent is 0.1 in. for inch of snow The about specific increases with time as the snow remains on the ground and may reach a maximum of abou t 0.5 in heavy mountain snowpacks.1 The term density of snow is often

1 If the pack accumulates, it may change to ice with a density of 0.92, as in a glacier.

16

WATER-RESOURCES ENGINEERING

used synonymously with specific gravity, although this usage is not in accord with the common meanings of the two terms. The area covered by snow may be mapped from aircraft or by satellite. The water equivalent of snowpacks in relatively flat areas has also been mapped from an aircraft flying at about 500 ft (150 m) altitude with a gamma ray c ounter.1 The natural gamma emission from the soil is attenuated by the water in the snow so that flights with and without snow permit estimating snow water equivalents up to a maximum of about 12 in. (300 mm) with accuracy on the order of 0.5 in. (12 mm).

2.8

Variations in Precipitation

The complex pattern of precipitation in the United States (Fig. 2.5) reflects several interacting influences. In general, precipitation decreases with increasing latitude because decreasing tem peratures reduce atmospheric moisture. A more important control in the United States is distance from a moisture source, as evidenced by the concentration of precipitation along the coasts and to some extent to the leeward of the Great Lakes. The importance of mountains as a factor in the production of precipitation by orographic lifting is evident in the isohyetal pattern in the Wester n states and a long the Appalachian M ountains. Heavier precipitation normally occurs along the windward slope of a mounain range with a rain shadow on the leeward slope. From the engineering viewpoint, time variations in precipitation may be more important than regional variations. The most marked of these variations is the annual precipitation cycle shown for selected stations in Fig. 2.6. In the Far West precipitation is at a minimum during the summer because a large highpressure area in the Pacific blocks the path of storms. In contrast, a summer maximum of precipitation is observed in the Great Plains, where the cold continental high-pressure center recedes northward during the summer. An essenti ally uniform distribuion of precipitation prevails in the Eastern states. The dry summers of the West make irrigation a necessity for many crops and emphasize the importance of storage reservoirs. Variations in precipitation from year to year make it important to design reservoirs that are adequate during years of low rainfall. In some cases reservoirs must carry water in storage for a period of several years. Over 100 different cycles in precipitation with periods up to 700 yr in length have been reported by various investigators. Sunspots and planetary configurations have been among the factors suggested as controlling these cycles. No one has been successful, however, in

1E. L. Peck and V. C. Bissell, Aerial Measurement of Snow Water Equivalent by Terrestrial Gamma Radiation Survey, Bull Int. Assoc. Hydrol. Sel, Vol. 18., No. 1, pp. 47-62, 1973.

m an

tj

, b , FIGURE 2.5 Variation of mean annu al precipita tipn (in inches) in the Unite d States. (U. S. National Weather Service)

18

WATER-RESOURCES ENGINEERING

FIGURE 2.6 Typical monthly distributions of precipitation (in inches) in various climatic regimes in the United States.

employing cycles for forecasting precipitation several years in advance. The best evidence now available suggests that the occurrence of a series of wet or dry years is purely rand om, such as might be expected by succes sive tosses of a coin. Accurate precipitation records are too short for a really satisfactory analysis of cyclic variation, which, if it does occur, must be a complex variation consisting of several superimposed cycles of differing period.

E

FIGURE 2.7 Maximum observed world rainfalls for various durations.

DESCRIPTIVE HYDROLOGY

19

2 .1

table

M axim um recorded point

rainfall

(i n i nches)

Duration hr

Min Scatioii ^■xiiand, Oreg. i_.:* * Angeles, Calif. Idaho PV'enix, Ariz Gaiteston, Tex. York, N.Y. Pittsburgh, Pa. Msimi, Fla.

15

30

60

6

24

0.40 8/8/00 0.44 1/14/08 0.34 5/22/42 0.68 9/16/69 0.85 4/13/29 0.75 8/12/26

0.83 8/8/00 1.05 11/19/67 0.59 8/9/63 1.14 9/16/69 1.94 4/13/29 1.63 7/10/05

1.10 8/8/00 1.51 11/19/67 0.67 5/18/21 1.27 9/16/69 3.06 10/6/10 2.34 8/12/26

1.31 6/7/27 1.87 11/19/67 0.98 7/30/12 1.72 8/18/66 5.31 10/22/13 2.97 8/26/47

— — 3.37 3/2/38 — — 2.41 9/4/39 11.79 10/8/01 4.44 10/1/13

7.66 12/12/82 7.36 12/31/33 2.46 3/28/04 4.98 7/1/11 14.35 7/13/00 9.55 10/8/03

0.72 6/26/31 0.71 6/14/33

1.23 ■ 6/26/31 1.89 10/11/47

1.46 7/4/03 2.92 10/11/47

2.00 7/27/43 4.53 6/14/33

2.53 7/27/43 10.64 11/30/25

4.08 9/17/76 15.10 11/29/25

5

Figure 2.7 shows the w orld’s record rai nfalls for various du ratio ns .1 Most of the observations are derived from cooperative and unofficial stations. A similar pk>t for record rainfalls at U.S. First Order stations would fall at ab out one-third i#e magnitudes shown in Fig. 2.7. This difference reflects the more effective sampling of the large num ber of cooperative and unofficial statio ns and emphasizes the importance of a careful search for data when a study requires information on rainfall Intensities. Table 2.1 presents maximum observed intensities for various durations a t a nu mber of geographic ally distributed stations in the U nited States. STREAMFLOW

In the streamflow phase of the hydrologic cycle, the water from a given catchment usually concentrated in a single channel, and it is possible to measure the entire quantity of water in this phase of the cycle as it leaves the area.

e

19

Measurement of Strea mflo w

A continuous record of streamflow requires the establishment of a relation between rate of flow and water level in a channel. In small channels this may sometimes

1 J. L, H. Pa'ilh us, Indi an Ocean and Ta iwan Rainfalls Se t New Records, Monthly Weather Rev., Vol. *5. No. 5, pp. 331-335, May 1965.

20

WATER-RESOURCES ENGINEERING

be accomplished by the use of a weir or measuring flume (Chap. 10) for which a head-discharge relation can be determined in the laboratory. Measurements of head may then be converted to rates of flow. In large streams, the use of laboratory-rated flow-measuring devices becomes impracticable, and measurements of discharge are made with a current meter . A stage-discharge relation, or rating curve, is constructed by plotting the measured discharge against the stage (water-surface elevation) at the time of measurement (Fig. 2.8). If the station is located just upstream from a rapids or other natural control that fixes a definite relation between stage and discharge, an accurate and permanent rating is obtained. An artificial control consisting of a low weir of concrete or masonry is sometimes constructed on small streams. The rating curve depends on the geometry of the stream, and erosion or deposition of sediment may change the rating from time to time. Under these conditions a satisfactory streamflow record can be obtained only by frequent current-meter measurements to fix the position of the rating curve at any time. Even where a good control exists, routine check measurements are considered desirable. The simple stage-discharge relation of Fig. 2.8 is typical of most streamflow measuring stations. At some stations, however, backwater from an intersecting stream or from a reservoir may affect the rating curve. If the channel slope is flat, variations in water-surface slope resulting from rising or falling stages may also affect the rating curve. Under either of these conditions a slope-stage-discharge relation may be employed. For this purpose an auxiliary stage record is required near the main station. The distance between the two stations should be such that

Discharge in thousands of second-feet FIGURE 2.8 Stage-discharge relation for the Willamette River at Albany, Oregon ,.¿Data from the U S. Geological Survey)

DESCRIPTIVE HYDROLOGY

21

the difference in water-surface elevation is at least 1 ft (30 cm), so that errors in reading the gages will be small compared with the difference. The difference in elevation, or fa ll , is used as an index of the slope between the stations. A rating curve is then drawn relating discharge and stage for some fixed value of fall, Az0. If the discharge at any stage as read from this curve is Q0, then the discharge Qa for the same stage and a fall of Azfl is

With reasonably uniform flow between the two stations, the exponent n will be about 0.5, but in practice it often varies from this value. The Price current meter (Fig. 2.9) is most widely used in the United States. The meter assembly consists of a cup wheel rotating about a vertical axis, tail vanes to keep the meter headed into the current, and a weight to keep the meter cable as nearly vertical as possible. In deep water the meter is suspended from a bridge, cable car, or boat by a cable that serves also as a conductor to transmit electrical contacts made by the cup wheel to a counter or earphones worn by the

FIGURE 2.9 Price current meter and 30-lb C-type sounding weight. ( U.S . Geological Survey )

22

WATER-RESOURCES ENGINEERING

hydrographer. In shallow water the meter may be attached to a rod for wading measurements. The velocity variation with depth in most streams is logarithmic, and the average of the velocities at 0.2 and 0.8 of the depth is very nearly equal to the mean velocity in a vertical section. A single measurement at 0.6 depth below the surface is only slightly less accurate as an estimate of the mean velocity. A streamflow measurement is usually made by determining the mean velocity in a number of vertical sections across the stream. The velocity in any vertical section is assumed to represent the velocity in a portion of the total cross section extending halfway to the adjacent vertical sections. The discharge in this portion of the cross section is computed by multiplying its area by the mean velocity. The total discharge of the stream is the sum of the discharges in the several pa rtial sections. Discharge may also be estimated by application of open-channel formulas (Chap. 10), use of weir formulas for dams or spillways (Chap. 9), calculation of flow through a contracted opening at a bridge (Chap. 18), or timing the travel of floats in the stream. If surface floats are used, mean velocity is commonly assumed to be 85 percent of float velocity. These methods are dependent on the selection of proper coefficients and are often inaccurate. They are normally used for reconnaissance purposes or for computing flood flow in the absence of meter measurements. If a tracer solution is injected into a stream at a constant rate and samples are taken downstream at a point where turbulence has achieved complete mixing, the steady flow rate Q in the stream is given by1 Q = Q,

Ci - C2 '-2

—

(2.3)

^0

where Qt is the steady dosing rate, C0 the concentration of the tracer in the undosed fl ow, C x the concentration of the tracer in the dose, and C2 the concentration of the tracer in the dosed flow. The tracer may be a salt evaluated by titration, a dye evaluated colorimetrically, or a radioactive element evaluated with a suitable counting device. The procedure is well adapted to boulder-strewn streams where use of a conventional meter is difficult. If two ultrasonic transducers are installed on opposite banks of a stream such that their sonic beams follow reciprocal paths at an angle to the flow, the difference in time taken for the travel of a pulse in each direction is a measure of the mean water velocity. Several ultrasonic stations are in operation and may provp useful for a continuous record of discharge. When a stream of flowing water cuts the earth’s magnetic field, an electromotive force (emf) is induced tjaat can be measured and is proportional to the average velocity of the water. The small potential is difficult to detect in small streams, but by creating a magnetic force with a coil installed in the stream, measurements are possible. The electromagnetic

1H. Addison, “Applied Hydraulics,” 4th ed., pp. 583-584, Wiley, New York, 1954.

Í

DESCRIPTIVE HYDROLOGY

23

FIGURE 110

Aa electromagnetic current meter with recording gear.

(Montedoro-Whitney Company)

siethod has been incorporated into a small cutrent meter (Fig. 2.10) with a digital readout of the velocity at the meter location. The accuracy of streamflow records depends upon the physical features of the cross section, the frequency of measurement, and the quality of the stagezieasuring equipment. The adjective classification used by the U.S. Geological Survey is given in Table 2.2. 11 0

Measure ment of River Stage

The simplest device for measuring river stage is a sta ff gage, a scale graduated in feet or meters. Staff gages are usually read by an observer once or twice a day, but on streams subject to rapid changes in stage it is not possible to get a reliable record without use of recording equipment. The most common type of recording gage uses a float connected to the recording mechanism in such a way that motion of the float is recorded on a paper chart. A gage house and stilling well (Fig. 2.11) of corrugated steel, conprete, or timber is required to protect the recording

TABLE 2.2 Accuracy* o

f streamflow d

ata (percent)

Adjective

Individual

Published

classification

measurements