U.S. Geological Survey, Techniques of Water-Resources Investigations, Book 3, Chapter B2

By Gordon D. Bennett

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The series of manuals on techniques describes procedures for planning and executing specialized work in water-resources investigations. The material is grouped under major subject headings called books and further subdivided into sections and chapters; Section B of Book 3 is on ground-water techniques.

This chapter is an introduction to the hydraulics of ground-water flow. With the exception of a few discussions in standard text format, the material is presented in programed form. In this form, a short section involving one or two concepts is followed by a question dealing with these concepts. If the correct answer to this question is chosen, the reader is directed to a new section,in which the theory is further developed or extended. If a wrong answer is chosen, the reader is directed to a section in which the earlier material is reviewed, and the reasons why the answer is wrong are discussed; the reader is then redirected to the earlier section, to choose another answer to the question. This approach allows students who are either partially familiar with the subject, or well prepared for its study, to proceed rapidly through the material, while those who require more explanation are provided it within the sections that deal with erroneous answers.

In the preparation of any text, difficult choices arise as to the material to be included. Because this text is an introduction to the subject, the discussion has been restricted, for the most part, to the flow of homogeneous fluid through an isotropic and homogeneous porous medium-that is, through a medium whose properties do not change from place to place or with direction. Emphasis has been placed upon theory rather than application. Basic principles of ground-water hydraulics are outlined, their uses in developing equations of flow are demonstrated, representative formal solutions are considered, and methods of approximate solution are described. At some points, rigorous mathematical derivation is employed; elsewhere, the development relies upon physical reasoning and plausibility argument.

The text has been prepared on the assumption that the reader has completed standard courses in calculus and -college physics. Readers familiar with differential equations will find the material easier to follow than will readers who lack this advantage; and readers familiar with vector theory will notice that the material could have been presented with greater economy using vector notation.

The material is presented in eight parts. Part I introduces some fundamental hydrologic concepts and definitions, such as porosity, specific discharge, head, and pressure. Part II discusses Darcy's law for unidirectional flow; a text-format discussion at the end of Part II deals with some generalizations of Darcy's law. Part III considers the application of Darcy's law to some simple field problems. The concept of ground-water storage is introduced in Part IV. A text-format discussion at the beginning of Part V deals with partial derivatives and their use in ground-water equations; the basic partial differential equation for unidirectional nonequilibrium flow is developed in the programed material of Part V. In Part VI, the partial differential equation for radial confined flow is derived and the “slug-test” solution, describing the effects of an instantaneous injection of fluid into a well, is presented and verified. A text-format discussion at the end of Part VI outlines the synthesis of additional solutions, including the Theis equation, from the “slug-test” solution. Part VII introduces the general concepts of finite-difference analysis, and a text format discussion at the end of Part VII outlines some widely used finite-difference techniques. Part VIII is concerned with electric-analog techniques. The material in Part VI is not prerequisite to that in Parts VII and VIII; readers who prefer may proceed directly from Part V to Part VII.

A program outline is presented in the table of contents of this report. This outline indicates the correct-answer sequence through each of the eight parts and describes briefly the material presented in each correct-answer section. Readers may find the outline useful in review or in locating discussions of particular topics, or may wish to consult it for an overview of the order of presentation.

It is impossible, in this or any other form of instruction, to cover every facet of each development, or to anticipate every difficulty which a reader may experience, particularly in a field such as ground water, where readers may vary widely in experience and mathematical background. An additional difficulty inherent in the programed text approach is that some continuity may be lost in the process of dividing the material into sections. For all these reasons, it is suggested that the programed instruction presented here be used in conjunction with one or more of the standard references on ground-water hydraulics.

This text is based on a set of notes used by the author in presenting the subject of ground-water hydraulics to engineers and university students in Lahore, West Pakistan, while on assignment with the U.S. Agency for International Development. The material has been drawn from a number of sources. The chapter by Ferris (1959) in the text by Wisler and Brater and that by Jacob (1950) in “Engineering Hydraulics” were both used extensively. Water-Supply Paper 1536-E (1962) by Ferris, Knowles, Brown, and Stallman was an important source, as was the paper by Hubbert (1940) “The Theory of Ground Water Motion.” The text “The Flow of Homogeneous Fluids through Porous Media” by Muskat (1937) and the paper “Theoretical Investigation of the Motion of Ground Waters” by Slichter (1899) were both used as basic references. The development of the Theis equation from the “slug-test” solution follows the derivation given in the original reference by Theis (1935). The material on analog models is drawn largely from the tik, “Analog Simulation,” by Karplus (1958). In preparing the material on numerical methods, use was made of the book, “Finite-Difference Equations and Simulations,” by Hildebrand (1968) and the paper “Selected Digital Computer Techniques for Groundwater Resource Evaluation,” by Prickett and Lonnquist (1971). A number of additional references are mentioned in the text.

The author is indebted to Messrs. David W. Greenman and Maurice J. Mundorf, both formerly Project Advisors, U.S. Geological Survey-U.S.A.I.D., Lahore, for their support and encouragement during preparation of the original notes from which this text was developed. The author is grateful to Patricia Bennett for her careful reading and typing of the manuscript.

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