Water resources

THE McGRAW-HILL CIVIL ENGINEERING PE EXAM DEPTH GUIDE Water Resources THE McGRAW-HILL CIVIL ENGINEERING PE EXAM DEPTH GUIDE Water Resources Emmanuel U Nzewi, Ph.D., PE McGRAW-HILL New York Chicago San Francisco Lisbon London Madrid MexicoCity Milan New Delhi SanJuan Seoul Singapore Sydney Toronto Cataloging-in-Publication Data is on file with the Library of Congress bZ McGraw-Hill A Division ofTheMcGraw·HillCvmpanies Copyright © 2001 by The McGraw-Hill Companies, Inc All rights reserved Printed in the United States of America Except as permitted under the United States Copyright Act of 1976, no part of this publication may be reproduced or distributed in any form or by any means, or stored in a data base or retrieval system, without the prior written permission of the publisher AGM/ AGM ISBN 0-07-136183-9 The sponsoring editor for this book was Larry S Hager and the production supervisor was Sherri Souffrance It was set in Times Roman by Lone Wolf Enterprises, Ltd Printed and bound by QuebecorlMartinsburg I:i:Jt \%I This book is printed on recycled, acid-free paper containing a minimum of 50% recycled, de-inked fiber McGraw-Hill books are available at special quantity discounts to use as premiums and sales promotions, or for use in corporate training programs For more information, please write to the Director of Special Sales, McGraw-Hill, Professional Publishing, Two Penn Plaza, New York, NY 10121-2298 Or contact your local bookstore Preface viii About the Author ix CHAPTER 1: FUNDAMENTAL CONCEPTS AND PROPERTIESOF FLUIDS 1.0 Overview and List of Reference Formulas 1.01 List of Formulas 1.1 Fundamental 1.1 1.1 1.1 Ideas and Definitions 1.9 1.2 Properties of Fluids 1.9 1.2.1 Density (p) and Specific Weight ('}') 1.9 1.2.2 Viscosity-Dynamic 1.2.3 Surface Tension and Kinematic Viscosity 1.13 1.18 1.2.4 Vapor Pressure 1.22 1.2.5 Compressibility of Fluids 1.24 1.2.6 Specific Heat and Latent Heat 1.25 1.2.7 Ideal Gas Law 1.25 CHAPTER 2: FLUID STATICS 2.0 Fluid Statics 2.1 2.1 2.1 Concept of Pressure 2.1 2.2 Pressure Scales 2.2 2.3 Manometry and Pressure Measurement 2.4 Pascal's Law 2.10 2.5 Forces on a Submerged Surface 2.6 Forces on Plane Submerged 2.7 Forces of Curved Surfaces 2.8 Archimedes' Principle 2.25 2.11 Surfaces 2.22 2.4 2.13 CHAPTER3: FLUID DYNAMICS AND APPLIEDHYDRAULICS 3.0 Fluids in Motion 3.1 3.0.1 Characterization of Fluid Flows 3.0.2 Forces on a Fluid Element 3.0.3 Derivation 3.1 3.2 3.5 of Reynolds Number 3.6 3.1 The Viscous Wall Layer 3.7 3.2 Velocity Distribution and the Measurement 3.3 The Bernoulli Equation 3.4 Reynolds Transport Theorem 3.5 Conservation of Flow Rate 3.8 3.16 3.17 Laws in Fluid Flow 3.20 3.5.1 The Continuity Principle 3.20 3.5.2 The Energy Equation 3.23 3.5.3 Momentum 3.28 Equation 3.6 Pressurized Flow in Conduits 3.6.1 Continuity 3.32 Equation (Mass Conservation) 3.6.2 The Energy Equation (Conservation 3.6.3 Momentum Equation 3.33 of Energy) 3.40 3.6.4 Headloss Due to Pipe Friction 3.43 3.6.5 Minor Losses in Piping Systems 3.46 CHAPTER4: ENGINEERINGHYDROLOGY 4.0 Definition 4.1 and Scope 4.1 4.0.1 Watershed or Catchment 4.3 4.0.2 Runoff and Watershed Scale 4.3 4.0.3 List of Formulas 4.1 Introduction 4.5 4.13 4.2 Basic Probability and Statistics in Hydrology 4.2.1 Types of Random Variables 4.16 4.2.2 Determination Values 4.2.3 Continuous 4.2.4 Plotting 4.2.5 Statistical of Probability Random Variables Position Formula Moments 4.17 4.20 4.2.7 The Skew and Skew Coefficient 4.21 4.21 Distributions 4.22 4.3.1 Processes Leading to Precipitation 4.27 4.3 Precipitation 4.14 4.16 4.19 4.2.6 Variance and Standard Deviation 4.2.8 Standard Probability 3.35 4.26 CONTENTS 4.3.2 Distribution of Rainfall 4.27 4.3.3 Calculation of Average Rainfall in a Watershed 4.3.4 Estimating 4.28 Missing Rainfall Data 4.34 4.3.5 Testing the Consistency of Gage Records 4.37 4.4 The Hydrologic Cycle and the Hydrologic Budget Equation 4.4.1 The Hydrologic 4.5 Hydrologic Budget Equation Abstractions 4.5.3 Infiltration 4.46 4.5.4 Infiltration Rate Values 4.5.5 Instantaneous 4.5.4 Infiltration Infiltration 4.45 Methods 4.5.5 Evaporation 4.56 4.5.6 Estimation of Evaporation 4.47 Infiltration 4.7 Peak Runoff Models Rates 4.57 4.80 4.7.2 NRCS TR-55 Method 4.84 Runoff Models 4.8.2 Unit Hydrograph ETO or ET 4.71 4.80 4.7.1 Rational Method 4.87 Theory Unit Hydrographs 4.91 4.94 CHAPTER5: GROUNDWATERHYDRAULICS 5.0 Scope and Definitions 5.1 Groundwater 5.1 of Subsurface Media Recharge 5.5 Darcy's Law 5.18 5.6 General Groundwater 5.3 5.12 5.4 Hydraulics of Groundwater 5.13 Flow Equations 5.7 Flow Nets in Isotropic Media APPENDIXA: GROUNDWATER INDEX 5.1 Sources and Types 5.2 5.2 Characterizations 5.3 Groundwater Rate 4.52 (ET) 4.70 4.6.1 Models for Estimating 4.9 Synthetic 4.42 4.46 Indices-Average 4.6 Evapotranspiration 4.39 4.44 4.5.1 Interception 4.44 4.5.2 Surface or Depression Storage 4.8 Continuous vii 5.23 5.28 A.1 1.1 The main focus of this book is to provide the reader with a concise review of topics in water resources engineering (hydraulics and hydrology) The intended reader is an individual preparing to sit for the principles and practice exam (often called the PE exam) conducted by the National Council of Examiners for Engineering and Surveying (NCEES) The book is divided into six sections-five chapters and an appendix The entire book is illustrated with diagrams and figures which help provide the reader with a more concrete description of the engineering concepts discussed In general, each major concept presented is followed by an illustrative and non-trivial example It is hoped that these features of the book will make the review of water resources engineering topics more efficient because examples normally help to answer questions that the reader may have, and diagrams convey ideas more effectively than mere words Chapters One and Two provide an overview of the fundamental principles necessary for a good understanding of the topics presented in Chapter Three Thus, Chapters One and Two are the foundation of the rest of the book While some topics covered in Chapter One may be somewhat elementary, it is the belief of the author that incorrect assumptions usually spring from a poor understanding of these fundamental concepts Chapter Two includes detailed presentations of fluid statics, basic principles in manometry and flotation of objects In Chapter Three, hydraulics are presented along with illustrative examples The reader is encouraged to work out the example problems and then walk through the provided solutions for correction, reinforcement, and reflection Chapter Four is dedicated to engineering hydrology This part of the book presents an overview of engineering hydrology and culminates in the implementation approaches for the Rational or Lloyd-Davies formula, Unit Hydrograph techniques, Natural Resources Conservation Service (NRCS) methods (espe- cially the Curve Number method), and their a\'l\'llicationin storm water management In Chapter Five, a survey and overview of the major concepts in groundwater hydrology Topics include classification of groundwater, types of aquifers, basic parameters in groundwater storage and movement, Darcy's Law, and the Laplace equation for groundwater flow and flow nets Example problems are provided to demonstrate the proper application of these groundwater hydraulics concepts in solving engineering problems I would like to acknowledge the support of my wife, Sochi Caroline, and kids-Sammy, 'Gechi, Joshy, Ikenna and Toby The input of my students (in regular classes and review courses) on the technical aspects of the development of this book has been invaluable The assistance of the individuals who prepared some of the manuscript (Cheryl Simmons and Sherry Bittle) and others who supported me in the completion of this project is hereby noted and greatly appreciated The persistence and encouragement of the Lone Wolf crew in bringing this book to fruition is also acknowledged Above all, I thank my God, who provided the strength, grace, and perseverance to complete this work To Him be all the glory Emmanuel U Nzewi, Ph.D., PE viii EMMANUEL U NZEWI, Ph.D., PE Emmanuel U Nzewi, Ph.D., PE, has expert credentials in a number of water resources areas, including hydropower production, urban watershed analysis, modeling, and water distribution A professor of civil engineering at North Carolina A&T, he earned his doctorate from Purdue University ix In this chapter, the properties of fluids (gases and liquids) that are of interest to the civil engineer are presented It is assumed that the fluid is a continuum The fluid properties described include: density, specific weight, specific gravity, viscosity and the classification of fluids as Newtonian and non-Newtonian, the no-slip condition, surface tension, compressibility of fluids and vapor pressure concepts The specific capacity of gases is briefly discussed At the beginning of the chapter, a set of basic equations in hydraulics are listed and summarily described In general, Chapter One covers foundational issues with reference to fluid properties Although fluids are generally discussed, the emphasis is on liquids, particularly water 1.0 OVERVIEW AND LIST OF REFERENCE FORMULAS This chapter presents the principles of basic fluid mechanics necessary to solve problems in hydraulics and hydrostatics Because of the review nature of this text, these topics are summarily presented with illustrative examples where applicable Pertinent tables and figures are provided liberally so that the reader does not need to consult other reference texts or publications for common reference values and formulas 1.01 List of Formulas Density traditionally is represented by the Greek letter p p= Mass M =V olume V Specific weight traditionally is represented by the Greek letter 'Y Weight W 'Y= -=V olume V 1.1 A E Ambient pressure on surfaces, 2.18 Energy equation, 3.23, 3.35 Archimedes' principle, 2.2~ Enthalpy, change in, 1.26 Estimating ET, models for, 4.71 B Estimating missing rainfall data, 4.34 Bernoulli equation, 3.16 Evaporation, 4.56 C Evapotninspiration, 4.70 Evaporation rates, estimation of, 4.57 Catchment, 4.3 Cavitation, 1.23 F Compressibility of fluids, 1.24 Flow nets, constructing, 5.30 Confined aquifer, groundwater flow equations for, Procedure for developing, 5.28 5.24 Flow rates, measurement of, 3.8 Storage coefficient of, 5.8 Flow rate measurement in pipes, 3.9 Continuity equation, 3.33 Fluid flow, characterization of, 3.2 Continuity equation for I-dimensional flow, 3.21 Continuity principle, 3.20 Conservation laws in, 3.20 Governing equations for, 3.32 Continuous runoff models, 4.87 Fluid statics, 2.1 Fluids, compressibility of, 1.24 D Properties of, 1.9 Darcy's law, 5.18 Fluids in motion, 3.1 General form of, 5.23 Forces on asymmetrical plane surfaces, 2.18 Validity of, 5.22 Forces on curved surfaces, 2.22 Darcy velocity, 5.20 Forces on a fluid element, 3.5 Density, 1.9 Forces on plane submerged surfaces, 2.13 ¥- 1.1 1.2 INDEX Forces on a submerged surface, 2.11 M Formulas, list of, 1.1, 4.5 Manometers, use of U -tube, 2.4 Fundamental definitions, 1.9 Manometry measurement, 2.4 Fundamental ideas, 1.9 Minor losses in piping systems, 3.46 G Momentum equation, 3.28, 3.40 N Gage records, testing the consistency of, 4.37 Gases, density of, 1.12 Groundwater flow equations, 5.23 NRCS TR-55 method, 4.84 Groundwater recharge, 5.12 p Groundwater sources, 5.2 Pascal's law, 2.10 Groundwater types, 5.2 Peak runoff models, 4.80 Permeability, coefficient of, 5.13 H Headloss due to pipe friction, 3.43 Plotting position formula, 4.19 Porosity, 5.4 ' Heat, latent, 1.25 Precipitation, 4.26 Specific, 1.25 Horton's Equation, application of, 4.50 Processes leading to, 4.27 Pressure, concept of, 2.1 Hydraulic conductivity, 5.13 Pressure management, 2.4 Hydraulics of groundwater, 5.13 Pressure scales, 2.2 Hydrologic abstractions, 4.44 Pressurized flow in conduits, 3.32 Hydrologic budget equation, 4.39, 4.42 Hydrologic cycle, 4.39 Probability values, determination of, 4.16 R Hydrology, 4.1 Basic probability and statistics in, 4.14 Rainfall, distribution of, 4.27 Hydrostatic forces on surfaces, 2.18 Calculation of average, 4.28 Random variables, continuous, 4.17 I Ideal gas law, 1.25 Discrete, 4.16 Types of, 4.16 Infiltration, 4.46 Rational method, 4.80 Infiltration indices, 4.52 Reference formulas, 1.1 Infiltration rate values, 4.46 Reynolds number, derivation of, 3.6 Instantaneous infiltration methods, 4.47 Reynolds transport theorem, 3.17 Interception, 4.44 Internal energy, 1.26 Runoff, 4.3 Isotropic media, assumptions for flow nets in, S 5.28 Flow nets in, 5.28 Seepage velocity, 5.20 Skew, 4.21 - INDEX W Skew coefficient, 4.21 Specific weight, 1.9 W aters h e,d W aters h e d sca 1e, Standard deviation, 4.21 Standard probability distributions, 4.22 Statistical moments, 4.20 Steady flow conditions, 3.19 Storage, depression, 4.45 Surface, 4.45 Storativity, storage coefficient of, 5.8 Subsurface media, characterization of, 5.3 Subsurface water, zones of, 5.2 Surface tension, 1.18 Synthetic unit hydrographs, 4.94 System-to-control volume transformation, T 3.17 J Tailwater force, 2.17 Time-area models, 4.88 U Unconfined aquifer, groundwater flow equations for, 5.24 Specific yield of an, 5.7 Unit hydrograph theory, 4.91 Uplift forces, 2.16 V Vapor pressure, 1.22 Variance, 4.21 Velocity distribution, 3.8 Velocity measurement in pipes, 3.9 Viscosity, 1.13 Classification of fluids by, 1.15 Dynamic, 1.13 Kinematic, 1.13 Viscous wall layer, 3.7 Void ratio, 5.4 1.3 ... CHAPTER5: GROUNDWATERHYDRAULICS 5.0 Scope and Definitions 5.1 Groundwater 5.1 of Subsurface Media Recharge 5.5 Darcy's Law 5.18 5.6 General Groundwater 5.3 5.12 5.4 Hydraulics of Groundwater 5.13... groundwater hydrology Topics include classification of groundwater, types of aquifers, basic parameters in groundwater storage and movement, Darcy's Law, and the Laplace equation for groundwater... Ph.D., PE, has expert credentials in a number of water resources areas, including hydropower production, urban watershed analysis, modeling, and water distribution A professor of civil engineering