DOCSLIB.ORG

Hydraulic Geometry * of Stream Channels and Some Physiographic Implications

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text

Load more

The Hydraulic Geometry * of Stream Channels and Some Physiographic Implications By LUNA B. LEOPOLD and THOMAS MADDOCK, JR. GEOLOGICAL SURVEY PROFESSIONAL PAPER 252 Quantitative measurement of some of the hydraulic factors that help to determine the shape of natural stream channels: depth, width, velocity, and sus­ pended load, and how they vary with discharge as simple power functions. Their interrelations are described by the term "hydraulic geometry" UNITED STATES GOVERNMENT PRINTING OFFICE, WASHINGTON : 1953 UNITED STATES DEPARTMENT OF THE INTERIOR Oscar L. Chapman, Secretary GEOLOGICAL SURVEY W. E. Wrather, Director For sale by the Superintendent of Documents, U. S. Government Printing Office Washington 25, D. C. - Price 35 cents (paper cover) PREFACE This report was prepared by the Technical Coordination Branch of the Water Resources Division of the Geological Survey as a part of the investigation of water-utilization problems. The junior author, Mr. Maddock, is assistant chief of the Hydrology Division, Bureau of Reclamation. The authors have benefited greatly from constructive suggestions made by many friends and colleagues. Particular acknowledgment is due J. Hoover Mackin and Walter B. Langbein whose counsel and criticism contributed greatly to whatever of value is contained in this report. Among the persons who read an early draft and whose suggestions are highly valued are A. N. Strahler, John P. Miller, E. W. Lane, L. C. Gottschalk, K. B. Schroeder, C. C. Nikiforoff, Charles E. Stearns, and W. M. Borland. The continuous encouragement of W. W. Rubey is appreciated. L. B. L. HI GLOSSARY Antidune. A transient form of ripple on the stream bed analogous to a sand dune; an antidune progressively moves upstream. Control. The "control" of a stream-gaging station refers to the nature of the channel downstream from the meas­ uring section which determines the stage-discharge relation. Current meter. An instrument for measuring water speed; consists of cups which are rotated by the flowing water; rate of rotation is a function of water speed. Cumulative frequency, or flow-duration, curve. Graph of rate of daily discharge in relation to cumulative fre­ quency, indicating the percent of time a given discharge is equalled or exceeded. Discharge. The amount of water flowing in a channel expressed as volume per unit of time. i) Froude number. A measure of tranquility of flow defined as ~j== Gage height. Th'e' water-surface elevation referred to some arbitrary datum. Hydraulic gradient: The slope of the energy grade line; or slope of the line representing the sum of kinetic and • potential energy along the channel length. It is equal to the slope of the water surface in steady, uniform flow. Hydraulic radius. A measure of water depth in a channel defined as cross-sectional area of flowing water divided by the length of wetted perimeter; approximates mean depth in a wide channel. Manning formula. A formula including empiric constants relating open-channel water velocity to hydraulic gradient, hydraulic radius, and channel roughness. Rating curve. The graph of discharge plotted against water-surface elevation for a gjiven cross sectior of a stream. Sediment station. A river section where samples of suspended load are taken each day, or periodically. Stage, or river stage. Synonymous with gage height. Stream-gaging station. An installation including a mechanical continuous recorder of water-surface elevation; at the same cross section periodic velocity measurements are made, and are used to construct the rating curve for the station. These two types of data are used to furnish a continuous record of wate1* flow. Suspended sediment-discharge curve. A graph of water discharge plotted against concomitant m easured sus­ pended-sediment load. SYMBOLS a coefficient representing width at unit discharge k coefficient representing velocity at unit discharge 6 exponent in width-discharge relation L suspended-sediment load, weight per unit of time c coefficient representing depth at unit discharge m exponent in velocity-discharge relation C Chezy coefficient in v=C-^Rs n Manning roughness factor d mean depth p coefficient representing load at unit discharge D pipe diameter Q water discharge in cubic feet per second (cfs) / exponent in depth-discharge relation R hydraulic radius, approximately equal to mean F a function of depth in wide channels <7 sediment-grain diameter s slope of water surface in open channels g acceleration due to gravity v velocity j exponent in suspended load-discharge relation w width CONTENTS Page Page A bstract _ __________________________________________ 1 The hydraulic geometry of stream channels in relation to General statement- _________________________________ 1 sediment load—Continued The hydraulic geometry of stream channels ____________ 2 Interrelations of width, depth, velocity, and sus­ Concept of frequency of discharge._______________ 2 pended load to a variable discharge _____________ 24 Variation of hydraulic characteristics in a particular Interrelations of width, depth, velocity, and bed load cross section of a river____---_-________________ at a given discharge---________________________ 28 Variation of hydraulic characteristics in a down­ Channel-shape adjustment during individual floods-- 30 stream direction ______________________________ The role of channel roughness and slope in the adjust­ Relation of channel shape to frequency of discharge _ 16 ment of channel shape to sediment load_________ 35 The hydraulic geometry of stream channels in relation to Some physiographic implications-_____________________ 43 sediment load____________________________________ 19 The stable irrigation canal—an analogy to a graded Relations of suspended sediment to discharge in a river _ _______'_________----_----_------____--- 43 particular cross section of a river.______________ 19 Sediment and the longitudinal profile._____________ 48 Relations of suspended sediment to discharge in the Summary and interpretation_________________________ 51 downstream direction _________________________ 21 References.________________----_-___-__----------_- 53 Interrelations of width, depth, velocity, and sus­ Appendix___ _-_____----------_---------__-_--------. ' 54 pended load at a given discharge________________ 23 Index _____________________________________________ 57 ILLUSTRATIONS FIGURE 1. Cumulative frequency, or flow-duration, curve for Powder River at Arvada, WyO-____-_-___---_-_---------- 3 2. Comparison of different rates of discharge at a station and downstream._______________._______---_-_------ 4 3. Typical relations among width, depth, velocity, discharge, and gage height, Cheyenne River near Eagle Butte, S. Dak_ ______________________________________________________________________________.._ 5 4. Relation of width, depth, and velocity to discharge, Powder River at Arvada, Wyo., and at Locate, Mont_____ 6 5. Width, depth, and velocity in relation to mean annual discharge as discharge increases downstream, Powder River and tributaries, Wyoming and Montana_______ ___________________________-___-____-.----.--------. 10 6. Width, depth, and velocity in relation to mean annual discharge as discharge increases downstream, Bighorn River and tributaries, Wyoming and Montana______-___-_________-_-_-_---_----_--_------------------ H 7. Width, depth, and velocity in relation to mean annual discharge as discharge increases downstream, Arikaree, Republican, Smoky Hill, and Kansas Rivers in the Kansas River system, Kansas and Nebraska------------ 12 8. Width, depth, and velocity in relation to mean annual discharge as discharge increases downstream, main trunk of Missouri and lower Mississippi Rivers.____________-_______________-_--__-------___-___------------ 13 9. Width, depth, and velocity in relation to mean annual discharge as discharge increases downstream in various river systems.___________________________________-______-___-____----_-_-_-_---___---------_------ 15 10. Width, depth, and velocity in relation to discharges representing two frequencies, Maumee and Seioto River basins, Ohio.-__________________________________________-_______--_-______-----_--___-._----------- 17 11. Width, depth, and velocity in relation to discharge of various frequencies, Maumee and Seioto River basins, Ohio_ 18 12. Diagrammatic relations of width, depth, and velocity to discharge at a station and downstream._____________ 19 13. Relation of suspended-sediment load to discharge, Powder River at Arvada, Wyo___________________________ 20 14. Typical relations in the hydraulic geometry of natural stream channel systems._____________________________ 22 15. Average relation of suspended-sediment load to channel-shape factors at a constant discharge of 500 cfs (from river data in appendix)___________________________________________________________-__--__'•__________ 23 16. Average relation of suspended-sediment load to channel-shape factors at four discharge rates (from river data in appendix)______________!________________________________--_____-_________---_-_-_-------__----- 24 17. Example of width, depth, velocity in relation to discharge (constructed from fig. 16)________________________ 25 18. Relation of &,-p and j (constructed from fig. 16)_______________________________________________________ 25 19. Average hydraulic geometry of river channels___________________________________-__-__----_____------- 27 20. Relation of bed load to channel-shape factors at constant discharge, from Gilbert data_______________________ 29 21. Changes in
Recommended publications
  • Properties and Definitions

    Properties and Definitions

    Properties and Definitions Useful constants, properties, and conversions 2 2 gc = 32.2 ft/sec [lbm-ft/lbf-sec ] 3 ρwater = 1.96 slugs/ft 3 γwater = 62.4 lb/ft 1 ft3/sec = 449 gpm 1 mgd = 1.547 ft3/sec 1 foot of water = 0.433 psi 1 psi = 2.31 ft of water Definitions discharge: flow rate, usually in ft3/sec or gpm Properties Density Density (ρ) is mass per unit volume (slugs/ft3) Specific Weight (aka Unit Weight) Specific Weight (γ) is weight per unit volume (lb/ft3) = ρg Specific Gravity Specific Gravity (S) is the ratio of the weight (or mass) or a substance to the weight (or mass) of water. where the subscript "s" denotes of a given substance and the subscript "w" denotes of water. Given S of a substance, you can easily calculate ρ and γ using the equations Specific Volume Specific Volume is the volume per unit mass (usually in ft3/lbm) Viscosity Viscosity (υ) is a measure of a fluid's ability to resist shearing force (usually in 2 lbf·sec/ft ) υ is a proportionality constant and is also known as absolute viscosity or dynamic viscosity. Viscosity is often given in the SI unit of Poise. To convert to English units use the relationship Kinematic Viscosity where γ = kinematic viscosity (ft2/s) 2 υ = dynamic viscosity (lbf·sec/ft ) ρ = mass density (slugs/ft3) Note: See CERM Appendix 14.A (page A-13) for a listing of water properties at various temperatures. Absolute and Gauge Pressure Absolute Pressure (psia) = Atmospheric Pressure + Gauge Pressure (psig) Atmospheric Pressure changes with weather conditions and altitude though is usually assumed to be 14.7 psi at sea level.
  • 1948 MACKIN Gradedriver G

    1948 MACKIN Gradedriver G

    BULLETIN OF THE GEOLOGICAL SOCIETY OF AMERICA VOL. 69. PP. 463-512, 1 FIG. MAY 1948 CONCEPT OF THE GRADED RIVER BY J. HOOVER MACKIN CONTENTS Page Abstract 464 Introduction 465 Acknowledgments 466 Velocity and load 466 General statement 466 Energy and velocity 466 Competence 468 Capacity 468 The total load 469 The concept of grade 470 Examples of streams at grade 472 The graded stream as a system in equilibrium 475 The shifting equilibrium 477 Factors controlling the slope of the graded profile 479 General statement 479 Downvalley increase in discharge 479 Downvalley increase in ratio of load to discharge 480 Downvalley decrease in ratio of load to discharge 480 Downvalley decrease in caliber of load 481 Relationship between channel characteristics and slope 483 The concept of adjustment in section 484 Adjustment in section in the straight channel 485 Adjustment in section in the shifting channel 486 Effect of variation in channel characteristics on the graded profile 487 Local variation from mean slope 490 Backwater and draw-down effects 490 Effects of differences in rock resistance 491 Summary 491 Response of the graded stream to changes in control .. 492 General statement 492 Increase in load 493 Decrease in load 494 Changes in discharge 494 Rise of base level 496 Lowering of base level 498 Classification of changes in control 499 Regrading with progress of the erosion cycle 499 Short-term changes 501 Deposits of graded and aggrading streams 502 Secondary effects of aggradation 503 Decrease in supplied load 503 Decrease in discharge
  • Hydropower Engineering Ii Lecture Note Compiled By

    Hydropower Engineering Ii Lecture Note Compiled By

    Arbaminch University, Department of Hydraulic Eng’g HYDROPOWER ENGINEERING II LECTURE NOTE COMPILED BY: YONAS GEBRETSADIK LECTURER IN HYDRAULIC ENGINEERING DEPARTMENT OF HYDRAULIC ENGINEERING ARBA MINCH WATER TECHNOLOGY INSTITUTE ARBA MINCH UNIVERSITY JANUARY 2011 Hydropower Engineering-II Lecture Note/2010/2011 1 Arbaminch University, Department of Hydraulic Eng’g TABLE OF CONTENTS 1. HYDRAULIC TURBINES ............................................................................................................................. 5 1.1 GENERAL ............................................................................................................................................. 5 1.2 CLASSIFICATION .................................................................................................................................. 5 1.3 CHARACTERISTICS OF TURBINES ......................................................................................................... 6 1.4 PROCEDURE IN PRELIMINARY SELECTION OF TURBINES ...................................................................... 7 1.5 TURBINE SCROLL CASE ....................................................................................................................... 9 1.6 DRAFT TUBES .................................................................................................................................... 10 1.7 CAVITATION IN TURBINE & TURBINE SETTING ................................................................................. 11 1.8 GENERATORS AND TURBINE
  • The Depositional Signature of Strongly Aggradational Chute-And-Pool Bedforms

    The Depositional Signature of Strongly Aggradational Chute-And-Pool Bedforms

    Marine and River Dune Dynamics – MARID VI – 1-3 April 2019 - Bremen, Germany Build-up-and-fill structure: The depositional signature of strongly aggradational chute-and-pool bedforms Arnoud Slootman College of Petroleum Engineering & Geosciences, King Fahd University of Petroleum and Minerals, Dhahran, Saudi Arabia – [email protected] Matthieu J.B. Cartigny Department of Geography, Durham University, Durham, United Kingdom – [email protected] Age J. Vellinga National Oceanography Centre, University of Southampton Waterfront Campus, Southampton, United Kingdom – [email protected] ABSTRACT: Chute -and -pools are unstable, hybrid bedforms of the upper flo w-regime, pop u- lating the stability field in between two stable end-members (antidunes and cyclic steps). Chute-and-pools are manifested by supercritical flow (chute) down the lee side and subcritical flow (pool) on the stoss side, linked through a hydraulic jump in the trough. The associated sedimentary structures reported here were generated at the toe-of-slope of a Pleistocene car- bonate platform dominated by resedimentation of skeletal sand and gravel by supercritical density underflows. It is shown that wave-breaking on growing antidunes occurred without destruction of the antidune like commonly observed for antidunes in subaerial flows. This led to the formation of chute-and-pools that were not preceded by intense upstream scouring, in- terpreted to be the result of high bed aggradation rates. The term aggradational chute-and- pool is proposed for these
  • Innovative and Low Cost Technologies Utilized in Sewerage

    Innovative and Low Cost Technologies Utilized in Sewerage

    ENVIRONMENTAL HEALTH PROGRAM INNOVATIVE AND LOW COST TECHNOLOGIES UTILIZED IN SEWERAGE TECHNICAL SERIES No. 29 PAN AMERICAN H EAU H ORGANIZATION Pan American Sanitary Bureau, Regional Office of the WORLD HhALTH ORGANIZATION ENVIRONMENTAL HEALTH PROGRAM u, •:'< i .:••;: .•: a. ! 4 INNOVATIVE AND LOW COST TECHNOLOGIES UTILIZED IN SEWERAGE AUTHOR José M. Azevedo Netto EDITED Raymond Reid WASHINGTON, D.C., MARCH 1992 PROLOGUE This publication is the product of the last contract of the late Jose Martiniano de Azevedo Netto with the Pan American Health Organization and is a significant example of a relationship of more than 40 years duration —a relationship that was characterized always with a touch of daring, and clever, innovative approaches to the solution of environmental health problems and risks. The contribution of Azevedo Netto to sanitary engineering goes far beyond his countless books, papers and articles. Thousands of public health and sanitary engineering professionals in Latin America have been affected and influenced by his inspiring and dedicated teachings and instruction. Azevedo Netto was born in Brazil in 1918, graduated as a civil engineer from the University of Sao Paulo, and earned his masters degree in sanitary engineering from Harvard University and his doctorate in public health from the University of Sao Paulo. The professional life of Professor Azevedo Netto, as he liked to be called, took him to all continents as a teacher and as technical advisor to governments and institutions such as Pan American Health Organization, the World Bank, Inter- American Development Bank and others. A founding member of the Inter-American and the Brazilian Associations of Sanitary and Environmental Engineering, Azevedo Netto raised the consciousness of the importance of sanitary engineering to improvement of peoples' health and quality of life.
  • Oft/Milar/ON in SEWER. DESIGN Flold Cjjflr.T

    Oft/Milar/ON in SEWER. DESIGN Flold Cjjflr.T

    · COST EFFECTIVENESS IN SEWER DESIGN by Gary J. Diorio, P.E. SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS for the Degree of Master of Science in the Civil Engineering Program ~{).~. ADVISER DATE DEAN of the Graduate School DATE Youngstown State University December, 1986 COST EFFECTIVENESS IN SEWER DESIGN © 1986 GARY J. DIORIO, P.E. All Rights Reserved i ABSTRACT COST EFFECTIVENESS IN SEWER DESIGN GARY J. DIORIO, P.E. MASTER OF SCIENCE YOUNGSTOWN STATE UNIVERSITY Probably the most important challenge facing an engineer today is to ensure that his design is competitive in terms of costs. Besides being technically sound, the designer's objectives are to provide a cost effective solution. This thesis presents a computer program to be used as a guide for the design of storm sewers to ensure a cost effective solution. The computer program is compiled to generate overland flows to inlets by use of a combination of the Rational Method and the Soil Conservation Method. The cost effective solution is found by applying the cost function according to the constraints set forth in the program. The program ~ constraints involve minimum slopes to ensure proper velocities in the pipe, proper pipe sizes to ensure a technically sound design, and to provide a minimum depth of sewer throughout the entire length. A case study is also included and analyzed to provide reliability data for the computer program. The design process, including cost computation, is laborious to the extent that it discourages the effort to explore all situations to arrive at a cost effective design. The purpose of this thesis is to provide the designer with the following: ii 1.
  • Fluvial Sedimentary Patterns

    Fluvial Sedimentary Patterns

    ANRV400-FL42-03 ARI 13 November 2009 11:49 Fluvial Sedimentary Patterns G. Seminara Department of Civil, Environmental, and Architectural Engineering, University of Genova, 16145 Genova, Italy; email: [email protected] Annu. Rev. Fluid Mech. 2010. 42:43–66 Key Words First published online as a Review in Advance on sediment transport, morphodynamics, stability, meander, dunes, bars August 17, 2009 The Annual Review of Fluid Mechanics is online at Abstract fluid.annualreviews.org Geomorphology is concerned with the shaping of Earth’s surface. A major by University of California - Berkeley on 02/08/12. For personal use only. This article’s doi: contributing mechanism is the interaction of natural fluids with the erodible 10.1146/annurev-fluid-121108-145612 Annu. Rev. Fluid Mech. 2010.42:43-66. Downloaded from www.annualreviews.org surface of Earth, which is ultimately responsible for the variety of sedi- Copyright c 2010 by Annual Reviews. mentary patterns observed in rivers, estuaries, coasts, deserts, and the deep All rights reserved submarine environment. This review focuses on fluvial patterns, both free 0066-4189/10/0115-0043$20.00 and forced. Free patterns arise spontaneously from instabilities of the liquid- solid interface in the form of interfacial waves affecting either bed elevation or channel alignment: Their peculiar feature is that they express instabilities of the boundary itself rather than flow instabilities capable of destabilizing the boundary. Forced patterns arise from external hydrologic forcing affect- ing the boundary conditions of the system. After reviewing the formulation of the problem of morphodynamics, which turns out to have the nature of a free boundary problem, I discuss systematically the hierarchy of patterns observed in river basins at different scales.
  • Guide for Selecting Manning's Roughness Coefficients

    Guide for Selecting Manning's Roughness Coefficients

    GUIDE FOR SELECTING MANNING’S ROUGHNESS Turner-Fairbank Highway COEFFICIENTS FOR NATURAL CHANNELS Research Center 6300 Georgetown Pike AND FLOOD PLAINS McLean, Virginia 22101 Report No. 3 t u FHWA-TS-84-204 U.S. Department of Transportation Final Report April 1984 -1 HishrwaV AdministrWon Archived ‘This document is available to the U.S. public through the National Technical Information Service, Springfield, Virginia 2216 FOREWORD This Technology Sharing Report provides procedures for determining Manning's roughness coefficient for densely vegetated flood plains. The guidelines should be of interest to hydraulic and bridge engineers. Environmental specialists concerned with flood plains and wetlands may also find this report useful. The report was prepared by the United States Geological Survey, Water Resources Division, with technical guidance from the FHWA Office of Engineering and Highway Operations Research and Development. Sufficient copies of the publication are being distributed to provide a minimum of one copy to each FHWA region office, division office, and to each State highway agency. Additional copies of the report can be obtained from the National Technical Information Service, Springfield, Virginia 22161. DirectdrJ Office of / Director, Office of Engineering and Highway Implementation Operations R&D NOTICE This document is disseminated under the sponsorship of the Department of Transportation in the interest of information exchange. The United States Government assumes no liability for its contents or use thereof. The contents of this report reflect the views of the contractor, who is responsible for the accuracy of the data presented herein. The contents do not necessarily reflect the official views or policy of the Department of Transportation.
  • The Origins and Dynamics of Phosphorus in Maine's Lake

    The Origins and Dynamics of Phosphorus in Maine's Lake

    The Origins and Dynamics of Phosphorus in Maine’s Lake Auburn Watershed An Honors Thesis Presented to The Faculty of the Environmental Studies Program Bates College In partial fulfillment of the requirements for the Degree of Bachelor of Arts By Lars Gundersen Lewiston, Maine March 31st, 2020 ACKNOWLEDGEMENTS When I came to Bates, I did not expect to write a scientific thesis. I had enjoyed natural and field science throughout high school, but found it intimidating. Then, as a second semester first- year, I took Scientific Approaches to Environmental Issues with my future advisor, Holly Ewing. This was the class that, far more so than any other class I took at Bates, changed the trajectory of my academic, intellectual, and career interests. Holly thinks and talks about the natural sciences in a way that makes sense to me and has consistently gone out of her way to help me and my learning. Throughout our three classes together, a summer research job (when the groundwork for this thesis was laid), and the process of researching, writing and revising this thesis, she has approached my position as a relative newcomer to science with humor, generosity, and mentorship and pushed me to the edge of my intellectual abilities. Thank you, Holly. Thanks also to Ellen Labbe, my high school biology teacher, who introduced me to the natural and field sciences and piqued my interest in learning more in college. Thank you to Dan Fortin, Chris Curtis, and everyone at the AWD/LWD for providing me with data, teaching me the basics of watershed sampling (both as a summer research assistant with Holly and this year), and answering all my questions.
  • Calculating Resistance to Flow in Open Channels 1. Introduction

    Calculating Resistance to Flow in Open Channels 1. Introduction

    Alternative Hydraulics Paper 2, 5 April 2010 Calculating resistance to flow in open channels John D. Fenton http://johndfenton.com/Alternative-Hydraulics.html [email protected] Abstract The Darcy-Weisbach formulation of flow resistance has advantages over the Gauckler-Manning- Strickler form. It is more fundamental, and research results for it should be able to be used in practice. A formula for the dimensionless resistance coefficient was presented by Yen (1991, equa- tion 30), which bridges between the limits of smooth flow and fully rough flow, to give a general formula for calculating resistance as a function of relative roughness and Reynolds number, appli- cable for a channel Reynolds number R>30 000 and relative roughness ε<0.05. In this paper, the author shows how a closely similar formula was obtained which is in terms of natural loga- rithms, which are simpler if further operations such as differentiation have to be performed. The formulae are shown to agree with predictions from the Gauckler-Manning-Strickler form, and with a modified form for open channels, have advantages that the equations are simpler and terms are more physically-obvious, as well as using dimensionless coefficients with a greater connectedness to other fluid mechanics studies. 1. Introduction The ASCE Task Force on Friction Factors in Open Channels (1963) expressed its belief in the general utility of using the Darcy-Weisbach formulation for resistance to flow in open channels, noting that it was more fundamental, and was based on more fundamental research. The
  • PDF, Bottom Friction Models for Shallow Water Equations: Manning's

    PDF, Bottom Friction Models for Shallow Water Equations: Manning's

    Journal of Physics: Conference Series PAPER • OPEN ACCESS Related content - Model reduction of unstable systems using Bottom friction models for shallow water balanced truncation method and its application to shallow water equations Kiki Mustaqim, Didik Khusnul Arif, Erna equations: Manning’s roughness coefficient and Apriliani et al. small-scale bottom heterogeneity - An averaging method for the weakly unstable shallow water equations in a flat inclined channel To cite this article: Tatyana Dyakonova and Alexander Khoperskov 2018 J. Phys.: Conf. Ser. 973 Richard Spindler 012032 - Computational multicore on two-layer 1D shallow water equations for erodible dambreak C A Simanjuntak, B A R H Bagustara and P H Gunawan View the article online for updates and enhancements. Recent citations - Numerical hydrodynamic model of the Lower Volga A Yu Klikunova and A V Khoperskov - Flow resistance in a variable cross section channel within the numerical model of shallow water T Dyakonova and A Khoperskov This content was downloaded from IP address 170.106.35.234 on 23/09/2021 at 14:15 AMSCM IOP Publishing IOP Conf. Series: Journal of Physics: Conf. Series1234567890 973 (2018) ‘’“” 012032 doi :10.1088/1742-6596/973/1/012032 Bottom friction models for shallow water equations: Manning's roughness coefficient and small-scale bottom heterogeneity Tatyana Dyakonova, Alexander Khoperskov Volgograd State University, Department of Information Systems and Computer Simulation, Volgograd, 400062, Russia E-mail: [email protected] Abstract. The correct description of the surface water dynamics in the model of shallow water requires accounting for friction. To simulate a channel flow in the Chezy model the constant Manning roughness coefficient is frequently used.
  • The Water' Cycle

    The Water' Cycle

    'I ." Name'~~_~__-,,__....,......,....,......, ~ Class --,-_......,...._------,__ Date ....,......,-.:-_ ..: .•..'-' .. M.ODERN EARTH SCIENCE Section 1s.i The Water' Cycle • Read each statement below. If the statement .ls true, write T in the space provided. If the statement is false, write Fin tbe space provided. -'- 1. The hydrologic cycle is also called the water cycle. 2. Most water evaporating from the earth's surface evaporates from rivers and lakes. 3. When water vapor rises in the atmosphere, it expands and cools. 4. Evapotranspiration increases with increasing temperature. 5. Most water used by industry is recycled. 6. Irrigation is often necessary in areas having high evapotranspiration. Cboose the one best response. Write tbe letter of tbat cboice in tbe space provided. 7. Which of the following is an artificial means of producing fresh water from ocean water? .--i a. desalination b. saltation • c. evapotranspiration d. condensation 8. Which of the following is represented by this diagram? a. the earth's water budget b. local water budget . c. groundwater movement -·d. surface runoff 9. The arrow labeled X represents: a. absorption. b. evaporation.. c. rejuvenation. d. transpiration. _ 10. Approximately what percentage of the earth's precipitation falls-on the ocean? a. 5% b. 25% c. 750/0 d. 99% t • Chapter 13 47 l H_R_w_..._"_ter"_:_al_....._p_yrighted undernotice appearing earlier in thisworic. .'. Name _ Class _ Date -­ MODERN EARTH SCIENCE .... '''; ... .secti~n'· if2 River Systems Choose the one best response. Write the letter of that choice in the space provided. 1. What is the term for the main stream and tributaries of a river? a.