DOCSLIB.ORG

Cavitation in Hydraulic Structures

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
Cavitation in Hydraulic Structures CAVITATION IN HYDRAULIC STRUCTURES: Occurrence and Prevention by R W P May Repo~tNo SR 79 March 1987 Registered Office: Hydraulics Research Limited, Wallingford, Oxfordshire 0x10 8BA. Telephone: 0491 35381. Telex: 848552 This report describes work funded by the Department of the Environment under Research Contract PECD 7/6/46. It is published on behalf of the Department of the Environment, but any opinions expressed in this report are not necessarily those of the funding Department. The work was carried out by Mr R W P May in Mr J A Perkin's section of the River Engineering Department of Hydraulics Research, Wallingford, headed by Dr W R White. The nominated project officers were Dr R P Thorogood for DOE and Dr W R White for HR. @ Crown copyright 1987 Published by permission of the Controller of Her Majesty's Stationery Office A review is made of literature on cavitation in large hydraulic structures in order to summarise the present state of knowledge, provide guidance to designers, and idencify areas requiring further research. The topics covered include: (1) mechanisms of cavity focaation and collapse; (2) cavitation at surface irregularities, gate slots, and energy dissipators; (3) cavitation resistance of engineering materials; (4) self-aeration and use of aerators for preventing cavitation damage; (5) modelling of cavitation and aeration; (6) research needs. The first part of the report provides summaries of the available information on each topic. The second part consists of a series of Appendices which describe in more detail the information contained in over 200 references. Page INTRODUCTION 1 MECHANISM OF CAVITATION 2.1 Description 2.2 Cavitation pafameters OCCURRENCE IN HYDRAULIC STRUCTURES CAVITATION AT SURFACE IRREGULARITIES TUNNELS AND GATES ENERGY DISSIPATORS MATERIALS AERATION 8.1 Self-aeration 8.2 Aerators on spillways 8.3 Tunnels MODELLING CONCLUSION ACKNOWLEDGEMENTS TABLES : 1. Properties of pure water 2. Values of Ki for surface irregularities 3. Data on prototype aerators FIGURES : Types of surface irregularity Cavfcation damage curve Values of Kid for surface irregularities Values of Ki for surface irregularities Types of gate slot Cavitation parameters of gate slots Types of baffle block Types of aerator Types of air supply system comparison of predicted air demands in tunnels CONTENTS (CONT'D) Page APPENDICES : A. List of Symbols B. Cavitation at Surface Irregularities B.l General 8.2 Theoretical studies 8.3 Laboratory studies R.4 Field studies C. Tunnels and Gates C.l Tunnel inlets C.2 Prototype data on gates C.3 Design of gates D. Energy Dissipators E. Cavitation Resistance of Materials E.l Concrete E.2 Metals E.3 Epoxy and polyester resins E.4 Plastics and other materials F. Air Entrainment F.l Effect on cavitation F.2 Self-aeration F.3 Aeracors on spillways F.4 Aerators in tunnels G. Modelling and Instrumentation G .l Cavitation G.2 Aeration G.3 Instrumentation for aerated flows H. Future Research 1 INTRODUCTION The purpose of this literature review is firstly to describe the present state of knowledge about the occurrence and prevention of cavitation in large hydraulic structures, and secondly to identify areas where further research is needed. The study has been carried out as part of a research programme funded by the Construction Industry Directorate of the Department of the Environment. Since the survey is concerned with cavitation produced by the flow of water in high-head structures, it does not cover other specialist areas such as pumps and ship propellers. Despite this restriction, there exists a very large amount of information spread across several disciplines, and therefore it is posstble that some significant references may have been inadvertently omitted. Many useful studies have been carried out in the USSR and P R China, and for descriptions of these it has been necessary to rely mainly on papers presented at international conferences or on English-language summaries. It is intended that the review should be of use to engineers as well as researchers, and it therefore covers a fairly broad field. Sections 2 and 3 of the report give a general description of the nature of cavitation and of the factors which govern its occurrence. Sections 4 to 9 briefly summarise the available information on individual topics, and are linked to Appendices B to G which give more detailed descriptions of the relevant information in the references. The first group of topics deals with the main sources of cavitation in hydraulic structures: surEace irregularities in channels (Section 4 and Appendix B); tunnel inlets and high-head gates (Section 5 and Appendix C); and energy dissipators (Section 6 and Appendix D). The cavitation resistances of engineering materials, such as concrete, steel, resins and plastics, are considered in Section 7 and Appendix E. Since the presence of air in water has the beneficial effect of reducing or preventing cavitation damage, Section 8 and Appendix F describe information on self-aeration and the design of aerators for spillways and tunnels. Most studies on cavitation and aeration have been carried out in the laboratory, so the problems of scale effects in modelling are dealt with in Section 9 and Appendix G. Finally, topics requiring further research are identified in Appendix H. Within the Appendices, references on a particular subject have normally been presented in chronological sequence; also Figures are numbered in the order in which they are referred to in the Appendices. Comparing results and drawing conclusions from different, and sometimes conflicting, studies can be difticult because there are usually variations in the experimental conditions, the techniques of measurement, or the methods of analysis. The summaries in Sections 4 to 9 therefore concentrate on general areas of agreement, and for more detailed information readers should refer to the Appendices and the original references. 2 MRCBANISM OF CAVITATION 2.1 Description This brief description of the cavitation phenomenon is based on information contained in a comprehensive textbook by Knapp et a1 (1970) and in surveys produced by Eisenberg (1961), Johnson (1963). Kenn (1968) and Knapp (1952). A suicable definition for the type of cavitation which will be considered in this report was given by Knapp (1952) as "the formation and collapse of cavities in a stream of flowing liquid which results from pressure changes within the stream caused by changes in the velocity of flow". This excludes cavitation associated with the vibration of bodies in stationary fluids. Throughout this report it will be assumed that the liquid in question is water and that the gas is either air or water vapour. The negative pressure required to form a cavity within pure water is extremely high and can be of the order of several hundred atmospheres. The fact that normal samples of water form cavities at much smaller pressures indicates that the cavities grow from pre-existing nuclei containing either water vapour or water vapour and air. The sizes of these nuclei need to be in the range 0.1 to lop, and two theories have been proposed to explain their existence and persistence. The first is that the nuclei are stabilized within the interstices of microscopic dust particles; the second is that an organic film forms around a nucleus and thereby maintains the internal pressure and prevents diffusion of air. When the ambient pressure in the liquid falls close to the vapour pressure, the nuclei grow rapidly and become visible as a cloud of tiny cavitation bubbles. The inception pressure which triggers this growth is usually slightly lower than the vapour pressure, hut depends upon the initial size of the nuclei and upon the ratio of air pressure to vapour pressure within them. The ultimate size of the cavities is determined by the time that they are subject co pressures lower than the inception pressure. The main types of cavitation encountered in civil engineering situations are: 1. "travelling cavitation" in which cavities form in areas of low pressure, travel with the flow and collapse in regions of higher pressure; 2. "fixed cavitation" in which flow separates from a body and forms a quasi-steady cavity attached to the boundary; when the cavity extends beyond the generating body it is referred to as "super-cavitation"; 3. "vortex cavitation" in which cavities form in the cores of fast-rotating eddies created in regions of high shear. When the ambient pressure in the fluid exceeds the vapour pressure, cavities collapse very rapidly and generate extremely high pressures in their immediate vicinity; pressures of up to 15,000 atmospheres (1500MPa approx) were measured by Lesleighter (1983). Sound is also generated when cavities collapse and provides a method of determining the onset of cavitation. In some situations collapsing cavities are observed to rebound and go through several cycles of expansion and contraction. However, when the air content in the cavity is low, the bubble collapses without rebounding. Solid surfaces are damaged by pitting when cavities collapse close up against them. Measurements of rates of pitting indicate that only a very small proportion of the available cavities are large enough and collapse close enough to a boundary to cause damage. During most of their life travelling cavities appear to remain spherical, but experimental evidence suggests that they may distort when collapsing close to boundaries. In these circumstances the wall of the cavity remote from the boundary may fold inwards to form a needle-like jet of fluid. The micro-jet passes through the cavity and emerges at very high velocity into the fluid adjacent to the boundary. Damage to solid surfaces may be caused by the impact of micro-jets and also by shock waves generated during the rapid collapse of cavities. However, experimental work by Tomita h Shima (1986) indicated that there is a third and more damaging mechanism, that of ultra-jets.
Load more

Recommended publications
  • DETERMINING the LOCATION of HYDRAULIC JUMP by MODEL TEST and HEC-2 FLOW ROUTING/ a Thesis Presented to the Faculty of the Fritz
    L-DETERMINING THE LOCATION OF HYDRAULIC JUMP BY MODEL TEST AND HEC-2 FLOW ROUTING/ A Thesis Presented to The Faculty of the Fritz J. and Dolores H. Russ College of Engineering and Technology Ohio University In Partial Fulment of the Requirement for the Degree Master of Science by Chen-Feng Li, 4 August, 1995 ACKNOWLEDGEMENTS The author gratefdly acknowledges the hanicial support fiom my family, advisor Dr. Chang (Civil Engineering Dept., Ohio University) and Feng Chia University (Taiwan). The author would like to thank the Civil Engineering Department for the help they provided by supplying the various equipment used for my studies. The author also wants to thank those who have helped in my thesis writing. TABLE OF CONTENTS TABLE OF CONTENTS ................................iv LIST OF TABLES ...................................vii LIST OF FIGURES .................................. viii LIST OF SYMBOLS ..................................xii I. INTRODUCTION .................................. 1 I. 1 Background of Study .......................... 1 1.2 Purpose of Study ............................ 2 1.3 Buckingham PI Theorem and Dynamic Simulation ........... 2 1.4 Experiments and Requirements ..................... 3 I .5 The FUTURE Development of the Study ................ 4 I1 . SELECTED LITERATURE REVIEW ..................... 6 11 . 1 Theoretical Development of Hydraulic Jump .............. 6 II.2 Studies of Hydraulic Jump ....................... 6 LI.3 Channel Slope and Hydraulic Jump ................... 8 v 11.4 Length and Location of Hydraulic Jump .................11 II.5 Force and Hydraulic Jump ........................14 II.6 Hydraulic Structures and Hydraulic Jump ................16 II.6.1 Hydraulic Jump in A Stilling Basin ...............17 II.6.2 Sluice Gate and Hydraulic Jump ................17 11.6.3 Sill and Hydraulic Jump ....................19 11.7 Computer Simulation ofHydraulic Jump Surface Profiles ........24 m .
    [Show full text]
  • Characteristics of Undular Hydraulic Jump Downstream of a Sluice Gate
    CHARACTERISTICS OF UNDULAR HYDRAULIC JUMP DOWNSTREAM OF A SLUICE GATE KARAKTERISTIK LONCATAN HIDROLIK UNDULAR DI HILIR PINTU AIR Komang Arya Utama 1), Bambang Yulistiyanto 2), and Budi S. Wignyosukarto 2) 1) Lecturer in Civil Engineering Department, Faculty of Engineering, Gorontalo State University 2) Lecturer in Civil and Environmental Engineering Department, Faculty of Engineering, Gadjah Mada University ABSTRACT Undular hydraulic jump is a hydraulic jump with a low Froude number which is marked by the emergence of a fixed roller. Information about the characteristics of undular hydraulic jump is still very poor. In order for the interests of the development of science, it is necessary to in-depth study of the hydraulic characteristics and phenomenon that appear on the undular hy- draulic jump. This research is applying the 2D physical model that used a tilting flume. Sluice gate is used as a tool to gene- rate the undular hydraulic jump. Measurement of distance and depth using a point gauge while the flow velocity was measu- red using a Nixon Streamflo 422 Currentmeter. Circulation flow is driven by using water pumps with discharge 15 l/s and 30 l/s. The results of this study indicate that the maximum flow velocity of dimensionless velocity distribution are at 0.5 - 0.9. Lowest value of Froude number obtained in running model Q9A1 is Fr1 = 1.197 and its highest value obtained in running mo- del Q3A1 is Fr1 limit = 2.258. The wave steepness is mild with a slope range are 0.1 to 0.3 or 10% to 30%. The length and height of the wave form are reduce at the first, second, third and so on until the condition of conjugate depth (y3).
    [Show full text]
  • Analysis of Turbulent Hydraulic Jump Over a Transitional Rough Bed of a Rectangular Channel: Universal Relations Noor Afzal Aligarh Muslim University, India
    University of Nebraska - Lincoln DigitalCommons@University of Nebraska - Lincoln Civil Engineering Faculty Publications Civil Engineering 2011 Analysis of Turbulent Hydraulic Jump over a Transitional Rough Bed of a Rectangular Channel: Universal Relations Noor Afzal Aligarh Muslim University, India A. Bushra University of Nebraska-Lincoln Abu Seena Korea Advanced Institute of Science and Technology, Daejeon, Korea Follow this and additional works at: http://digitalcommons.unl.edu/civilengfacpub Part of the Hydraulic Engineering Commons Afzal, Noor; Bushra, A.; and Seena, Abu, "Analysis of Turbulent Hydraulic Jump over a Transitional Rough Bed of a Rectangular Channel: Universal Relations" (2011). Civil Engineering Faculty Publications. 54. http://digitalcommons.unl.edu/civilengfacpub/54 This Article is brought to you for free and open access by the Civil Engineering at DigitalCommons@University of Nebraska - Lincoln. It has been accepted for inclusion in Civil Engineering Faculty Publications by an authorized administrator of DigitalCommons@University of Nebraska - Lincoln. Published in Journal of Engineering Mechanics 137:12 (2011), pp. 835-845; doi: 10.1061/(ASCE)EM .1943-7889.0000294 Copyright © 2011 American Society of Civil Engineers. Used by permission. Submitted August 9, 2010; approved June 27, 2011; published online June 29, 2011. digitalcommons.unl.edu Analysis of Turbulent Hydraulic Jump over a Transitional Rough Bed of a Rectangular Channel: Universal Relations Noor Afzal,1 A. Bushra,2 and Abu Seena3 1. Visiting Professor, Department of Mechanical Engineering, Korea Advanced Institute of Science and Technology, Daejeon, Korea, and Faculty of Engineering, Aligarh Muslim University, Aligarh, India 2. Department of Civil Engineering, University of Nebraska 3. Department of Mechanical Engineering, Korea Advanced Institute of Science and Technology, Daejeon, Korea.
    [Show full text]
  • Undular Jump, Numerical Model and Sensitivity
    Alma Mater Studiorum - Università di Bologna FACOLTÀ DI SCIENZE MATEMATICHE, FISICHE E NATURALI Corso di Laurea specialistica in Fisica Dipartimento di Fisica UNDULAR JUMP NUMERICAL MODEL AND SENSITIVITY ANALYSIS Tesi di laurea di: Relatore: MICHELE RAMAZZA Prof. RAMBALDI SANDRO Correlatori: Prof. MANSERVISI SANDRO Dott. CERVONE ANTONIO Sessione III Anno Accademico 2007-2008 2 CONTENTS Abstract................................................................................................................................................5 Sommario.............................................................................................................................................5 List of symbol ....................................................................................................................................6 1.Introduction ....................................................................................................................................8 1.1.Open channel flow.................................................................................................................8 1.1.1.Introduction....................................................................................................................8 1.1.2.Classification of open channel flows.........................................................................8 1.1.3.Complexity ....................................................................................................................8 1.2.Bases of open channel hydraulics ...................................................................................10
    [Show full text]
  • Shallow-Water Theory and Channel Flow with Hydraulic Jump: Non-Steady Consideration
    www.ccsenet.org/mas Modern Applied Science Vol. 6, No. 1; January 2012 Shallow-Water Theory and Channel Flow with Hydraulic Jump: Non-Steady Consideration Asuquo E Eyo Department of Mathematics and Statistics, University of Uyo, Uyo, Nigeria E-mail: [email protected] Received: August 15, 2011 Accepted: November 17, 2011 Published: January 1, 2012 doi:10.5539/mas.v6n1p50 URL: http://dx.doi.org/10.5539/mas.v6n1p50 Abstract We examine the classical hydraulic jump in an open channel flow and show that it can be qualitatively understood using the model, namely, equations of shallow-water type. In the analysis, we consider the following cases: (i) unsteady, one dimensional flow of a liquid in an open channel, (ii) uniform and smooth flow with the channel bed flat and viscosity neglected almost everywhere, and (iii) a steady uniform flow U from left (positive flux) with the flow elsewhere taken to be two dimensional. Based on this model the relation for the speed of propagation of the jump in terms of depth ratio is obtained. We employ the method of characteristics and the Riemann invariants to determine the precise location and time of the onset of the hydraulic ump. Our analysis reveals that the location xJ and time tJ of the jump formation are influenced by the initial acceleration of the fluid. Specializations are later made to the cases where the initial acceleration is positive and finite, negative, infinite. Results are obtained in each of these cases. Keywords: Equations of shallow-water type, Channel flow, Hydraulic jump, Method of characteristics, Remann inivariants 1.
    [Show full text]
  • Flow and Sediment Transport at Hydraulic Jumps
    FLOW AND SEDIMENT TRANSPORT AT HYDRAULIC JUMPS BY ROBERT GORDON MACDONALD A thesis submitted to the School of Environmental Sciences at the University of East Anglia for the degree of Doctor of Philosophy © This copy of the thesis has been supplied on condition that anyone who consults it is understood to recognise that its copyright rests with the author and that no quotation from the thesis, nor any information derived therefrom, may be published without the author's prior, written consent. i Acknowledgements Thank you to Jan Alexander, Mark Cooker and John Bacon for all their help supervising this research. Jan has paid particular attention to provide me academic opportunities and I am grateful for the experience I have gained under her supervision. Mark has influenced me to present difficult discussions calmly and his quiet humour is an inspiration. John remained enthusiastic even after moving into a commercial job. Various people helped the physical undertaking of the research. Trevor Panter and Gareth Flowerdew made most of the equipment mounts for the UEA research flume, and provided engineering advice for my less than usual requests. Trevor also made the conveyor that I used to put sediment into the flume. Brendan, Emily, Estelle, James, John Brindle, Judith, Rob, Sheila and Stuart helped with the experiments. James had the dubious pleasure of being my best man and John Brindle the dubious pleasure of being my passenger the first time I drove a van, and of “reading the map”. I am grateful to Jan Alexander and Sheila Davies who took some of the laboratory photographs.
    [Show full text]
  • Erosion of Rock and Soil Best Practices in Dam and Levee Safety Risk Analysis Section D – Embankments and Foundations Chapter D-1
    Erosion of Rock and Soil Best Practices in Dam and Levee Safety Risk Analysis Section D – Embankments and Foundations Chapter D-1 Last modified July 2018, presented July 2019 Outline • Objectives • Key Concepts • Erosion Process • Rock Erosion Considerations • Soil Erosion • Takeaway Points Objectives • Understand the input to methods and models for estimating erosion, and how it is obtained • Be able to use this information as part of estimating the probability of erosion leading to failure under various potential failure modes • (Estimating the probability of failure due to rock or soil erosion is covered in other chapters) Key Concepts • Many potential failure modes require erosion of rock or soil to result in dam breach, such as: • Overtopping erosion of an embankment • Overtopping erosion of a concrete dam abutment or foundation • Erosion of an unlined spillway or river channel • Erosion of an unlined plunge pool (leading structural undermining) • Erosion of the spillway foundation where floor slabs have been damaged or lost • Initiation of erosion does not equate to failure • Judgement must be made concerning the progression of erosion over time (rate of erosion, duration of loading, progressive failure, etc.) • It is important to consider erosion extent as well as the erosion potential 4 Erosion Process How Erosion Starts • Erosion can occur under high velocity flows which cause high soil/rock detachment/plucking rates • A discontinuity exists which allows flow to concentrate, or changes the flow regime from sheet to turbulent • Possible sources of discontinuities are: • Slope changes in downstream slope (flat slope changes to steep slope) • Obstacles such as trees, vegetation, guard rails, etc.
    [Show full text]
  • Overtopping of Walls and Stilling Basin Failure
    Overtopping of Walls and Stilling Basin Failure Best Practices in Dam and Levee Safety Risk Analysis Part F – Hydraulic Structures Chapter F-2 Last modified June 2017, presented July 2019 Objectives • Understand the factors and mechanisms that affect spillway chute wall overtopping failure • Understand how to construct an event tree to represent spillway chute wall overtopping failure • Understand how to consider stilling basin sweepout and failure Dam and Levee Overtopping of Walls and Stilling Basin Failure Modes • Failure of dams and levees due to overtopping is a common failure mode • 30% of dam failures in U.S. are attributed to overtopping • Many spillways are under designed for large discharges and could be vulnerable to chute capacity issues. • Many older dams and levees may have been designed for floods that no longer represent a remote flood event and design flood estimates have increased Case History: Failure of El Guapo Dam, Venezuela • El Guapo Dam spillway failed December 16, 1999 as a result of spillway failure from chute wall overtopping • Hydrology to size spillway based on hydrologic data transferred from another drainage basin (site specific hydrology is best) • During spillway construction chute walls were overtopped during a flood which triggered a new flood study (added a tunnel spillway) • El Guapo Dam never overtopped • Overtopping of chute walls initiated erosion of backfill behind chute walls and undermining and failure of spillway chute • Headcutting progressed upstream and led to reservoir breach • Spillway
    [Show full text]
  • Hazard Classification and Hydraulic Remediation Options for Flat- Topped and Ogee-Crested Low-Head Dams
    View metadata, citation and similar papers at core.ac.uk brought to you by CORE provided by DigitalCommons@USU Utah State University DigitalCommons@USU All Graduate Theses and Dissertations Graduate Studies 5-2013 Hazard Classification and Hydraulic Remediation Options for Flat- Topped and Ogee-Crested Low-Head Dams Riley J. Olsen Utah State University Follow this and additional works at: https://digitalcommons.usu.edu/etd Part of the Civil Engineering Commons Recommended Citation Olsen, Riley J., "Hazard Classification and Hydraulic Remediation Options for Flat-Topped and Ogee- Crested Low-Head Dams" (2013). All Graduate Theses and Dissertations. 1538. https://digitalcommons.usu.edu/etd/1538 This Thesis is brought to you for free and open access by the Graduate Studies at DigitalCommons@USU. It has been accepted for inclusion in All Graduate Theses and Dissertations by an authorized administrator of DigitalCommons@USU. For more information, please contact [email protected]. i HAZARD CLASSIFICATION AND HYDRAULIC REMEDIATION OPTIONS FOR FLAT-TOPPED AND OGEE-CRESTED LOW-HEAD DAMS by Riley J. Olsen A thesis submitted in partial fulfillment of the requirements for the degree of MASTER OF SCIENCE in Civil and Environmental Engineering Approved: ________________________________ ________________________________ Michael C. Johnson Steven L. Barfuss Major Professor Committee Member ________________________________ ________________________________ Joseph A. Caliendo Mark R. McLellan Committee Member Vice President for Research and Dean of the School of Graduate Studies UTAH STATE UNIVERSITY Logan, Utah 2013 ii Copyright © Utah State University 2013 All Rights Reserved iii ABSTRACT Hazard Classification and Hydraulic Remediation Options for Flat-Topped and Ogee-Crested Low-Head Dams by Riley J.
    [Show full text]
  • Section 2F-2 - Open Channel Flow
    2F-2 Design Manual Chapter 2 - Stormwater 2F - Open Channel Flow Open Channel Flow A. Introduction The beginning of any channel design or modification is to understand the hydraulics of the stream. The procedures for performing uniform flow calculations aid in the selection or evaluation of appropriate depths and grades for natural or man-made channels. Allowable velocities are provided, along with procedures for evaluating channel capacity using Manning’s equation. All the methods described herein will be based on the conservation of mass, momentum and energy (in the form of Bernoulli’s theorem), and the Manning formula for frictional resistance. Steady uniform flow and steady non-uniform flow are the types of flow addressed in this section. B. Definitions Critical Flow: The variation of specific energy with depth at a constant discharge shows a minimum in the specific energy at a depth called critical depth at which the Froude number has a value of one. Critical depth is also the depth of maximum discharge, when the specific energy is held constant. Froude Number: The Froude number is an important dimensionless parameter in open-channel flow. It represents the ratio of inertia forces to gravity forces. This expression for Froude number applies to any single-section channel of nonrectangular shape. Hydraulic Jump: Hydraulic jumps occur at abrupt transitions from supercritical to subcritical flow in the flow direction. There are significant changes in the depth and velocity in the jump, and energy is dissipated. For this reason, the hydraulic jump is often employed to dissipate energy and control erosion at stormwater management structures.
    [Show full text]
  • Hydraulic Research in the United States 1959
    Hydraulic Research in the United States 1959 United States Department of Commerce National Bureau of Standards Miscellaneous Publication 227 THE NATIONAL BUREAU OF STANDARDS Functions and Activities The functions of the National Bureau of Standards are set forth in the Act of Congress, March 3, 1901, as amended by Congress in Public Law 619, 1950. These include the development and maintenance of the national standards of measurement and the provision of means and methods for making measurements consistent with these standards; the determination of physical constants and properties of materials; the development of methods and instruments for testing materials, devices, and structures; advisory services to government agencies on scientific and technical problems; in- vention and development of devices to serve special needs of the Government; and the development of standard practices, codes, and specifications. The work includes basic and applied research, development, engineering, instrumentation, testing, evaluation, calibration services, and various consultation and information services. Research projects are also performed for other government agencies when the work relates to and supplements the basic program of the Bureau or when the Bureau's unique competence is required. The scope of activities is suggested by the listing of divisions and sections on the inside of the back cover. Publications The results of the Bureau's work take the form of either actual equipment and devices or pub- lished papers. These papers appear either in
    [Show full text]
  • Beyond Shallow Water: Appraisal of a Numerical Approach to Hydraulic Jumps Based Upon the Boundary Layer Theory
    Beyond Shallow Water: appraisal of a numerical approach to hydraulic jumps based upon the Boundary Layer Theory. Francesco De Vitaa,∗, Pierre-Yves Lagr´eeb, Sergio Chibbarob, St´ephanePopinetb aLinn´eFLOW Centre and SeRC (Swedish e-Science Research Centre), KTH Mechanics, S-100 44 Stockholm, Sweden bSorbonne Universit´e,CNRS, Institut Jean le Rond d'Alembert, 75005 Paris France Abstract We study the flow of a thin layer of fluid over a flat surface. Commonly, the 1-D Shallow-water or Saint- Venant set of equations are used to compute the solution of such flows. These simplified equations may be obtained through the integration of the Navier-Stokes equations over the depth of the fluid, but their solution requires the introduction of constitutive relations based on strict hypothesis on the flow r´egime. Here, we present an approach based on a kind of boundary layer system with hydrostatic pressure. This relaxes the need for closure relations which are instead obtained as solutions of the computation. It is then demonstrated that the corresponding closures are very dependent on the type of flow considered, for example laminar viscous slumps or hydraulic jumps. This has important practical consequences as far as the applicability of standard closures is concerned. Keywords: Shallow Water, Saint-Venant, boundary layer flows. 1. Introduction The "shallow water equations" or "Saint-Venant Equations", from the author of the first proposition [1], are a classical model useful for a large variety of practical configurations in coastal and hydraulic engineering. For example, they are used to predict flows in rivers, in open channels, in lakes, in shallow seas.
    [Show full text]