DOCSLIB.ORG

CFD Analysis of Flow Through Integral Orifice Plate Assemblies Under Diverse Working Conditions

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
CFD Analysis of Flow Through Integral Orifice Plate Assemblies Under Diverse Working Conditions International Research Journal of Engineering and Technology (IRJET) e-ISSN: 2395-0056 Volume: 06 Issue: 06 | June 2019 www.irjet.net p-ISSN: 2395-0072 CFD Analysis of Flow through Integral Orifice Plate Assemblies under Diverse Working Conditions MANU B V1, Prof. YOGESH KUMAR2 K J and Dr. V. SESHADRI3 1M.Tech student, Department of Mechanical Engineering, Maharaja Institute of Technology, Mysore. 2Assistant Professor, Department of Mechanical Engineering, Maharaja Institute of Technology, Mysore. 3Professor (Emeritus), Department of Mechanical Engineering, Maharaja Institute of Technology, Mysore. ---------------------------------------------------------------------***--------------------------------------------------------------------- Abstract – The performance of characteristics of various for geometry and flow characteristics of integral orifice types of integral orifice plates for diverse working conditions meters but there is not much research work done or are analyzed using commercially available CFD software, information available on this type of orifice meters. ANSYS FLUENT. Several manufacturers like Yokogawa, Honeywell and others In this present work, ANSYS FLUENT software is used for the manufacture the integral orifice meters assemblies and they analysis of both compressible and incompressible flow have conducted the experiments on these particular orifice through the various types of integral orifice plates namely, meters and given the data for geometry and flow square edge, conical entrance and quarter circle integral characteristic for certain range of diameters and Reynolds orifice plate assemblies. numbers. But there is no computational validation for experimental results and there is no further information on The flow through the standard orifice plate is analyzed flow characteristics if orifice meters operate outside the according to BS 1042 and computational results are specified range of Reynolds number and diameters. validated with standard results. Hence this research work is an attempt to simulate the flow The experimental results given by MARCELO FILARDI et through the integral orifice meter which operates outside al[5] and by Yokogawa electronic corporation[10] are the specified conditions, that is under diverse conditions. validated by using ANSYS FLUENT and same computational methodology is used to study the variation of co-efficient of The computational fluid dynamics (CFD) ANALYSIS FLUENT discharge (Cd) and permanent pressure loss co-efficient (CL) is used as a tool for modeling and analysis of integral orifice with Reynolds number, diameter ratio and effect of absence meters. Initially the simulation is carried out according BS of upstream and downstream pipelines. 1042 and ISO 5167 standards and results are validated with the standards. Further the analysis is carried out for The compressible flow through standard orifice plate is nonstandard conditions of Reynolds numbers and diameter validated with CFD and same methodology is used to predict ratio for both compressible and incompressible flows for the variation of expansibility factor with Reynolds number integral orifices and studying the effects of these parameters for the various types of integral orifice plate assemblies. on coefficient of discharge, permanent pressure loss coefficient and expansibility coefficient. Key Words: Co-efficient of discharge (Cd), Permanent pressure loss (CL), CFD, ANSYS FLUENT, Integral orifice 1.1 OPERATING PRINCIPLE OF ORIFICE METER plates, Reynolds number, Expansibility factor, Diameter ratio. With an orifice plate installed in a flow stream, increases in a fluid flow velocity through the reduced area of the orifice, 1. INTRODUCTION develop a differential pressure across the orifice. The differential pressure generated is related to the diameter Orifice meter is an obstruction type of flow meter, which is ratio of the orifice plate. The smaller beta ratio causes the widely used for flow measurement in most of the industries higher the differential pressure to be generated. In practice like food, chemical, water supply Industries etc. BS 1042 and the choice of beta ratio is a compromise between the ISO 5167 standards provide the coefficient of discharge for differential pressure desired and the flow rate required. certain range of diameter ratios and Reynolds numbers. But in case of specialized industrial applications the orifice meter With the orifice plate in the pipe work, the static pressure operates at diverse conditions, that are outside the standard upstream the plate increases slightly due to back pressure diameter and Reynolds number ranges. effect and then decreases sharply as the flow passes through the orifice. Flow downstream the orifice reaches minimum at The integral orifice meters are special type of obstruction a point called the Vena contracta where the velocity of the type flow meters, which are used for small diameters and flow is at a maximum. Beyond Vena contracta, static low flows. BS 1042 standard also provides the specifications pressure start to recover but it never gets to the upstream © 2019, IRJET | Impact Factor value: 7.211 | ISO 9001:2008 Certified Journal | Page 1699 International Research Journal of Engineering and Technology (IRJET) e-ISSN: 2395-0056 Volume: 06 Issue: 06 | June 2019 www.irjet.net p-ISSN: 2395-0072 value. In other words, with an orifice meter installation, QActual = Cd QTheoritical =Cd there is always a permanent pressure loss. In addition to pressure loss, some of the pressure energy is converted into sound and heat at an orifice plate. for compressible flows. When a fluid (whether liquid or gas) passes through the Cd is defined as the ratio of the actual flow to the ideal flows orifice, its pressure builds up slightly upstream of the and is always less than one. orifice but as the fluid is forced to converge to pass through the hole, the velocity increases and the fluid pressure When the orifice meter is operating at elevated decreases. A little downstream of the orifice the flow reaches temperatures, an area correction factor Fα needs to be its point of maximum convergence, the vena-contracta, included to account for the change in the area of the orifice where the velocity reaches its maximum and the pressure hole due to thermal expansion. reaches its minimum. Beyond that, the flow expands, the velocity falls and the pressure increases. By measuring the When the fluid is compressible an additional factor ε the difference in fluid pressure across tappings upstream and expansibility coefficient needs to be introduced which takes downstream of the plate, the flow rate can be obtained from account of the difference between the discharge co-efficient Bernoulli's equation for compressible and incompressible flows. It is given by, Fig1. represents the flow of fluid through orifice meter and ε = let us consider section 1-1 at the upstream of the pipe and section 2-2 at the downstream where the pressure are to be Where noted . Let P1, V1 and A1 are the pressure, velocity and the cross-sectional area of the pipeline at section 1-1 Cdc is discharge co-efficient for compressible flow. Cdi is discharge co-efficient for incompressible flow. respectively and P2, V2 and A2 are the pressure, velocity and the cross sectional area of the pipe line, at section 2-2 respectively. Calculation of Cd can be done using the formula specified in ISO-5167. The discharge coefficient is given by the Reader- The expression for theoretical flow rate is given by, Harries/Gallagher equation given by, 2 8 6 Cd = 0.5961 + 0.0261β – 0.216β + 0.000521[10 β/ReD] + 3.5 5 -10L QTheoretical = = [0.0188 + 0.0063A]β [10 /ReD] + [0.043 + 0.080 e 1 – -7L 1.1 1.3 0.123e 1][1 – 0.11A][ – 0.031[M2 – 0.08M2 ]β If D <71.12mm (2.8 inch), the following term should be added to the equation. + 0.011[0.075 –β][ 2.8 - ] Where D is the diameter of pipe in mm Diameter ratio, β = d/D ReD = Pipe Reynolds number 0.8 A = [19000β/ReD] Fig1: FLOW THROUGH THE ORIFICE METER M2 = Constant = 2L2 / (1-β) 1.2 DISCHARGE COEFFICIENT OF ORIFICE PLATE L1 and L2 are distance from upstream and downstream The flow expression obtained in the above equation is not depending on the type of pressure tappings used. accurate in the actual case and some correction factor, such as discharge coefficient (Cd) has to be incorporated. Thus the The above equation has its own limitations. The equation is equation becomes, completely empirical and is derived on the basis of extensive experimental data. It is only applicable when pipe diameter QActual = Cd QTheoritical =Cd is within 50mm<D<1000mm when diameter ratio is within 0.1<β<0.75, plate thickness between 0.005D and 0.002D, bevel angle of 45°±15°.The upstream edge of the orifice hole for incompressible flows. © 2019, IRJET | Impact Factor value: 7.211 | ISO 9001:2008 Certified Journal | Page 1700 International Research Journal of Engineering and Technology (IRJET) e-ISSN: 2395-0056 Volume: 06 Issue: 06 | June 2019 www.irjet.net p-ISSN: 2395-0072 should be sharp and a radius of curvature not greater than loss caused by the orifice meter may be determined by the 0.0004d. Further the pipe surface should be smooth. pressure measurements made with the same pipe line before and after the insertion of the orifice meter as well as the The geometry and dimensions should be as per ISO 5167 pressure differential indicated by the flow meter. standards for the equation to be applicable. For any other non-standard cases lying outside of the mentioned range, the If ΔP` is the difference in pressure, measured prior to the Reader-Harries/Gallagher Equation is invalid. installation of the orifice plate between two pressure tappings one of which is situated far upstream of the flanges Discharge coefficient depends on Reynolds number and where the orifice will be inserted and the other which is far 4 diameter ratio, β. But it has been observed that for Re>10 , downstream of the same flanges and if ΔP`` is the difference the flow is totally turbulent and Discharge coefficient is fairly in the pressure measured between the same pressure independent for Reynolds number.
Load more

Recommended publications
  • Understanding Binomial Sequential Testing Table of Contents of Two START Sheets
    Selected Topics in Assurance Related Technologies START Volume 12, Number 2 Understanding Binomial Sequential Testing Table of Contents of two START sheets. In this first START Sheet, we start by exploring double sampling plans. From there, we proceed to • Introduction higher dimension sampling plans, namely sequential tests. • Double Sampling (Two Stage) Testing Procedures We illustrate their discussion via numerical and practical examples of sequential tests for attributes (pass/fail) data that • The Sequential Probability Ratio Test (SPRT) follow the Binomial distribution. Such plans can be used for • The Average Sample Number (ASN) Quality Control as well as for Life Testing problems. We • Conclusions conclude with a discussion of the ASN or “expected sample • For More Information number,” a performance measure widely used to assess such multi-stage sampling plans. In the second START Sheet, we • About the Author will discuss sequential testing plans for continuous data (vari- • Other START Sheets Available ables), following the same scheme used herein. Introduction Double Sampling (Two Stage) Testing Determining the sample size “n” required in testing and con- Procedures fidence interval (CI) derivation is of importance for practi- tioners, as evidenced by the many related queries that we In hypothesis testing, we often define a Null (H0) that receive at the RAC in this area. Therefore, we have expresses the desired value for the parameter under test (e.g., addressed this topic in a number of START sheets. For exam- acceptable quality). Then, we define the Alternative (H1) as ple, we discussed the problem of calculating the sample size the unacceptable value for such parameter.
    [Show full text]
  • Reading Inventory Technical Guide
    Technical Guide Using a Valid and Reliable Assessment of College and Career Readiness Across Grades K–12 Technical Guide Excepting those parts intended for classroom use, no part of this publication may be reproduced in whole or in part, or stored in a retrieval system, or transmitted in any form or by any means, electronic, mechanical, photocopying, recording, or otherwise, without written permission of the publisher. For information regarding permission, write to Scholastic Inc., 557 Broadway, New York, NY 10012. Scholastic Inc. grants teachers who have purchased SRI College & Career permission to reproduce from this book those pages intended for use in their classrooms. Notice of copyright must appear on all copies of copyrighted materials. Portions previously published in: Scholastic Reading Inventory Target Success With the Lexile Framework for Reading, copyright © 2005, 2003, 1999; Scholastic Reading Inventory Using the Lexile Framework, Technical Manual Forms A and B, copyright © 1999; Scholastic Reading Inventory Technical Guide, copyright © 2007, 2001, 1999; Lexiles: A System for Measuring Reader Ability and Text Difficulty, A Guide for Educators, copyright © 2008; iRead Screener Technical Guide by Richard K. Wagner, copyright © 2014; Scholastic Inc. Copyright © 2014, 2008, 2007, 1999 by Scholastic Inc. All rights reserved. Published by Scholastic Inc. ISBN-13: 978-0-545-79638-5 ISBN-10: 0-545-79638-5 SCHOLASTIC, READ 180, SCHOLASTIC READING COUNTS!, and associated logos are trademarks and/or registered trademarks of Scholastic Inc. LEXILE and LEXILE FRAMEWORK are registered trademarks of MetaMetrics, Inc. Other company names, brand names, and product names are the property and/or trademarks of their respective owners.
    [Show full text]
  • Reconciling Situation Calculus and Fluent Calculus
    Reconciling Situation Calculus and Fluent Calculus Stephan Schiffel and Michael Thielscher Department of Computer Science Dresden University of Technology stephan.schiffel,mit @inf.tu-dresden.de { } Abstract between domain descriptions in both calculi. Another ben- efit of a formal relation between the SC and the FC is the The Situation Calculus and the Fluent Calculus are successful possibility to compare extensions made separately for the action formalisms that share many concepts. But until now two calculi, such as concurrency. Furthermore it might even there is no formal relation between the two calculi that would allow to formally analyze the relationship between the two allow to translate current or future extensions made only for approaches as well as between the programming languages one of the calculi to the other. based on them, Golog and FLUX. Furthermore, such a formal Golog is a programming language for intelligent agents relation would allow to combine Golog and FLUX and to ana- that combines elements from classical programming (condi- lyze which of the underlying computation principles is better tionals, loops, etc.) with reasoning about actions. Primitive suited for different classes of programs. We develop a for- statements in Golog programs are actions to be performed mal translation between domain axiomatizations of the Situ- by the agent. Conditional statements in Golog are composed ation Calculus and the Fluent Calculus and present a Fluent of fluents. The execution of a Golog program requires to Calculus semantics for Golog programs. For domains with reason about the effects of the actions the agent performs, deterministic actions our approach allows an automatic trans- lation of Golog domain descriptions and execution of Golog in order to determine the values of fluents when evaluating programs with FLUX.
    [Show full text]
  • The Features-And-Fluents Semantics for the Fluent Calculus
    The Features-and-Fluents Semantics for the Fluent Calculus Michael Thielscher and Thomas Witkowski Department of Computer Science Dresden University of Technology, Germany Abstract fluent calculus, is expressive enough to be applicable to the full test suite of example reasoning problems in (Sandewall Based on an elaborate ontological taxonomy, the Features- 1994), let alone to be provably sound and complete wrt. one and-Fluents framework provides an independent action se- of the more expressive ontological classes in the taxonomy. mantics for assessing the range of applicability of action cal- culi. In this paper, we show how the fluent calculus can In this paper, we present a version of the fluent calculus be used to capture the full range of phenomena in K-IA, that is sufficiently expressive to capture K-IA, which is the the broadest ontological class that has been fully formalized broadest class that has been rigorously formalized and in- in (Sandewall 1994). To this end, we develop a significant tensively studied in (Sandewall 1994) and in which correct extension of the fluent calculus for modeling actions with du- knowledge and a fully inertial world is assumed. To this rations and with specific trajectories of changes. We present a end, we develop a significant extension of the basic fluent provably correct translation of scenario descriptions from the calculus by introducing an explicit model for the duration Features-and-Fluents semantics into fluent calculus axioma- of actions and for trajectories of changes. On this basis, we tizations. present a translation function that maps any K-IA scenario into a fluent calculus axiomatization, and we prove that the Introduction intended models of the former coincide with the classical models of the latter.
    [Show full text]
  • Fluent Tips & Tricks
    FluentFluent TipsTips && TricksTricks UGMUGM 20042004 Sutikno Wirogo Samir Rida 1/ 75 Outline List of Tips and Tricks collected from: Solution database available through the Online Technical Support (OTS) portal http://www.fluentusers.com Frequently Asked Questions Know-how of Fluent’s technical staff This presentation provides Tips and Tricks: For IO and Batch For Case Set-up and Mesh For Solving For Post-Processing For Reporting 2/ 75 This presentation provides Tips and Tricks: For IO and Batch For Case Set-up and Mesh For Solving For Post-Processing For Reporting 3/ 75 Miscellaneous on Parallel IO In parallel, the mesh is first read into the host and then distributed to the compute nodes If reading case into parallel solver takes unusually long time, do the following: • Merge as many zones as possible • Put the host and compute-node-0 on the same machine • Put the case and data files on a disk on the machine running the host and compute-node-0 processes Parallel Fluent will allocate buffers for exchanging messages while reading and building the grid • Default buffer size depends of the case that is being read For 4 million cell case on 4 CPUs, the buffer size will be 4M/4 = 1M • To query buffer size, use the following scheme command: (%query-parallel-io-buffers) • If the host machine does not have enough memory, using a large buffer will slow down the read case stage and thus can limit the maximum buffer size using: (%limit-parallel-io-buffer-size 0) ¾ Needs to be executed before reading the case file ¾ Will increase
    [Show full text]
  • Fluent Getting Started Guide
    ANSYS Fluent Getting Started Guide ANSYS, Inc. Release 19.1 Southpointe April 2018 2600 ANSYS Drive Canonsburg, PA 15317 ANSYS, Inc. and [email protected] ANSYS Europe, Ltd. are UL http://www.ansys.com registered ISO (T) 724-746-3304 9001: 2008 (F) 724-514-9494 companies. Copyright and Trademark Information © 2018 ANSYS, Inc. Unauthorized use, distribution or duplication is prohibited. ANSYS, ANSYS Workbench, AUTODYN, CFX, FLUENT and any and all ANSYS, Inc. brand, product, service and feature names, logos and slogans are registered trademarks or trademarks of ANSYS, Inc. or its subsidiaries located in the United States or other countries. ICEM CFD is a trademark used by ANSYS, Inc. under license. CFX is a trademark of Sony Corporation in Japan. All other brand, product, service and feature names or trademarks are the property of their respective owners. FLEXlm and FLEXnet are trademarks of Flexera Software LLC. Disclaimer Notice THIS ANSYS SOFTWARE PRODUCT AND PROGRAM DOCUMENTATION INCLUDE TRADE SECRETS AND ARE CONFID- ENTIAL AND PROPRIETARY PRODUCTS OF ANSYS, INC., ITS SUBSIDIARIES, OR LICENSORS. The software products and documentation are furnished by ANSYS, Inc., its subsidiaries, or affiliates under a software license agreement that contains provisions concerning non-disclosure, copying, length and nature of use, compliance with exporting laws, warranties, disclaimers, limitations of liability, and remedies, and other provisions. The software products and documentation may be used, disclosed, transferred, or copied only in accordance with the terms and conditions of that software license agreement. ANSYS, Inc. and ANSYS Europe, Ltd. are UL registered ISO 9001: 2008 companies. U.S. Government Rights For U.S.
    [Show full text]
  • The Calculus of Newton and Leibniz CURRENT READING: Katz §16 (Pp
    Worksheet 13 TITLE The Calculus of Newton and Leibniz CURRENT READING: Katz §16 (pp. 543-575) Boyer & Merzbach (pp 358-372, 382-389) SUMMARY We will consider the life and work of the co-inventors of the Calculus: Isaac Newton and Gottfried Leibniz. NEXT: Who Invented Calculus? Newton v. Leibniz: Math’s Most Famous Prioritätsstreit Isaac Newton (1642-1727) was born on Christmas Day, 1642 some 100 miles north of London in the town of Woolsthorpe. In 1661 he started to attend Trinity College, Cambridge and assisted Isaac Barrow in the editing of the latter’s Geometrical Lectures. For parts of 1665 and 1666, the college was closed due to The Plague and Newton went home and studied by himself, leading to what some observers have called “the most productive period of mathematical discover ever reported” (Boyer, A History of Mathematics, 430). During this period Newton made four monumental discoveries 1. the binomial theorem 2. the calculus 3. the law of gravitation 4. the nature of colors Newton is widely regarded as the most influential scientist of all-time even ahead of Albert Einstein, who demonstrated the flaws in Newtonian mechanics two centuries later. Newton’s epic work Philosophiæ Naturalis Principia Mathematica (Mathematical Principles of Natural Philosophy) more often known as the Principia was first published in 1687 and revolutionalized science itself. Infinite Series One of the key tools Newton used for many of his mathematical discoveries were power series. He was able to show that he could expand the expression (a bx) n for any n He was able to check his intuition that this result must be true by showing that the power series for (1+x)-1 could be used to compute a power series for log(1+x) which he then used to calculate the logarithms of several numbers close to 1 to over 50 decimal paces.
    [Show full text]
  • A Streaming Implementation of the Event Calculus
    TECHNICAL UNIVERSITY OF CRETE MASTER THESIS A Streaming Implementation of the Event Calculus Author: Supervisor: Alexandros MAVROMMATIS Prof. Minos GAROFALAKIS THESIS COMMITTEE Prof. Minos GAROFALAKIS (Technical University of Crete) Assoc. Prof. Michail G. LAGOUDAKIS (Technical University of Crete) Dr. Alexander ARTIKIS (University of Piraeus, N.C.S.R. Demokritos) Technical University of Crete School of Electronic & Computer Engineering in collaboration with the National Centre for Scientific Research “Demokritos” Institute of Informatics and Telecommunications April 2016 Abstract Events provide the fundamental abstraction for representing time-evolving information that may affect situations under certain circumstances. The research domain of Complex Event Recognition focuses on tracking and analysing streams of events, in order to detect event patterns of special significance. The event streams may originate from various sources, such as sensors, video tracking systems, computer networks, etc. Furthermore, the event stream velocity and volume pose significant challenges to event processing systems. We propose dRTEC, an event recognition system that employs the Event Cal- culus formalism and operates in multiple computer cores for scalable distributed event recognition. We evaluate dRTEC experimentally using two real world applications and we show that it is capable of real-time and efficient event recognition. PerÐlhyh Ta gegoνόta parèqoun thn jemeli¸dh afaÐresh gia thn αναπαράσtash miac qroνικά exe- liσσόμενης plhroforÐac, h opoÐa mporeÐ na επηρεάσει katastάσειc κάτw από orismènec συνθήκες. To pedÐo èreunac thc Anagn¸rishc Σύνθετwn Gegoνόtwn epikentr¸netai sthn parakoλούθηση kai ανάλυση ro¸n από gegoνόta, me stόqo ton entopiσμό proτύπων από gegoνόta idiaÐterhc shmasÐac. Oi roèc από gegoνόta μπορούν na proèrqontai από διάφορες phgèc, όπως aiσθητήρες, susτήματa parakoλούθησης me bÐnteo, dÐktua upologist¸n k.lp.
    [Show full text]
  • Introduction to the Fluent Calculus
    Linkoping Electronic Articles in Computer and Information Science Vol nr Intro duction To The Fluent Calculus Michael Thielscher Department of Computer Science Dresden UniversityofTechnology Dresden Germany Linkoping University Electronic Press Linkoping Sweden httpwwwepliuseeacis Revised version Revised version publishedonFebruary by Linkoping University Electronic Press Linkoping Sweden Original version was published on October Linkoping Electronic Articles in Computer and Information Science ISSN Series editor Erik Sandewal l c Michael Thielscher A Typeset by the author using L T X E Formattedusingetendu style Recommended citation Author Title Linkoping Electronic Articles in Computer and Information Science Vol nr http wwwepliuseeacisOctober The URL wil l also contain links to both the original version and the present revised version as wel l as to the authors home page The publishers wil l keep this article online on the Internet or its possible replacement network in the future for a periodofyears from the date of publication barring exceptionalcircumstances as describedseparately The online availability of the article implies apermanent permission for anyone to read the article online to print out single copies of it and to use it unchanged for any nonc ommercial research and educational purpose including making copies for classroom use This permission can not berevoked by subsequent transfers of copyright Al l other uses of the article are conditional on the consent of the copyright owner The publication of
    [Show full text]
  • Comparison of American and Chinese College Students by Means of The
    Eastern Illinois University The Keep Masters Theses Student Theses & Publications 1973 Comparison of American and Chinese College Students by Means of the Holtzman Inkblot Technique Te Jung Chang Eastern Illinois University This research is a product of the graduate program in Psychology at Eastern Illinois University. Find out more about the program. Recommended Citation Chang, Te Jung, "Comparison of American and Chinese College Students by Means of the Holtzman Inkblot Technique" (1973). Masters Theses. 3809. https://thekeep.eiu.edu/theses/3809 This is brought to you for free and open access by the Student Theses & Publications at The Keep. It has been accepted for inclusion in Masters Theses by an authorized administrator of The Keep. For more information, please contact [email protected]. PAPER CERTIFICATE #2 TO: Graduate Degree Candidates who have written formal theses. SUBJECT: Permission to reproduce theses. The University Library is receiving a number of requests from other institutions asking permission to reproduce dissertations for inclusion in their library holdings. Although no copyright laws are involved, we feel that professional courtesy demands that permission be obtained from the author before we allow theses to be copied. Please sign one of the following statements: Booth Library of Eastern Illinois University has my permission to lend my thesis to a reputable college or university for the purpose of copying it for inclusion in that institution's library or research holdings. Date Author I respectfully request Booth Library
    [Show full text]
  • Introduction to the Fluent Calculus
    Linkoping Electronic Articles in Computer and Information Science Vol nr Intro duction To The Fluent Calculus Michael Thielscher Department of Computer Science Dresden UniversityofTechnology Dresden Germany Linkoping University Electronic Press Linkoping Sweden httpwwwepliuseeacis Revised version Revised version publishedonFebruary by Linkoping University Electronic Press Linkoping Sweden Original version was published on October Linkoping Electronic Articles in Computer and Information Science ISSN Series editor Erik Sandewal l c Michael Thielscher A Typeset by the author using L T X E Formattedusingetendu style Recommended citation Author Title Linkoping Electronic Articles in Computer and Information Science Vol nr http wwwepliuseeacisOctober The URL wil l also contain links to both the original version and the present revised version as wel l as to the authors home page The publishers wil l keep this article online on the Internet or its possible replacement network in the future for a periodofyears from the date of publication barring exceptionalcircumstances as describedseparately The online availability of the article implies apermanent permission for anyone to read the article online to print out single copies of it and to use it unchanged for any nonc ommercial research and educational purpose including making copies for classroom use This permission can not berevoked by subsequent transfers of copyright Al l other uses of the article are conditional on the consent of the copyright owner The publication of
    [Show full text]
  • Review of the July 2011 Draft of the Texas Mathematics Standards
    Review of the July 2011 Draft of the Texas Mathematics Standards Wilfried Schmid Professor of Mathematics, Harvard University In some ways, the current draft improves upon the “Commissioner’s Draft”, on which it is based. Many – but not all – cases of imprecise or mathematically questionable language have been dealt with. However, serious problems remain. In the elementary grades, the draft consistently underemphasizes computational facility. On the other hand, the major results of the high school and late middle school curriculum are generally presented only as results to be applied by students, but not meant to be understood. As the National Mathematics Panel has pointed out, conceptual understanding and computational practice develop in tandem. To ask for under- standing in the early grades without addressing computation is just as wrong as asking students to merely apply, but not truly understand the binomial theorem and other major theorems in high school. Even when the language of the draft is sufficiently precise, it often reads awkwardly. I would advise the authors to have the entire document examined by an individual who is not only mathematically competent, but also has stylistic flair. Several “model frameworks” exist that could be used as linguistic models. Computational facility in the elementary grades At each grade level, the standards are preceded by a statement of the relevant “Focal Points”, with wording that is often borrowed from the NCTM Focal Points. The authors would do well to actually follow the suggestions of the latter! Automatic recall of number facts serves as the foundation for computational facility. The draft standard 2N10, fluently apply basic fact strategies to add and subtract with sums to 20 and differences from 20, and its multiplication counterpart 3N20 send the wrong message.
    [Show full text]