THE DANIEL SENIORSONIC MULTIPATH GAS FLOWMETER THE DANIEL SENIORSONIC METER AND FLOWCONDITIONERS
|
|
- Dora Lang
- 5 years ago
- Views:
Transcription
1 Danel SenorSonc The Use of Flow Condtoners Page 1 THE DANIEL SENIORSONIC MULTIPATH GAS FLOWMETER THE DANIEL SENIORSONIC METER AND FLOWCONDITIONERS
2 Danel SenorSonc The Use of Flow Condtoners Page 2 1. Introducton It s becomng ncreasngly common to use flow condtoners wth ultrasonc meters for a majorty of ther applcatons. However, the overall effect on the meter s not been clearly known. Certan brands of flow condtoners may mprove the SenorSonc meter s nstalled performance. However, often they are not needed, and some can actually cause the overall performance to be less than f no condtoner were used. Most users have assumed that usng a flow condtoner mproves meter performance. Ths document dscusses the advantages and dsadvantages of usng flow condtoners wth the Danel SenorSonc meter, and what effect they may have on the calbraton results. The use of flow condtoners n natural gas meterng has been accepted for many years. Ther prmary use n the past has been wth orfce and turbne meters as both are known to be senstve to swrl. The most common flow condtoner n servce s the 19-tube bundle. Ths desgn conssts of 19 small tubes, usually the same dameter, welded together and arranged n a pattern that fts nsde the ppe. The devce s located upstream of the meterng element at a dstance varyng from 5 to 11 dameters, dependng upon the prmary element and user preference. A sgnfcant amount of work has been done n recent years to mprove on the tradtonal 19-tube bundle desgn. These new hgh performance condtoners take the tradtonal flow condtoner to a new level. They attempt to solate the meter from a second upstream ppng effect typcally known as non-symmetrcal velocty profle (also knows as an asymmetrcal profle). Brands of hgh performance condtoners nclude Gallagher, Nova, Vortab and Zanker. Research n recent years has shown the effects of a non-symmetrcal velocty profle on orfce meters to be sgnfcant. A non-symmetrcal profle s one where unequal veloctes exst n the ppe at the same dstance from the ppe wall. These nonsymmetrcal velocty profles are generated by varous ppng confguratons ncludng headers, elbows, tees, flters, valves and other devces. The dfgure shown above shows two dfferent symmetrcal velocty profles n a ppelne. A flow profle wth non-symmetry would have a non-unform shape.
3 Danel SenorSonc The Use of Flow Condtoners Page 3 The Danel SenorSonc ultrasonc flowmeter was desgned to be nstalled wthout flow condtoners. A sgnfcant amount of research durng the past 15 years has proven the desgn works well wth no flow condtoner. However, many users stll prefer to use flow condtoners as nsurance that the flow profle (hence the meter s accuracy), at the tme of calbraton, wll reman the same once the meter s nstalled. The belef that the flow condtoner totally solates the upstream effects from the meter s not always true. Durng the past few years GRI has funded extensve testng on ultrasonc meters at the Southwest Research Insttute n San Antono. The prmary purpose s to determne how well an ultrasonc meter performs n typcal ppng confguratons, both wth and wthout the varous flow condtoners currently avalable. A.G.A. 9 requres a manufacturer to mantan meterng accuracy wthn ±0.3% from calbraton to nstallaton wth typcal ppng desgns. As orfce meters typcally can be effected by much more than 0.3%, t was assumed by the customer that an ultrasonc meter would also be mpacted sgnfcantly. Followng s a bref summary of test data recently released to the GRI commttee members. It shows the effect on accuracy wth no flow condtoner, wth varous brands of flow condtoners,and wth dfferent upstream ppng confguratons. The numbers reflect the weghted error dfference from the test condton relatve to the orgnal calbraton (typcally wth 100D of straght ppe and the same flow condtoner nstalled). In other words, each result from the varous upstream tests s compared to a baselne test wth the same flow condtoner nstalled n the same locaton (relatve to the meter), but wth 100D upstream n leu of the nstallaton effect. 12 ANSI 600 SENIORSONIC Installaton Effect Sngle Elbow Elbows Out Elbows In Meter Orentaton 0deg 90deg 0deg 90deg 0deg 90deg Bare at 10D Bare at 20D Tube Vortab CPA 50E GFC PASSES AGA 9 REQUIREMENT FAILS AGA9 REQUIREMENT Numbers that are n the green background are results that meet or exceed A.G.A. 9 accuracy requrements (less than 0.3% nstallaton effect). Two meter orentatons were tested (meter mounted normal, then rotated 90 degrees) to smulate the dfferent nstallatons that mght be encountered n the feld. Important to notce s the result of No Condtoner, 20D. The results clearly show the SenorSonc meter easly meets the nstallaton effects requrements of A.G.A. 9 n all tests. In fact, the Danel SenorSonc was the only meter tested that meets the A.G.A. 9 nstallaton accuracy requrement wthout flow condtonng.
4 Danel SenorSonc The Use of Flow Condtoners Page 4 The reference paper by GRI s attached to ths document for nformaton. Addtonally, only one flow condtoner even comes close to the same results. Ths summary s the frst real commercal result showng the SenorSonc meets or exceeds A.G.A. 9 nstalled performance requrements wth no flow condtoner. Interestngly, no other USM manufacturer s devce passed ths AGA9 requrement. Flow condtoners often have another effect on an ultrasonc meter. In the process of changng the velocty profle, they often create a flow profle that can bas the meter and cause t to regster dfferent. Ths dfference can be seen when comparng calbraton results of a meter wth and wthout the flow condtoner. In other words, f a meter needed to be adjusted by 0.2% relatve to the calbraton faclty, the amount of adjustment may be on the order of 0.5% wth the flow condtoner nstalled. The ntent of a flow condtoner s to return a swrlng, non-symmetrcal flow profle to a condton many consder equal to 100D of straght ppe (symmetrcal wth no swrl). Ths equvalent length of straght ppe s thought to (and data has been obtaned to verfy t) elmnate any upstream flow dsturbances and create a very consstent, reproducble profle. However, often these hgh performance flow condtoners generate a profle that s somewhat dfferent than the 100D baselne profle. The prmary purpose of a meter calbraton s to determne the amount of error from the reference (laboratory). Ths dfference can also be thought of as the meter s accuracy. However, other ssues should be consdered when revewng calbraton results. Besdes absolute accuracy, lnearty and repeatablty are mportant to the customer. Thus, not only s the amount of adjustment mportant, but the queston s often asked What mpact does the flow condtoner have on the meter s lnearty? Only a lmted amount of nformaton s avalable to answer the queston regardng lnearty and repeatablty wth all types of nstallaton condtons. However, the results from several calbratons at a varety of laboratores, all usng a sgnfcant numbers of straght ppe upstream, suggest there s no detrmental effect on the SenorSonc s lnearty and repeatablty. The only documented effect s to the meter s adjust factor. That s, f a flow condtoner s used, regardless of brand, the Meter Factor wll be dfferent than f t were calbrated wthout the flow condtoner, but the lnearty and repeatablty wll reman vrtually unchanged. At frst glance ths shft n Meter Factor doesn t appear to be a problem. Once the meter s calbrated, overall accuracy remans the same. However, some users nterpret a meter that s outsde the basc as found A.G.A 9 accuracy requrement of ±0.7% for 12-nch and larger, and ±1.0% for 10-nch and smaller, to not be n complance. Ths poses a problem for the manufacturer snce some flow condtoners can mpact some meter desgns by a sgnfcant amount. The desgn used n the SenorSonc has been shown to be somewhat nsenstve to most flow condtoner desgns. However, there s an effect wth all desgns of flow condtoners. Typcally a bas to the Meter Factor can be approxmately %, but ths depends upon meter sze and brand of flow condtoner. That s, the meter error wll be hgher (Meter Factor lower) than f t were calbrated wthout the condtoner.
5 Danel SenorSonc The Use of Flow Condtoners Page 5 2. Ax Symmetrc Changes To Flow Profle The Danel SenorSonc meter can tolerate ax-symmetrc changes n profle wth no mpact on meter accuracy. AGauss-Jacob numercal ntegraton gves the average flow velocty V avg over the area of the ppe from the weghted sum of the lne averages along the chords V where the weghtng factors, W, are determned for the specfc chord locatons. Note that t s sgnfcant that ntegraton of a unform velocty profle, usng ths method would gve the correct answer. Another nterpretaton of the weghtng factors W s the proporton of ppe area assocated wth each chord to obtan the flow, the sum of whch must be unty. For an ndvdual chord, 2 L t V ( r ) =. 2x t du ud t. t du ud The average gas velocty s calculated usng equ(1) V = 4 = 1 V ( r ) W equ(2) where the wghtng factors are Chord A = Chord B = Chord C = Chord D = Note that the sum of the factors equals unty. Fgure 1 shows the locatons for the four chords.
6 Danel SenorSonc The Use of Flow Condtoners Page 6 Fgure 1 Chord Locatons For SenorSonc Usng a power law, shown n equaton 3, dfferent flow profles can be generated as shown n Fgure 2. v V max y = R 1 n equ(3) These profles are calculated usng n = 7 and n = 12. Both of the profles represents an average velocty of unty. Usng the SenorSonc algorthm,.e. takng the pont velocty at each chord locaton and ntegratng usng the weghtng factors gven above, t s proven that the meter s completely mmune to ax-symmetrc changes n profle. Ths s demonstrated n the tabulated calculaton n Fgure 3.
7 Danel SenorSonc The Use of Flow Condtoners Page 7 Fgure 3 SenorSonc Immunty to Changes n Ax-Symmetrc Profle Another manufacturer uses a fve path confguraton where three of the velocty measurements are made through the centre secton of the flow usng a sngle bounce traverse. Ths type of measurement requres a correcton based upon Reynolds number. However, Reynolds number correctons rely on a fully developed flow profle and accurate knowledge of the ppe wall roughness. Wth these chord confguratons, f the flow s not full developed,.e. a flow condtoner s ntroduced, then the Reynolds number correcton wll be erroneous. In addton, f the ppewall roughness changes, then there s no way of knowng ths and agan the Reynolds number correcton wll be errouneous. Ths theoretcal approach hghlghts the fundamental advantage the Danel SenorSonc four path meter has over other meters such as a fve path cnetre lne measurng devce. The Danel meter samples the flow profle and does not make any assumptons about the nature of the profle. 4. Swrlng Flow Profle The followng s an explanaton on how the Danel SenorSonc copes wth swrlng gas flow. To ad the reader, a quck remnder on the chord arrangement and ntegraton technques for the SenorSonc s provded.
8 Danel SenorSonc The Use of Flow Condtoners Page 8 The meter s symmetrcal about the centre lne wth chords A and D postoned 0.809R from the centre lne and chords B and C beng postoned 0.309R from the centrelne. These locatons are fxed such that each meter sze s geometrcally smlar. For these locatons the chord weghtng factors are; W A = W B = W C = W D = Chords A and B are crss-crossed as are C and D The average gas velocty s calculated by ntegratng the product of measured velocty and weghtng factor for each chord..e. V = 4 = 1 V ( r ) W BULK SWIRL If there s a bulk swrl wth angular velocty, ω, around the ppe axs then at a radus, r, ths wll gve a velocty of ωr perpendcular to r. The component along the chord wll be ωr cosθ cos45 as shown n the fgure below,.e. the swrl component along
9 Danel SenorSonc The Use of Flow Condtoners Page 9 the chord s constant at ωz cos45. So on chords A and B we have swrl components S A and S B gven by S A S B = (0.707 ω).0.809r = (0.707 ω).0.309r Applyng the weghtng factors for the chords as per the ntegraton, we fnd that V SA V SB = (0.707 ω).0.809r = (0.707 ωr) = (0.707 ω).0.309r = (0.707 ωr) Thus the contrbuton of swrl on these two chords s equal, but s opposte drectons snce the chords are crossed. Ths means that ther contrbutons exactly cancel each other. Smlarly, the swrl components on the C and D chord exactly cancel each other. Ths feature s unque to the SenorSonc desgn where weghtng factors are nversely proportonal to the chord radal locaton from the centre.
10 Danel SenorSonc The Use of Flow Condtoners Page 10 Concluson The SenorSonc meter was desgned to be nstalled wth no flow condtoner. Some of today s hgh performance flow condtoners may mprove overall nstalled accuracy. However, not all flow condtoners mprove the SenorSonc s performance. Usng a flow condtoner, regardless of the brand, wll mpact the nstrument s Meter Factor. The bas typcally causes the meter to over-regster by %, but s somewhat dependent upon meter sze and brand of flow condtoner. The mpact of ths bas may cause the amount of adjustment to exceed A.G.A. 9 requrements. It s Danel s opnon that any mpact that causes the meter s adjustment (Meter Factor) to be outsde of A.G.A. Report No. 9 does not cause our meter to be n non-complance.
11. TRADITIONAL MEASUREMENT OF VOLUME FLOW RATE Volume flow rate deduced from velocity measurement data Application example
11. TRADITIONAL MEASUREMENT OF VOLUME FLOW RATE 11.1. Volume flow rate deduced from velocty measurement data 11.1.1. Applcaton example 11.1.. Prncple and layouts = ' ' A V da v q = A da v = A da v A A
More informationIndeterminate pin-jointed frames (trusses)
Indetermnate pn-jonted frames (trusses) Calculaton of member forces usng force method I. Statcal determnacy. The degree of freedom of any truss can be derved as: w= k d a =, where k s the number of all
More informationWeek3, Chapter 4. Position and Displacement. Motion in Two Dimensions. Instantaneous Velocity. Average Velocity
Week3, Chapter 4 Moton n Two Dmensons Lecture Quz A partcle confned to moton along the x axs moves wth constant acceleraton from x =.0 m to x = 8.0 m durng a 1-s tme nterval. The velocty of the partcle
More informationNUMERICAL DIFFERENTIATION
NUMERICAL DIFFERENTIATION 1 Introducton Dfferentaton s a method to compute the rate at whch a dependent output y changes wth respect to the change n the ndependent nput x. Ths rate of change s called the
More informationGravitational Acceleration: A case of constant acceleration (approx. 2 hr.) (6/7/11)
Gravtatonal Acceleraton: A case of constant acceleraton (approx. hr.) (6/7/11) Introducton The gravtatonal force s one of the fundamental forces of nature. Under the nfluence of ths force all objects havng
More informationPsychology 282 Lecture #24 Outline Regression Diagnostics: Outliers
Psychology 282 Lecture #24 Outlne Regresson Dagnostcs: Outlers In an earler lecture we studed the statstcal assumptons underlyng the regresson model, ncludng the followng ponts: Formal statement of assumptons.
More informationUncertainty in measurements of power and energy on power networks
Uncertanty n measurements of power and energy on power networks E. Manov, N. Kolev Department of Measurement and Instrumentaton, Techncal Unversty Sofa, bul. Klment Ohrdsk No8, bl., 000 Sofa, Bulgara Tel./fax:
More informationDUE: WEDS FEB 21ST 2018
HOMEWORK # 1: FINITE DIFFERENCES IN ONE DIMENSION DUE: WEDS FEB 21ST 2018 1. Theory Beam bendng s a classcal engneerng analyss. The tradtonal soluton technque makes smplfyng assumptons such as a constant
More informationKernel Methods and SVMs Extension
Kernel Methods and SVMs Extenson The purpose of ths document s to revew materal covered n Machne Learnng 1 Supervsed Learnng regardng support vector machnes (SVMs). Ths document also provdes a general
More informationExperience with Automatic Generation Control (AGC) Dynamic Simulation in PSS E
Semens Industry, Inc. Power Technology Issue 113 Experence wth Automatc Generaton Control (AGC) Dynamc Smulaton n PSS E Lu Wang, Ph.D. Staff Software Engneer lu_wang@semens.com Dngguo Chen, Ph.D. Staff
More informationCopyright 2017 by Taylor Enterprises, Inc., All Rights Reserved. Adjusted Control Limits for P Charts. Dr. Wayne A. Taylor
Taylor Enterprses, Inc. Control Lmts for P Charts Copyrght 2017 by Taylor Enterprses, Inc., All Rghts Reserved. Control Lmts for P Charts Dr. Wayne A. Taylor Abstract: P charts are used for count data
More informationχ x B E (c) Figure 2.1.1: (a) a material particle in a body, (b) a place in space, (c) a configuration of the body
Secton.. Moton.. The Materal Body and Moton hyscal materals n the real world are modeled usng an abstract mathematcal entty called a body. Ths body conssts of an nfnte number of materal partcles. Shown
More informationDepartment of Statistics University of Toronto STA305H1S / 1004 HS Design and Analysis of Experiments Term Test - Winter Solution
Department of Statstcs Unversty of Toronto STA35HS / HS Desgn and Analyss of Experments Term Test - Wnter - Soluton February, Last Name: Frst Name: Student Number: Instructons: Tme: hours. Ads: a non-programmable
More informationAPPLICATION OF EDDY CURRENT PRINCIPLES FOR MEASUREMENT OF TUBE CENTERLINE
APPLICATION OF EDDY CURRENT PRINCIPLES FOR MEASUREMENT OF TUBE CENTERLINE DEFLECTION E. J. Chern Martn Maretta Laboratores 1450 South Rollng Road Baltmore, MD 21227 INTRODUCTION Tubes are a vtal component
More informationChapter 13: Multiple Regression
Chapter 13: Multple Regresson 13.1 Developng the multple-regresson Model The general model can be descrbed as: It smplfes for two ndependent varables: The sample ft parameter b 0, b 1, and b are used to
More informationFREQUENCY DISTRIBUTIONS Page 1 of The idea of a frequency distribution for sets of observations will be introduced,
FREQUENCY DISTRIBUTIONS Page 1 of 6 I. Introducton 1. The dea of a frequency dstrbuton for sets of observatons wll be ntroduced, together wth some of the mechancs for constructng dstrbutons of data. Then
More informationThe optimal delay of the second test is therefore approximately 210 hours earlier than =2.
THE IEC 61508 FORMULAS 223 The optmal delay of the second test s therefore approxmately 210 hours earler than =2. 8.4 The IEC 61508 Formulas IEC 61508-6 provdes approxmaton formulas for the PF for smple
More informationPhysics 5153 Classical Mechanics. Principle of Virtual Work-1
P. Guterrez 1 Introducton Physcs 5153 Classcal Mechancs Prncple of Vrtual Work The frst varatonal prncple we encounter n mechancs s the prncple of vrtual work. It establshes the equlbrum condton of a mechancal
More informationHomework Assignment 3 Due in class, Thursday October 15
Homework Assgnment 3 Due n class, Thursday October 15 SDS 383C Statstcal Modelng I 1 Rdge regresson and Lasso 1. Get the Prostrate cancer data from http://statweb.stanford.edu/~tbs/elemstatlearn/ datasets/prostate.data.
More informationENGN 40 Dynamics and Vibrations Homework # 7 Due: Friday, April 15
NGN 40 ynamcs and Vbratons Homework # 7 ue: Frday, Aprl 15 1. Consder a concal hostng drum used n the mnng ndustry to host a mass up/down. A cable of dameter d has the mass connected at one end and s wound/unwound
More informationSINGLE EVENTS, TIME SERIES ANALYSIS, AND PLANETARY MOTION
SINGLE EVENTS, TIME SERIES ANALYSIS, AND PLANETARY MOTION John N. Harrs INTRODUCTION The advent of modern computng devces and ther applcaton to tme-seres analyses permts the nvestgaton of mathematcal and
More informationAnswers Problem Set 2 Chem 314A Williamsen Spring 2000
Answers Problem Set Chem 314A Wllamsen Sprng 000 1) Gve me the followng crtcal values from the statstcal tables. a) z-statstc,-sded test, 99.7% confdence lmt ±3 b) t-statstc (Case I), 1-sded test, 95%
More informationLAB # 4 - Torque. d (1)
LAB # 4 - Torque. Introducton Through the use of Newton's three laws of moton, t s possble (n prncple, f not n fact) to predct the moton of any set of partcles. That s, n order to descrbe the moton of
More informationSecond Order Analysis
Second Order Analyss In the prevous classes we looked at a method that determnes the load correspondng to a state of bfurcaton equlbrum of a perfect frame by egenvalye analyss The system was assumed to
More informationSupplementary Notes for Chapter 9 Mixture Thermodynamics
Supplementary Notes for Chapter 9 Mxture Thermodynamcs Key ponts Nne major topcs of Chapter 9 are revewed below: 1. Notaton and operatonal equatons for mxtures 2. PVTN EOSs for mxtures 3. General effects
More informationComparison of Regression Lines
STATGRAPHICS Rev. 9/13/2013 Comparson of Regresson Lnes Summary... 1 Data Input... 3 Analyss Summary... 4 Plot of Ftted Model... 6 Condtonal Sums of Squares... 6 Analyss Optons... 7 Forecasts... 8 Confdence
More informationEN40: Dynamics and Vibrations. Homework 7: Rigid Body Kinematics
N40: ynamcs and Vbratons Homewor 7: Rgd Body Knematcs School of ngneerng Brown Unversty 1. In the fgure below, bar AB rotates counterclocwse at 4 rad/s. What are the angular veloctes of bars BC and C?.
More informationGraph Reconstruction by Permutations
Graph Reconstructon by Permutatons Perre Ille and Wllam Kocay* Insttut de Mathémathques de Lumny CNRS UMR 6206 163 avenue de Lumny, Case 907 13288 Marselle Cedex 9, France e-mal: lle@ml.unv-mrs.fr Computer
More informationA PAPER CLOCK MODEL FOR THE CESIUM CLOCK ENSEMBLE OF TL
A PAPER CLOCK MODEL FOR THE CESIUM CLOCK ESEMBLE OF TL Shnn Yan Ln and Hsn Mn Peng atonal Standard Tme and Frequency Lab., TL, Chunghwa Telecom Co., Ltd. o. Lane 55, Mn-Tsu Rd. Sec. 5, YangMe, TaoYuan,
More informationCopyright 2017 by Taylor Enterprises, Inc., All Rights Reserved. Adjusted Control Limits for U Charts. Dr. Wayne A. Taylor
Taylor Enterprses, Inc. Adjusted Control Lmts for U Charts Copyrght 207 by Taylor Enterprses, Inc., All Rghts Reserved. Adjusted Control Lmts for U Charts Dr. Wayne A. Taylor Abstract: U charts are used
More informationChapter 3 Describing Data Using Numerical Measures
Chapter 3 Student Lecture Notes 3-1 Chapter 3 Descrbng Data Usng Numercal Measures Fall 2006 Fundamentals of Busness Statstcs 1 Chapter Goals To establsh the usefulness of summary measures of data. The
More informationChapter 5. Solution of System of Linear Equations. Module No. 6. Solution of Inconsistent and Ill Conditioned Systems
Numercal Analyss by Dr. Anta Pal Assstant Professor Department of Mathematcs Natonal Insttute of Technology Durgapur Durgapur-713209 emal: anta.bue@gmal.com 1 . Chapter 5 Soluton of System of Lnear Equatons
More information3.1 Expectation of Functions of Several Random Variables. )' be a k-dimensional discrete or continuous random vector, with joint PMF p (, E X E X1 E X
Statstcs 1: Probablty Theory II 37 3 EPECTATION OF SEVERAL RANDOM VARIABLES As n Probablty Theory I, the nterest n most stuatons les not on the actual dstrbuton of a random vector, but rather on a number
More informationLinear Feature Engineering 11
Lnear Feature Engneerng 11 2 Least-Squares 2.1 Smple least-squares Consder the followng dataset. We have a bunch of nputs x and correspondng outputs y. The partcular values n ths dataset are x y 0.23 0.19
More informationBOOTSTRAP METHOD FOR TESTING OF EQUALITY OF SEVERAL MEANS. M. Krishna Reddy, B. Naveen Kumar and Y. Ramu
BOOTSTRAP METHOD FOR TESTING OF EQUALITY OF SEVERAL MEANS M. Krshna Reddy, B. Naveen Kumar and Y. Ramu Department of Statstcs, Osmana Unversty, Hyderabad -500 007, Inda. nanbyrozu@gmal.com, ramu0@gmal.com
More informationRotational Dynamics. Physics 1425 Lecture 19. Michael Fowler, UVa
Rotatonal Dynamcs Physcs 1425 Lecture 19 Mchael Fowler, UVa Rotatonal Dynamcs Newton s Frst Law: a rotatng body wll contnue to rotate at constant angular velocty as long as there s no torque actng on t.
More informationWeek 9 Chapter 10 Section 1-5
Week 9 Chapter 10 Secton 1-5 Rotaton Rgd Object A rgd object s one that s nondeformable The relatve locatons of all partcles makng up the object reman constant All real objects are deformable to some extent,
More informationOutline. Communication. Bellman Ford Algorithm. Bellman Ford Example. Bellman Ford Shortest Path [1]
DYNAMIC SHORTEST PATH SEARCH AND SYNCHRONIZED TASK SWITCHING Jay Wagenpfel, Adran Trachte 2 Outlne Shortest Communcaton Path Searchng Bellmann Ford algorthm Algorthm for dynamc case Modfcatons to our algorthm
More information(Online First)A Lattice Boltzmann Scheme for Diffusion Equation in Spherical Coordinate
Internatonal Journal of Mathematcs and Systems Scence (018) Volume 1 do:10.494/jmss.v1.815 (Onlne Frst)A Lattce Boltzmann Scheme for Dffuson Equaton n Sphercal Coordnate Debabrata Datta 1 *, T K Pal 1
More informationCHAPTER 5 NUMERICAL EVALUATION OF DYNAMIC RESPONSE
CHAPTER 5 NUMERICAL EVALUATION OF DYNAMIC RESPONSE Analytcal soluton s usually not possble when exctaton vares arbtrarly wth tme or f the system s nonlnear. Such problems can be solved by numercal tmesteppng
More informationGlobal Sensitivity. Tuesday 20 th February, 2018
Global Senstvty Tuesday 2 th February, 28 ) Local Senstvty Most senstvty analyses [] are based on local estmates of senstvty, typcally by expandng the response n a Taylor seres about some specfc values
More informationPivot-Wheel Drive Crab with a Twist! Clem McKown Team November-2009 (eq 1 edited 29-March-2010)
Pvot-Wheel Drve Crab wth a Twst! Clem McKown Team 1640 13-November-2009 (eq 1 edted 29-March-2010) 4-Wheel Independent Pvot-Wheel Drve descrbes a 4wd drve-tran n whch each of the (4) wheels are ndependently
More informationERROR RESEARCH ON A HEPA FILTER MEDIA TESTING SYSTEM OF MPPS(MOST PENETRATION PARTICLE SIZE) EFFICIENCY
Proceedngs: Indoor Ar 2005 ERROR RESEARCH ON A HEPA FILTER MEDIA TESTING SYSTEM OF MPPS(MOST PENETRATION PARTICLE SIZE) EFFICIENCY S Lu, J Lu *, N Zhu School of Envronmental Scence and Technology, Tanjn
More informationAP Physics 1 & 2 Summer Assignment
AP Physcs 1 & 2 Summer Assgnment AP Physcs 1 requres an exceptonal profcency n algebra, trgonometry, and geometry. It was desgned by a select group of college professors and hgh school scence teachers
More informationONE-DIMENSIONAL COLLISIONS
Purpose Theory ONE-DIMENSIONAL COLLISIONS a. To very the law o conservaton o lnear momentum n one-dmensonal collsons. b. To study conservaton o energy and lnear momentum n both elastc and nelastc onedmensonal
More informationNegative Binomial Regression
STATGRAPHICS Rev. 9/16/2013 Negatve Bnomal Regresson Summary... 1 Data Input... 3 Statstcal Model... 3 Analyss Summary... 4 Analyss Optons... 7 Plot of Ftted Model... 8 Observed Versus Predcted... 10 Predctons...
More information2016 Wiley. Study Session 2: Ethical and Professional Standards Application
6 Wley Study Sesson : Ethcal and Professonal Standards Applcaton LESSON : CORRECTION ANALYSIS Readng 9: Correlaton and Regresson LOS 9a: Calculate and nterpret a sample covarance and a sample correlaton
More informationx = , so that calculated
Stat 4, secton Sngle Factor ANOVA notes by Tm Plachowsk n chapter 8 we conducted hypothess tests n whch we compared a sngle sample s mean or proporton to some hypotheszed value Chapter 9 expanded ths to
More informationErrors for Linear Systems
Errors for Lnear Systems When we solve a lnear system Ax b we often do not know A and b exactly, but have only approxmatons  and ˆb avalable. Then the best thng we can do s to solve ˆx ˆb exactly whch
More informationPerformance of Different Algorithms on Clustering Molecular Dynamics Trajectories
Performance of Dfferent Algorthms on Clusterng Molecular Dynamcs Trajectores Chenchen Song Abstract Dfferent types of clusterng algorthms are appled to clusterng molecular dynamcs trajectores to get nsght
More informationMA 323 Geometric Modelling Course Notes: Day 13 Bezier Curves & Bernstein Polynomials
MA 323 Geometrc Modellng Course Notes: Day 13 Bezer Curves & Bernsten Polynomals Davd L. Fnn Over the past few days, we have looked at de Casteljau s algorthm for generatng a polynomal curve, and we have
More informationPRESSURE AND TEMPERATURE EFFECTS FOR ORMEN LANGE ULTRASONIC GAS FLOW METERS
25 th Internatonal North Sea Flow Measurement Workshop, Gardermoen, Norway, 16-19 October 2007 PRESSURE AND TEMPERATURE EFFECTS FOR ORMEN LANGE ULTRASONIC GAS FLOW METERS Per Lunde 1,2, Kjell-Evnd Frøysa
More informationExperiment 1 Mass, volume and density
Experment 1 Mass, volume and densty Purpose 1. Famlarze wth basc measurement tools such as verner calper, mcrometer, and laboratory balance. 2. Learn how to use the concepts of sgnfcant fgures, expermental
More informationUncertainty as the Overlap of Alternate Conditional Distributions
Uncertanty as the Overlap of Alternate Condtonal Dstrbutons Olena Babak and Clayton V. Deutsch Centre for Computatonal Geostatstcs Department of Cvl & Envronmental Engneerng Unversty of Alberta An mportant
More informationOne-sided finite-difference approximations suitable for use with Richardson extrapolation
Journal of Computatonal Physcs 219 (2006) 13 20 Short note One-sded fnte-dfference approxmatons sutable for use wth Rchardson extrapolaton Kumar Rahul, S.N. Bhattacharyya * Department of Mechancal Engneerng,
More informationGrover s Algorithm + Quantum Zeno Effect + Vaidman
Grover s Algorthm + Quantum Zeno Effect + Vadman CS 294-2 Bomb 10/12/04 Fall 2004 Lecture 11 Grover s algorthm Recall that Grover s algorthm for searchng over a space of sze wors as follows: consder the
More informationMeasurement Uncertainties Reference
Measurement Uncertantes Reference Introducton We all ntutvely now that no epermental measurement can be perfect. It s possble to mae ths dea quanttatve. It can be stated ths way: the result of an ndvdual
More informationLecture 4. Macrostates and Microstates (Ch. 2 )
Lecture 4. Macrostates and Mcrostates (Ch. ) The past three lectures: we have learned about thermal energy, how t s stored at the mcroscopc level, and how t can be transferred from one system to another.
More informationUsing Spectrophotometric Methods to Determine an Equilibrium Constant Prelab
Usng Spectrophotometrc Methods to Determne an Equlbrum Constant Prelab 1. What s the purpose of ths experment? 2. Wll the absorbance of the ulbrum mxture (at 447 nm) ncrease or decrease as Fe soluton s
More informationA Robust Method for Calculating the Correlation Coefficient
A Robust Method for Calculatng the Correlaton Coeffcent E.B. Nven and C. V. Deutsch Relatonshps between prmary and secondary data are frequently quantfed usng the correlaton coeffcent; however, the tradtonal
More informationMathematical Preparations
1 Introducton Mathematcal Preparatons The theory of relatvty was developed to explan experments whch studed the propagaton of electromagnetc radaton n movng coordnate systems. Wthn expermental error the
More informationChapter 6. Supplemental Text Material
Chapter 6. Supplemental Text Materal S6-. actor Effect Estmates are Least Squares Estmates We have gven heurstc or ntutve explanatons of how the estmates of the factor effects are obtaned n the textboo.
More informationModule 11 Design of Joints for Special Loading. Version 2 ME, IIT Kharagpur
Module 11 Desgn o Jonts or Specal Loadng Verson ME, IIT Kharagpur Lesson 1 Desgn o Eccentrcally Loaded Bolted/Rveted Jonts Verson ME, IIT Kharagpur Instructonal Objectves: At the end o ths lesson, the
More informationImage Processing for Bubble Detection in Microfluidics
Image Processng for Bubble Detecton n Mcrofludcs Introducton Chen Fang Mechancal Engneerng Department Stanford Unverst Startng from recentl ears, mcrofludcs devces have been wdel used to buld the bomedcal
More informationModule 3 LOSSY IMAGE COMPRESSION SYSTEMS. Version 2 ECE IIT, Kharagpur
Module 3 LOSSY IMAGE COMPRESSION SYSTEMS Verson ECE IIT, Kharagpur Lesson 6 Theory of Quantzaton Verson ECE IIT, Kharagpur Instructonal Objectves At the end of ths lesson, the students should be able to:
More informationInductance Calculation for Conductors of Arbitrary Shape
CRYO/02/028 Aprl 5, 2002 Inductance Calculaton for Conductors of Arbtrary Shape L. Bottura Dstrbuton: Internal Summary In ths note we descrbe a method for the numercal calculaton of nductances among conductors
More informationNice plotting of proteins II
Nce plottng of protens II Fnal remark regardng effcency: It s possble to wrte the Newton representaton n a way that can be computed effcently, usng smlar bracketng that we made for the frst representaton
More informationLectures - Week 4 Matrix norms, Conditioning, Vector Spaces, Linear Independence, Spanning sets and Basis, Null space and Range of a Matrix
Lectures - Week 4 Matrx norms, Condtonng, Vector Spaces, Lnear Independence, Spannng sets and Bass, Null space and Range of a Matrx Matrx Norms Now we turn to assocatng a number to each matrx. We could
More informationLab 2e Thermal System Response and Effective Heat Transfer Coefficient
58:080 Expermental Engneerng 1 OBJECTIVE Lab 2e Thermal System Response and Effectve Heat Transfer Coeffcent Warnng: though the experment has educatonal objectves (to learn about bolng heat transfer, etc.),
More informationEcon107 Applied Econometrics Topic 3: Classical Model (Studenmund, Chapter 4)
I. Classcal Assumptons Econ7 Appled Econometrcs Topc 3: Classcal Model (Studenmund, Chapter 4) We have defned OLS and studed some algebrac propertes of OLS. In ths topc we wll study statstcal propertes
More informationCOS 511: Theoretical Machine Learning. Lecturer: Rob Schapire Lecture #16 Scribe: Yannan Wang April 3, 2014
COS 511: Theoretcal Machne Learnng Lecturer: Rob Schapre Lecture #16 Scrbe: Yannan Wang Aprl 3, 014 1 Introducton The goal of our onlne learnng scenaro from last class s C comparng wth best expert and
More informationPHYS 1101 Practice problem set 12, Chapter 32: 21, 22, 24, 57, 61, 83 Chapter 33: 7, 12, 32, 38, 44, 49, 76
PHYS 1101 Practce problem set 1, Chapter 3: 1,, 4, 57, 61, 83 Chapter 33: 7, 1, 3, 38, 44, 49, 76 3.1. Vsualze: Please reer to Fgure Ex3.1. Solve: Because B s n the same drecton as the ntegraton path s
More informationISQS 6348 Final Open notes, no books. Points out of 100 in parentheses. Y 1 ε 2
ISQS 6348 Fnal Open notes, no books. Ponts out of 100 n parentheses. 1. The followng path dagram s gven: ε 1 Y 1 ε F Y 1.A. (10) Wrte down the usual model and assumptons that are mpled by ths dagram. Soluton:
More informationComparative Studies of Law of Conservation of Energy. and Law Clusters of Conservation of Generalized Energy
Comparatve Studes of Law of Conservaton of Energy and Law Clusters of Conservaton of Generalzed Energy No.3 of Comparatve Physcs Seres Papers Fu Yuhua (CNOOC Research Insttute, E-mal:fuyh1945@sna.com)
More informationLecture 12: Discrete Laplacian
Lecture 12: Dscrete Laplacan Scrbe: Tanye Lu Our goal s to come up wth a dscrete verson of Laplacan operator for trangulated surfaces, so that we can use t n practce to solve related problems We are mostly
More informationLecture 12: Classification
Lecture : Classfcaton g Dscrmnant functons g The optmal Bayes classfer g Quadratc classfers g Eucldean and Mahalanobs metrcs g K Nearest Neghbor Classfers Intellgent Sensor Systems Rcardo Guterrez-Osuna
More informationFirst Law: A body at rest remains at rest, a body in motion continues to move at constant velocity, unless acted upon by an external force.
Secton 1. Dynamcs (Newton s Laws of Moton) Two approaches: 1) Gven all the forces actng on a body, predct the subsequent (changes n) moton. 2) Gven the (changes n) moton of a body, nfer what forces act
More informationDefinition. Measures of Dispersion. Measures of Dispersion. Definition. The Range. Measures of Dispersion 3/24/2014
Measures of Dsperson Defenton Range Interquartle Range Varance and Standard Devaton Defnton Measures of dsperson are descrptve statstcs that descrbe how smlar a set of scores are to each other The more
More informationONE DIMENSIONAL TRIANGULAR FIN EXPERIMENT. Technical Advisor: Dr. D.C. Look, Jr. Version: 11/03/00
ONE IMENSIONAL TRIANGULAR FIN EXPERIMENT Techncal Advsor: r..c. Look, Jr. Verson: /3/ 7. GENERAL OJECTIVES a) To understand a one-dmensonal epermental appromaton. b) To understand the art of epermental
More informationA particle in a state of uniform motion remain in that state of motion unless acted upon by external force.
The fundamental prncples of classcal mechancs were lad down by Galleo and Newton n the 16th and 17th centures. In 1686, Newton wrote the Prncpa where he gave us three laws of moton, one law of gravty,
More informationStatistics Chapter 4
Statstcs Chapter 4 "There are three knds of les: les, damned les, and statstcs." Benjamn Dsrael, 1895 (Brtsh statesman) Gaussan Dstrbuton, 4-1 If a measurement s repeated many tmes a statstcal treatment
More informationAnnexes. EC.1. Cycle-base move illustration. EC.2. Problem Instances
ec Annexes Ths Annex frst llustrates a cycle-based move n the dynamc-block generaton tabu search. It then dsplays the characterstcs of the nstance sets, followed by detaled results of the parametercalbraton
More informationSection 8.1 Exercises
Secton 8.1 Non-rght Trangles: Law of Snes and Cosnes 519 Secton 8.1 Exercses Solve for the unknown sdes and angles of the trangles shown. 10 70 50 1.. 18 40 110 45 5 6 3. 10 4. 75 15 5 6 90 70 65 5. 6.
More informationSpatial Statistics and Analysis Methods (for GEOG 104 class).
Spatal Statstcs and Analyss Methods (for GEOG 104 class). Provded by Dr. An L, San Dego State Unversty. 1 Ponts Types of spatal data Pont pattern analyss (PPA; such as nearest neghbor dstance, quadrat
More informationSection 8.3 Polar Form of Complex Numbers
80 Chapter 8 Secton 8 Polar Form of Complex Numbers From prevous classes, you may have encountered magnary numbers the square roots of negatve numbers and, more generally, complex numbers whch are the
More informationElectrical double layer: revisit based on boundary conditions
Electrcal double layer: revst based on boundary condtons Jong U. Km Department of Electrcal and Computer Engneerng, Texas A&M Unversty College Staton, TX 77843-318, USA Abstract The electrcal double layer
More informationPHYS 450 Spring semester Lecture 02: Dealing with Experimental Uncertainties. Ron Reifenberger Birck Nanotechnology Center Purdue University
PHYS 45 Sprng semester 7 Lecture : Dealng wth Expermental Uncertantes Ron Refenberger Brck anotechnology Center Purdue Unversty Lecture Introductory Comments Expermental errors (really expermental uncertantes)
More informationCS 468 Lecture 16: Isometry Invariance and Spectral Techniques
CS 468 Lecture 16: Isometry Invarance and Spectral Technques Justn Solomon Scrbe: Evan Gawlk Introducton. In geometry processng, t s often desrable to characterze the shape of an object n a manner that
More informationTHE CHINESE REMAINDER THEOREM. We should thank the Chinese for their wonderful remainder theorem. Glenn Stevens
THE CHINESE REMAINDER THEOREM KEITH CONRAD We should thank the Chnese for ther wonderful remander theorem. Glenn Stevens 1. Introducton The Chnese remander theorem says we can unquely solve any par of
More informationANSWERS. Problem 1. and the moment generating function (mgf) by. defined for any real t. Use this to show that E( U) var( U)
Econ 413 Exam 13 H ANSWERS Settet er nndelt 9 deloppgaver, A,B,C, som alle anbefales å telle lkt for å gøre det ltt lettere å stå. Svar er gtt . Unfortunately, there s a prntng error n the hnt of
More informationRECEIVED. Negative Transverse Impedance
RECEVED SEP 2 3 996 OSTt > LS- 4 O C a f L W. Chou March 2, 989 (Rev. June 2, 9S9) Negatve Transverse mpedance ntroducton n Ref. ( we report an observaton that the horzontal and the vertcal loss factors
More informationInner Product. Euclidean Space. Orthonormal Basis. Orthogonal
Inner Product Defnton 1 () A Eucldean space s a fnte-dmensonal vector space over the reals R, wth an nner product,. Defnton 2 (Inner Product) An nner product, on a real vector space X s a symmetrc, blnear,
More informationModule 9. Lecture 6. Duality in Assignment Problems
Module 9 1 Lecture 6 Dualty n Assgnment Problems In ths lecture we attempt to answer few other mportant questons posed n earler lecture for (AP) and see how some of them can be explaned through the concept
More informationCSci 6974 and ECSE 6966 Math. Tech. for Vision, Graphics and Robotics Lecture 21, April 17, 2006 Estimating A Plane Homography
CSc 6974 and ECSE 6966 Math. Tech. for Vson, Graphcs and Robotcs Lecture 21, Aprl 17, 2006 Estmatng A Plane Homography Overvew We contnue wth a dscusson of the major ssues, usng estmaton of plane projectve
More informationConservation of Angular Momentum = "Spin"
Page 1 of 6 Conservaton of Angular Momentum = "Spn" We can assgn a drecton to the angular velocty: drecton of = drecton of axs + rght hand rule (wth rght hand, curl fngers n drecton of rotaton, thumb ponts
More informationIntroduction to Vapor/Liquid Equilibrium, part 2. Raoult s Law:
CE304, Sprng 2004 Lecture 4 Introducton to Vapor/Lqud Equlbrum, part 2 Raoult s Law: The smplest model that allows us do VLE calculatons s obtaned when we assume that the vapor phase s an deal gas, and
More informationTemperature. Chapter Heat Engine
Chapter 3 Temperature In prevous chapters of these notes we ntroduced the Prncple of Maxmum ntropy as a technque for estmatng probablty dstrbutons consstent wth constrants. In Chapter 9 we dscussed the
More informationChapter 4. Velocity analysis
1 Chapter 4 Velocty analyss Introducton The objectve of velocty analyss s to determne the sesmc veloctes of layers n the subsurface. Sesmc veloctes are used n many processng and nterpretaton stages such
More informationLecture 10: May 6, 2013
TTIC/CMSC 31150 Mathematcal Toolkt Sprng 013 Madhur Tulsan Lecture 10: May 6, 013 Scrbe: Wenje Luo In today s lecture, we manly talked about random walk on graphs and ntroduce the concept of graph expander,
More informationDETERMINATION OF ERRANT RUN-OUT OF THE AXIS OF ROTATION OF OBJECTS, PERFORMING ACCURATE ROTATIONAL MOVEMENTS
DETERMINATION OF ERRANT RUN-OUT OF THE AXIS OF ROTATION OF OBJECTS, PERFORMING ACCURATE ROTATIONAL MOVEMENTS Hrsto K. RADEV, Vassl J. BOGEV, Velzar A. VASSILEV Techncal Unversty of Sofa, Bulgara Abstract.
More information