Aerodynamic Separability in Tip Speed Ratio and Separability in Wind Speed- a Comparison
|
|
- Emmeline French
- 5 years ago
- Views:
Transcription
1 Jurnal f Physics: Cnference Series OPEN ACCESS Aerdynamic Separability in Tip Speed Rati and Separability in Wind Speed- a Cmparisn T cite this article: M L Gala Sants et al 14 J. Phys.: Cnf. Ser View the article nline fr updates and enhancements. Related cntent - Wind tunnel experiments t prve a hydraulic passive trque cntrl cncept fr variable speed wind turbines N F B Diepeveen and A Jarquin-Laguna - Mitigating the Lng term Operating Extreme Lad thrugh Active Cntrl Christina Kukura and Anand Natarajan - Extending wind turbine peratinal cnditins; a cmparisn f set pint adaptatin and LQG individual pitch cntrl fr highly turbulent wind W P Engels, S Subhani, H Zafar et al. This cntent was dwnladed frm IP address n 3/9/18 at 1:59
2 The Science f Making Trque frm Wind 1 Jurnal f Physics: Cnference Series 555 (14) 139 di:1.188/ /555/1/139 Aerdynamic Separability in Tip Speed Rati and Separability in Wind Speed- a Cmparisn M L Gala Sants 1, W E Leithead and P Jamiesn 3 1 CDT Wind Energy Systems, Department f Electrnic and Electrical Engineering, University f Strathclyde. Ryal Cllege Building, rm 3.36, 4 Gerge Street, Glasgw G1 1XW, UK Industrial Cntrl Centre, Department f Electrnic and Electrical Engineering, University f Strathclyde. Ryal Cllege Building, rm.16, 4 Gerge Street, Glasgw G1 1XW, UK 3 CDT Wind Energy Systems, Department f Electrnic and Electrical Engineering., University f Strathclyde. Ryal Cllege Building, rm 3.36, 4 Gerge Street, Glasgw G1 1XW, UK 1 maria.gala-sants@strath.ac.uk, w.leithead@strath.ac.uk, 3 peter.jamiesn@strath.ac.uk Abstract. Frm extensive applicatin ver a number f years, it has been established that the nnlinear rtr aerdynamics f typical medium and large wind turbines exhibit an effectively glbal separability prperty, in ther wrds the aerdynamic trque f the machine can be defined by tw independent additive functins. Tw versins f the separability f aerdynamic trque fr variable speed wind turbines are investigated here; the separated functin, related t wind speed, in the first versin is nly dependent n that variable and nt rtr speed and in the secnd versin is nly dependent n tip speed rati. Bth prvide very gd apprximatins t the aerdynamic trque ver extensive neighburhds f T, at least frm t T. 1. Intrductin The aerdynamic trque, T, fr a wind turbine is dependent n the wind speed, V, the blade pitch angle,, and rtr speed, ; that is, T 1 ARV C (, ) ; R / V (1) Q where is the density f air, A is the rtr area, C Q is the trque cefficient and the tip speed rati. The separatin f aerdynamics int tw additive cmpnents, the first independent f wind speed and the secnd independent f pitch angle, is discussed in Jamiesn et al [1], Leithead et al [], [3], [4], [6] and Leith et al [7]. Surprisingly, this separability hlds nt just at the equilibrium perating pints fr variable speed wind turbines in abve rated cnditins, but ver an extensive regin f the perating space. Fr cnstant speed wind turbines, f curse, neither cmpnent depends n rtr speed which des nt vary. Cntent frm this wrk may be used under the terms f the Creative Cmmns Attributin 3. licence. Any further distributin f this wrk must maintain attributin t the authr(s) and the title f the wrk, jurnal citatin and DOI. Published under licence by Ltd 1
3 The Science f Making Trque frm Wind 1 Jurnal f Physics: Cnference Series 555 (14) 139 di:1.188/ /555/1/139 In this paper, tw different frms f separability f the aerdynamics fr variable speed wind turbines are cmpared. The first frm is purely empiric in derivatin and is a direct extensin f separability fr a cnstant speed wind turbine. The secnd frm is derived frm the nature f the physical relatinship (1). The paper is rganised as fllws. In sectin and sectin 3, separability f the aerdynamics fr cnstant speed wind turbines and fr variable speed wind turbines, respectively, are discussed. In sectin 4, separability f the aerdynamics fr variable speed wind turbines, based n empirical extensin f the cnstant speed case, is presented. In sectin 5, separability f / (, ) / T CQ () is discussed and, in sectin 6, separability f the aerdynamics fr variable speed wind turbines, based n the nature f this physical relatinship, is presented. In sectin 7, the tw frms f separability are discussed and, in sectin 8, sme cncluding remarks are made.. Cnstant speed wind turbines Fr a cnstant speed wind turbine, the rtr speed is and rated trque is T. In abve rated cnditins, there is a pitch angle at which rated trque is attained fr each wind speed; that is, there is a lcus f equilibrium perating pints n which the trque is T. Prvided ( ) is mntnic, where ( ) is the relatinship f t alng this lcus f equilibrium pints, and ( ) and ( ) are chsen such that ( ) ( ( )) (3) ( ) ( ( ) ) (4) then, n the lcus, ( ) ( ) ( ) ( ( ) ( )) (5) Furthermre, the partial derivatives by cnstructin are, als, crrect n the lcus. The relatinship f ( ) t ( ) is ( ) ( ) ( ( )) (6) Hence, n the lcus, ( ( ) ( )). ( ) ( ( )) (7) Lcally t the lcus f equilibrium perating pints, ( ) is a gd representatin f ( ), that is, within a sufficiently small neighburhd f the lcus the difference can be made arbitrarily small. Mre generally, near the lcus, fr any functin ( ) ( ) ( ( ( ) ( ))) (8) such that, ( ) (9) i ( ) (1) By judicius chice f ( ), the size f the neighburhd can be maximised. In effect, in a regin that includes the whle set f equilibrium perating pints, the dependence f aerdynamic i On the lcus f equilibrium pints ( ) ( ) and
4 The Science f Making Trque frm Wind 1 Jurnal f Physics: Cnference Series 555 (14) 139 di:1.188/ /555/1/139 trque n pitch angle is thrugh ( ) and n wind speed thrugh ( ) whilst the dependence n displacement f the perating pint frm the lcus is thrugh [5]. Smewhat surprisingly, ( ) ( ( ( ) ( ))) applies fr a large neighburhd fr all rtrs, catering satisfactrily fr a very brad range f values f pitch angle and wind speed that includes all the nrmal perating pints. Furthermre, ( ), is generally a very weak nnlinear functin. Typically, the neighburhd includes values f aerdynamic trque frm t 3T. Indeed, it nly starts t break dwn n the rtr entering stall. The significance f the abve, particularly in the cntext f wind turbine cntrl, is that the wind turbine can be viewed as a nnlinear dynamic system dependant nly n the pitch angle (the nnlinearity ( )) with an additive external disturbance dependent nly n wind speed ( ( )) ii [5]. In Figure 1, the aerdynamic trque fr a 3MW HAWT is pltted against its separated representatin, ( ). The range f pitch angles is frm 3 t 19 and wind speed frm 11.41m/s t 4.1 m/s. Rated trque is 1 6. Clearly, ( ) is a gd apprximatin t ( ) even fr perating pints far frm rated trque. A best fit t the data wuld be an apprpriate chice fr ( ). 8 x 16 x 1 6 Figure 1. Separability fr a cnstant speed pitch regulated wind turbine. 3. Variable speed wind turbines Fr variable speed wind turbines, separatin functins, ( ), ( ) and ( ), can be determined fr different values f rtr speeds,. Hence, fr the lcus f equilibrium perating pints, i.e all perating pints, (, V, ), fr which T (, V, ) is T, where ( ) and ( ) are defined by (,V) 8 ( ) ( ( ) ( )) (11) ( ) ( ) (1) ( ) ( ) (13) ii Functins ( ) and ( ) are unique fr each and rtr 3
5 The Science f Making Trque frm Wind 1 Jurnal f Physics: Cnference Series 555 (14) 139 di:1.188/ /555/1/139 Nte, has a range f pssible values, that includes rated rtr speed,, and the lcus is nw a -dimensinal surface in a 4-dimensinal space. In the neighburhd f the lcus f equilibrium perating pints ( ) ( ( ( ) ( ))) (14) where ( ) ( ). Cnsider the set f pints, ( ), n the lcus, fr which the aerdynamic trque has cnstant value, such that Since ( ). These pints can be cntinuusly parameterised by ( ) ( ( ) ( ) ( )) (15) ( ) the partial derivative with respect t is simply related t the ther tw partial derivatives. Since the partial derivatives with respect t and V f the separated frm, ( ( ) ( )), n the lcus f equilibrium pints are crrect by cnstructin, the partial derivative with respect t is als crrect. ( ) ( ) (16) 8 x V 8% V 1% V 1% wind velcity [m/s] Figure. Functin ( ) fr 8%, 1% and 1% f ω. 5 x 16 1 x % 1% 1% [degree] Figure 3. Functin ( ) fr 8%, 1% and 1% f ω. 8 x 16 8% 1% 1% 5 8 T + [h(, )-g(v, )] x 1 6 T + [h(, )-g(v, )] x 1 6 Figure 4. Functin fr 8%, 1% and 1% f Figure 5. Separability fr case studi 8%, 1% ω. and 1% f ω. The separated representatin f the aerdynamics is determined fr a variable speed HAWT with the same rtr characteristics as the cnstant speed HAWT in sectin 1. The rtr speed range is 8% 1% 1% 4
6 The Science f Making Trque frm Wind 1 Jurnal f Physics: Cnference Series 555 (14) 139 di:1.188/ /555/1/139 between 8% and 1% f rated rtr speed,. The functins, ( ) and ( ), are depicted in Figures and 3, respectively, with values f 8%, 1% and 1%. The similarity f the functins, ( ), is striking. In Figure 4, the aerdynamic trque ( ), is pltted against its separated representatin, ( ( ) ( )). The separated representatin is again a gd apprximatin. 4. Separability in wind speed The bservatin, that the plts in Figure are very similar, suggests strngly that separability culd have a simplified frm with ( ) nly dependent n V; that is, n the lcus f equilibrium perating pints ( ) ( ) ( ( ) ( )) (17) Fr any chice f cnstant rtr speed,, n the lcus f equilibrium perating pints, ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ( )) ( ( )) ( ) ( ( )) ( ) Hence, chsing ( ) t be ( ), the functin at, an apprpriate chice fr ( ) is (18) ( ) ( ( )) (19) In Figure 6, ( ) and ( ( )) are cmpared with values f 8%, 1% and 1%. The pairs f functins match clsely. 1 x h ( ), 8% h ( ), 1% h ( ), 1% g (f ( ), 8% g (f ( ), 1% g (f ( ), 1% [degree] Figure 6. Validatin f simplified wind speed separability 5. Separability in tip speed rati The aerdynamic trque is defined as ( ) ( ) ( ) () ( ) where is a cnstant. Separability is applied t ( ) alng the lcus f perating pints n which ( ) ( ) with such that ( ) ( ( ) ( )) (1) 5
7 The Science f Making Trque frm Wind 1 Jurnal f Physics: Cnference Series 555 (14) 139 di:1.188/ /555/1/139 n the lcus. It can be seen frm Figure 7 that the separated frm, ( ( ) ( )), is a gd representatin fr ( ) fr a very large neighburhd enclsing the lcus f equilibrium pints. It includes values f ( ) that vary frm t. 5 x 1-3 Cq/.6694 Figure 7. Separabity fr cnstant This suggests strngly that separability culd have the frm fr variatins f 8%, 1% and 1% f ω and ( ) ( ( ( ) ( ))) () n the lcus f equilibrium pints with ( ). Nte, the lcus, n which ( ), is different frm that, n which ( ). Mre generally, ( ) ( ( ( ) ( ))) (3) fr sme ( ) such that ( ) and ( ). The functins, ( ) and ( ), are determined fr the separated frm f ( ) using data sets fr 8%, 9%, 1%, 11%, 1% and 14% fr which ( ) is clse t. Of curse, these n lnger remain lcal t as varies. It can be seen frm Figure 8 that the separated representatin, ( ( ( ) ( ))), is a gd representatin fr ( ). The functin, ( ) is als determined independently using data sets fr 8%, 1% and 1%. In Figure 9, the ( ) scaled by are shwn. T/ 8 x Figure 8. Equilibrium pints after separatin & T, 8% & T, 1% & T, 1% C + [H( )-G( )] 5 x 1-3 Equilibrium pints linear fit T / x [H( )+G( )] 7 x 16 8% 1% 1% 7 T x [H( )+G( )] Figure 9. Functin ( ) scaled by 6. Cmparisn f the tw versins f separability In Sectins 4 and 5, tw different versins f separability are discussed, specifically, a separatin using wind speed, (17), and a separatin using tip speed rati, (3); that is, 6
8 The Science f Making Trque frm Wind 1 Jurnal f Physics: Cnference Series 555 (14) 139 di:1.188/ /555/1/139 g(v) h(, ) x % 1% 6 1% g(v) OPTIMISED 4 1 x V [m/s] ( ( ( ) ( ))) ( ( ( ) ( ))) (4) Fr wind speed separability, ( ) and ( ) tgether with ptimised plynmial fits, ( ) and g( V ) av bv c, are depicted in Figure 1. Fr tip speed rati separability, ( ) and ( ), tgether with ptimised fits ( ) and ( ) ( ), are depicted in Figure 11. g( ) h( ) 4 x % 1% 1% x [degree] Figure 1. Wind speed separability equatins [degree] Figure 11. Tip speed rati separability equatins In Figures 1, Figure 13 and Figure 14 the tw versins f separability are directly cmpared fr rtr speed f 8%, 1% and 1%, respectively. Bth are gd apprximatins t the aerdynamic trque fr large neighburhds enclsing the lcus f equilibrium pints. As wuld be expected, the 1% case exhibits the clsest match. The least accurate is the 8% case but that is nt unexpected since its perating pints are the clsest t stall. Fr the tip speed rati separability, the neighburhd, fr which the separated representatin is a clse apprximatin, extends in every case at least frm t, expanding as the set f perating pints fr the different rtr speeds mve away frm the stall regin. It is particularly gd apprximatin when. Fr wind speed separability, the neighburhd, fr which the separated representatin is a clse apprximatin, als extends in every case at least frm t, It is particularly gd when Althugh there is n first principle justificatin fr the wind speed versin f separability, i.e. fr a ( ) being independent f, the latter even lcally t T, it is at least as gd as tip speed rati separability. Each figure is further accmpanied by a blw up f the data clse t, i.e. the data lcal t the equilibrium perating pints. It can be seen that there is a small inaccuracy, particularly clear in Figure 1, in the tip speed rati versin f separability. The underlying reasn fr this inaccuracy is the implicit assumptin in Sectin 5 that the data sets fr 8%, 9%, 1%, 11%, 1% and 14% shuld all lie n a straight line; that is ( ) n the perating regin defined by these data sets. That this assumptin is nt apprpriate can be seen frm Figure 7 r frm Figure 9. 7
9 The Science f Making Trque frm Wind 1 Jurnal f Physics: Cnference Series 555 (14) 139 di:1.188/ /555/1/139 8 x 16.1 x 16 8 x x x x 1 6 T +h( )-g(v) T +h( )-g(v) [T +[h( )+g( )] ]x [T +[h( )+g( )]] x 8 8 x 1 6 x 1 6 Figure 1. Separability cmparisn ω 8% Figure 13. Separability cmparisn ω 1% 9 x x x 1 6 T +h( )-g(v) [T +[h( )+g( )]] x 8 x 1 6 Figure 14. Separability cmparisn ω 1% 7. Cnclusin Tw versins f separability f aerdynamic trque fr variable speed wind turbines are investigated; the separated functin, related t wind speed, in the first versin is nly dependent n that variable and nt n rtr speed and in the secnd versin is nly dependent n tip speed rati. Bth prvide very gd apprximatins t the aerdynamic trque ver extensive neighburhds f, at least frm t. If anything, the wind speed separability is the mre accurate but has the least analytic supprt being purely empirically mtivated. The tw versins f separability are illustrated by applicatin t a 3MW HAWT. Acknwledgments Authrs wish t thank EPSRC fr their supprt t the prject thrugh the CDT Wind Energy Systems based at the University f Strathclyde, Glasgw, UK. References [1] Jamiesn, P., Leithead, W.E., Gala Sants, M.L., The Aerdynamic Basis f a Trque Separability Prperty. Prceedings f EWEA 11, Brussels, 11. [] Leithead, W.E., Rgers, M.C.M., Agius, RR.D., Dynamic analysis f the cmpliant tip, University f Strathclyde, Reprt prepared fr A.E.A. Technlgy, May 199. [3] Leithead, W.E., Rgers, M.C.M., Leith, D.J., Cnnr, B., Design f Wind Turbine Cntrllers. Prceedings f EURACO Wrkshp Recent Results in Rbust & Adaptive Cntrl, Flrence, [4] Leithead, W., Leith, D., Harden, F., Marku, H., Glbal gain-scheduling cntrl fr variable speed wind turbines, (Nice, France) EWEC, 1999 [5] Leithead W.E., D.J. Leith, On the Separability f Wind Turbine Rtr Aerdynamics. Internal Reprt, University f Strathclyde, 8
10 The Science f Making Trque frm Wind 1 Jurnal f Physics: Cnference Series 555 (14) 139 di:1.188/ /555/1/139 [6] Leithead, W., Harden, F., Leith, D., Identificatin f aerdynamics and drive-train dynamics fr variable speed wind turbines, (Madrid, Spain), EWEC, July 3. [7] Leith, D.J., Leithead, W.E., Implementatin f Wind Turbine Cntrllers, Int. J. Cntrl, 66, pp ,
Differentiation Applications 1: Related Rates
Differentiatin Applicatins 1: Related Rates 151 Differentiatin Applicatins 1: Related Rates Mdel 1: Sliding Ladder 10 ladder y 10 ladder 10 ladder A 10 ft ladder is leaning against a wall when the bttm
More information, which yields. where z1. and z2
The Gaussian r Nrmal PDF, Page 1 The Gaussian r Nrmal Prbability Density Functin Authr: Jhn M Cimbala, Penn State University Latest revisin: 11 September 13 The Gaussian r Nrmal Prbability Density Functin
More information^YawataR&D Laboratory, Nippon Steel Corporation, Tobata, Kitakyushu, Japan
Detectin f fatigue crack initiatin frm a ntch under a randm lad C. Makabe," S. Nishida^C. Urashima,' H. Kaneshir* "Department f Mechanical Systems Engineering, University f the Ryukyus, Nishihara, kinawa,
More informationCS 477/677 Analysis of Algorithms Fall 2007 Dr. George Bebis Course Project Due Date: 11/29/2007
CS 477/677 Analysis f Algrithms Fall 2007 Dr. Gerge Bebis Curse Prject Due Date: 11/29/2007 Part1: Cmparisn f Srting Algrithms (70% f the prject grade) The bjective f the first part f the assignment is
More informationThe blessing of dimensionality for kernel methods
fr kernel methds Building classifiers in high dimensinal space Pierre Dupnt Pierre.Dupnt@ucluvain.be Classifiers define decisin surfaces in sme feature space where the data is either initially represented
More informationSurface and Contact Stress
Surface and Cntact Stress The cncept f the frce is fundamental t mechanics and many imprtant prblems can be cast in terms f frces nly, fr example the prblems cnsidered in Chapter. Hwever, mre sphisticated
More informationSections 15.1 to 15.12, 16.1 and 16.2 of the textbook (Robbins-Miller) cover the materials required for this topic.
Tpic : AC Fundamentals, Sinusidal Wavefrm, and Phasrs Sectins 5. t 5., 6. and 6. f the textbk (Rbbins-Miller) cver the materials required fr this tpic.. Wavefrms in electrical systems are current r vltage
More informationOn Boussinesq's problem
Internatinal Jurnal f Engineering Science 39 (2001) 317±322 www.elsevier.cm/lcate/ijengsci On Bussinesq's prblem A.P.S. Selvadurai * Department f Civil Engineering and Applied Mechanics, McGill University,
More informationPhysics 2010 Motion with Constant Acceleration Experiment 1
. Physics 00 Mtin with Cnstant Acceleratin Experiment In this lab, we will study the mtin f a glider as it accelerates dwnhill n a tilted air track. The glider is supprted ver the air track by a cushin
More informationChapter 2 GAUSS LAW Recommended Problems:
Chapter GAUSS LAW Recmmended Prblems: 1,4,5,6,7,9,11,13,15,18,19,1,7,9,31,35,37,39,41,43,45,47,49,51,55,57,61,6,69. LCTRIC FLUX lectric flux is a measure f the number f electric filed lines penetrating
More informationAP Statistics Practice Test Unit Three Exploring Relationships Between Variables. Name Period Date
AP Statistics Practice Test Unit Three Explring Relatinships Between Variables Name Perid Date True r False: 1. Crrelatin and regressin require explanatry and respnse variables. 1. 2. Every least squares
More informationthe results to larger systems due to prop'erties of the projection algorithm. First, the number of hidden nodes must
M.E. Aggune, M.J. Dambrg, M.A. El-Sharkawi, R.J. Marks II and L.E. Atlas, "Dynamic and static security assessment f pwer systems using artificial neural netwrks", Prceedings f the NSF Wrkshp n Applicatins
More informationDetermining the Accuracy of Modal Parameter Estimation Methods
Determining the Accuracy f Mdal Parameter Estimatin Methds by Michael Lee Ph.D., P.E. & Mar Richardsn Ph.D. Structural Measurement Systems Milpitas, CA Abstract The mst cmmn type f mdal testing system
More informationInterference is when two (or more) sets of waves meet and combine to produce a new pattern.
Interference Interference is when tw (r mre) sets f waves meet and cmbine t prduce a new pattern. This pattern can vary depending n the riginal wave directin, wavelength, amplitude, etc. The tw mst extreme
More informationSupport-Vector Machines
Supprt-Vectr Machines Intrductin Supprt vectr machine is a linear machine with sme very nice prperties. Haykin chapter 6. See Alpaydin chapter 13 fr similar cntent. Nte: Part f this lecture drew material
More informationModule 4: General Formulation of Electric Circuit Theory
Mdule 4: General Frmulatin f Electric Circuit Thery 4. General Frmulatin f Electric Circuit Thery All electrmagnetic phenmena are described at a fundamental level by Maxwell's equatins and the assciated
More informationMath Foundations 20 Work Plan
Math Fundatins 20 Wrk Plan Units / Tpics 20.8 Demnstrate understanding f systems f linear inequalities in tw variables. Time Frame December 1-3 weeks 6-10 Majr Learning Indicatrs Identify situatins relevant
More informationComputational modeling techniques
Cmputatinal mdeling techniques Lecture 2: Mdeling change. In Petre Department f IT, Åb Akademi http://users.ab.fi/ipetre/cmpmd/ Cntent f the lecture Basic paradigm f mdeling change Examples Linear dynamical
More informationPhysics 2B Chapter 23 Notes - Faraday s Law & Inductors Spring 2018
Michael Faraday lived in the Lndn area frm 1791 t 1867. He was 29 years ld when Hand Oersted, in 1820, accidentally discvered that electric current creates magnetic field. Thrugh empirical bservatin and
More informationCHAPTER 3 INEQUALITIES. Copyright -The Institute of Chartered Accountants of India
CHAPTER 3 INEQUALITIES Cpyright -The Institute f Chartered Accuntants f India INEQUALITIES LEARNING OBJECTIVES One f the widely used decisin making prblems, nwadays, is t decide n the ptimal mix f scarce
More informationAssume that the water in the nozzle is accelerated at a rate such that the frictional effect can be neglected.
1 HW #3: Cnservatin f Linear Mmentum, Cnservatin f Energy, Cnservatin f Angular Mmentum and Turbmachines, Bernulli s Equatin, Dimensinal Analysis, and Pipe Flws Prblem 1. Cnservatins f Mass and Linear
More informationThe influence of a semi-infinite atmosphere on solar oscillations
Jurnal f Physics: Cnference Series OPEN ACCESS The influence f a semi-infinite atmsphere n slar scillatins T cite this article: Ángel De Andrea Gnzález 014 J. Phys.: Cnf. Ser. 516 01015 View the article
More informationLecture 7: Damped and Driven Oscillations
Lecture 7: Damped and Driven Oscillatins Last time, we fund fr underdamped scillatrs: βt x t = e A1 + A csω1t + i A1 A sinω1t A 1 and A are cmplex numbers, but ur answer must be real Implies that A 1 and
More informationBASD HIGH SCHOOL FORMAL LAB REPORT
BASD HIGH SCHOOL FORMAL LAB REPORT *WARNING: After an explanatin f what t include in each sectin, there is an example f hw the sectin might lk using a sample experiment Keep in mind, the sample lab used
More informationI. Analytical Potential and Field of a Uniform Rod. V E d. The definition of electric potential difference is
Length L>>a,b,c Phys 232 Lab 4 Ch 17 Electric Ptential Difference Materials: whitebards & pens, cmputers with VPythn, pwer supply & cables, multimeter, crkbard, thumbtacks, individual prbes and jined prbes,
More informationPressure And Entropy Variations Across The Weak Shock Wave Due To Viscosity Effects
Pressure And Entrpy Variatins Acrss The Weak Shck Wave Due T Viscsity Effects OSTAFA A. A. AHOUD Department f athematics Faculty f Science Benha University 13518 Benha EGYPT Abstract:-The nnlinear differential
More informationPlan o o. I(t) Divide problem into sub-problems Modify schematic and coordinate system (if needed) Write general equations
STAPLE Physics 201 Name Final Exam May 14, 2013 This is a clsed bk examinatin but during the exam yu may refer t a 5 x7 nte card with wrds f wisdm yu have written n it. There is extra scratch paper available.
More informationFall 2013 Physics 172 Recitation 3 Momentum and Springs
Fall 03 Physics 7 Recitatin 3 Mmentum and Springs Purpse: The purpse f this recitatin is t give yu experience wrking with mmentum and the mmentum update frmula. Readings: Chapter.3-.5 Learning Objectives:.3.
More informationChapter Summary. Mathematical Induction Strong Induction Recursive Definitions Structural Induction Recursive Algorithms
Chapter 5 1 Chapter Summary Mathematical Inductin Strng Inductin Recursive Definitins Structural Inductin Recursive Algrithms Sectin 5.1 3 Sectin Summary Mathematical Inductin Examples f Prf by Mathematical
More informationPSU GISPOPSCI June 2011 Ordinary Least Squares & Spatial Linear Regression in GeoDa
There are tw parts t this lab. The first is intended t demnstrate hw t request and interpret the spatial diagnstics f a standard OLS regressin mdel using GeDa. The diagnstics prvide infrmatin abut the
More informationPattern Recognition 2014 Support Vector Machines
Pattern Recgnitin 2014 Supprt Vectr Machines Ad Feelders Universiteit Utrecht Ad Feelders ( Universiteit Utrecht ) Pattern Recgnitin 1 / 55 Overview 1 Separable Case 2 Kernel Functins 3 Allwing Errrs (Sft
More informationChE 471: LECTURE 4 Fall 2003
ChE 47: LECTURE 4 Fall 003 IDEL RECTORS One f the key gals f chemical reactin engineering is t quantify the relatinship between prductin rate, reactr size, reactin kinetics and selected perating cnditins.
More informationWhat is Statistical Learning?
What is Statistical Learning? Sales 5 10 15 20 25 Sales 5 10 15 20 25 Sales 5 10 15 20 25 0 50 100 200 300 TV 0 10 20 30 40 50 Radi 0 20 40 60 80 100 Newspaper Shwn are Sales vs TV, Radi and Newspaper,
More informationMODULE FOUR. This module addresses functions. SC Academic Elementary Algebra Standards:
MODULE FOUR This mdule addresses functins SC Academic Standards: EA-3.1 Classify a relatinship as being either a functin r nt a functin when given data as a table, set f rdered pairs, r graph. EA-3.2 Use
More informationEXPERIMENTAL STUDY ON DISCHARGE COEFFICIENT OF OUTFLOW OPENING FOR PREDICTING CROSS-VENTILATION FLOW RATE
EXPERIMENTAL STUD ON DISCHARGE COEFFICIENT OF OUTFLOW OPENING FOR PREDICTING CROSS-VENTILATION FLOW RATE Tmnbu Gt, Masaaki Ohba, Takashi Kurabuchi 2, Tmyuki End 3, shihik Akamine 4, and Tshihir Nnaka 2
More informationLecture 13: Electrochemical Equilibria
3.012 Fundamentals f Materials Science Fall 2005 Lecture 13: 10.21.05 Electrchemical Equilibria Tday: LAST TIME...2 An example calculatin...3 THE ELECTROCHEMICAL POTENTIAL...4 Electrstatic energy cntributins
More informationAdmissibility Conditions and Asymptotic Behavior of Strongly Regular Graphs
Admissibility Cnditins and Asympttic Behavir f Strngly Regular Graphs VASCO MOÇO MANO Department f Mathematics University f Prt Oprt PORTUGAL vascmcman@gmailcm LUÍS ANTÓNIO DE ALMEIDA VIEIRA Department
More informationEmphases in Common Core Standards for Mathematical Content Kindergarten High School
Emphases in Cmmn Cre Standards fr Mathematical Cntent Kindergarten High Schl Cntent Emphases by Cluster March 12, 2012 Describes cntent emphases in the standards at the cluster level fr each grade. These
More informationROUNDING ERRORS IN BEAM-TRACKING CALCULATIONS
Particle Acceleratrs, 1986, Vl. 19, pp. 99-105 0031-2460/86/1904-0099/$15.00/0 1986 Grdn and Breach, Science Publishers, S.A. Printed in the United States f America ROUNDING ERRORS IN BEAM-TRACKING CALCULATIONS
More informationPerfrmance f Sensitizing Rules n Shewhart Cntrl Charts with Autcrrelated Data Key Wrds: Autregressive, Mving Average, Runs Tests, Shewhart Cntrl Chart
Perfrmance f Sensitizing Rules n Shewhart Cntrl Charts with Autcrrelated Data Sandy D. Balkin Dennis K. J. Lin y Pennsylvania State University, University Park, PA 16802 Sandy Balkin is a graduate student
More informationLyapunov Stability Stability of Equilibrium Points
Lyapunv Stability Stability f Equilibrium Pints 1. Stability f Equilibrium Pints - Definitins In this sectin we cnsider n-th rder nnlinear time varying cntinuus time (C) systems f the frm x = f ( t, x),
More informationOn Huntsberger Type Shrinkage Estimator for the Mean of Normal Distribution ABSTRACT INTRODUCTION
Malaysian Jurnal f Mathematical Sciences 4(): 7-4 () On Huntsberger Type Shrinkage Estimatr fr the Mean f Nrmal Distributin Department f Mathematical and Physical Sciences, University f Nizwa, Sultanate
More informationFebruary 28, 2013 COMMENTS ON DIFFUSION, DIFFUSIVITY AND DERIVATION OF HYPERBOLIC EQUATIONS DESCRIBING THE DIFFUSION PHENOMENA
February 28, 2013 COMMENTS ON DIFFUSION, DIFFUSIVITY AND DERIVATION OF HYPERBOLIC EQUATIONS DESCRIBING THE DIFFUSION PHENOMENA Mental Experiment regarding 1D randm walk Cnsider a cntainer f gas in thermal
More informationLead/Lag Compensator Frequency Domain Properties and Design Methods
Lectures 6 and 7 Lead/Lag Cmpensatr Frequency Dmain Prperties and Design Methds Definitin Cnsider the cmpensatr (ie cntrller Fr, it is called a lag cmpensatr s K Fr s, it is called a lead cmpensatr Ntatin
More informationExaminer: Dr. Mohamed Elsharnoby Time: 180 min. Attempt all the following questions Solve the following five questions, and assume any missing data
Benha University Cllege f Engineering at Banha Department f Mechanical Eng. First Year Mechanical Subject : Fluid Mechanics M111 Date:4/5/016 Questins Fr Final Crrective Examinatin Examiner: Dr. Mhamed
More informationSupporting information
Electrnic Supplementary Material (ESI) fr Physical Chemistry Chemical Physics This jurnal is The wner Scieties 01 ydrgen perxide electrchemistry n platinum: twards understanding the xygen reductin reactin
More information1. Introduction. Lab 4 - Geophysics 424, October 29, One-dimensional Interpretation of Magnetotelluric Data
Lab 4 - Gephysics 424, Octber 29, 2018 One-dimensinal Interpretatin f Magnettelluric Data Lab reprt is due by 5 p.m. Nvember 5, 2018 All late reprts require a valid reasn t be accepted. Include answers
More informationSUPPLEMENTARY MATERIAL GaGa: a simple and flexible hierarchical model for microarray data analysis
SUPPLEMENTARY MATERIAL GaGa: a simple and flexible hierarchical mdel fr micrarray data analysis David Rssell Department f Bistatistics M.D. Andersn Cancer Center, Hustn, TX 77030, USA rsselldavid@gmail.cm
More informationDavid HORN and Irit OPHER. School of Physics and Astronomy. Raymond and Beverly Sackler Faculty of Exact Sciences
Cmplex Dynamics f Neurnal Threshlds David HORN and Irit OPHER Schl f Physics and Astrnmy Raymnd and Beverly Sackler Faculty f Exact Sciences Tel Aviv University, Tel Aviv 69978, Israel hrn@neurn.tau.ac.il
More informationThis section is primarily focused on tools to aid us in finding roots/zeros/ -intercepts of polynomials. Essentially, our focus turns to solving.
Sectin 3.2: Many f yu WILL need t watch the crrespnding vides fr this sectin n MyOpenMath! This sectin is primarily fcused n tls t aid us in finding rts/zers/ -intercepts f plynmials. Essentially, ur fcus
More informationRULES AND SUBMISSION GUIDE FOR PUBLICATION OF "WIPO-WTO COLLOQUIUM PAPERS"
Intrductin RULES AND SUBMISSION GUIDE FOR PUBLICATION OF "WIPO-WTO COLLOQUIUM PAPERS" The publicatin "WIPO-WTO Cllquium Research Papers" has been develped t shwcase the academic papers f participants.
More informationCHAPTER 8b Static Equilibrium Units
CHAPTER 8b Static Equilibrium Units The Cnditins fr Equilibrium Slving Statics Prblems Stability and Balance Elasticity; Stress and Strain The Cnditins fr Equilibrium An bject with frces acting n it, but
More informationAP Statistics Notes Unit Two: The Normal Distributions
AP Statistics Ntes Unit Tw: The Nrmal Distributins Syllabus Objectives: 1.5 The student will summarize distributins f data measuring the psitin using quartiles, percentiles, and standardized scres (z-scres).
More information( ) kt. Solution. From kinetic theory (visualized in Figure 1Q9-1), 1 2 rms = 2. = 1368 m/s
.9 Kinetic Mlecular Thery Calculate the effective (rms) speeds f the He and Ne atms in the He-Ne gas laser tube at rm temperature (300 K). Slutin T find the rt mean square velcity (v rms ) f He atms at
More informationChapter 39. A GUIDE TO THE DESIGN OP AIR BUBBLERS FOR MELTING ICE Simon Ince Hydraulics Section, National Research Council Ottawa, Canada
Chapter 39 A GUIDE T THE DESIGN P AIR BUBBLERS FR MELTING ICE Simn Ince Hydraulics Sectin, Natinal Research Cuncil ttawa, Canada INTRDUCTIN The use f air bubblers fr maintaining ice-free areas in lakes
More information3D KMC simulation on the precipitation in the annealed ternary alloy system
3D KM simulatin n the precipitatin in the annealed ternary ally system Xuan Zhang, Mengqi Huang Abstract Kinetic Mnte arl methd is used t study the precipitatin phenmenn in binary and ternary ally system,
More informationIntroductory Thoughts
Flw Similarity By using the Buckingham pi therem, we have reduced the number f independent variables frm five t tw If we wish t run a series f wind-tunnel tests fr a given bdy at a given angle f attack,
More informationDepartment of Electrical Engineering, University of Waterloo. Introduction
Sectin 4: Sequential Circuits Majr Tpics Types f sequential circuits Flip-flps Analysis f clcked sequential circuits Mre and Mealy machines Design f clcked sequential circuits State transitin design methd
More informationTHREE DIMENSIONAL SPACE-TIME Lu Shan No.1144, East of Jiuzhou Avenue, Zhuhai , Guangdong Province P. R. China
Vl.4, N., pp.4-8, Ma 016 THREE DIMENSIONAL SPACE-TIME Lu Shan N.1144, East f Jiuhu Avenue, Zhuhai 509015, Guangdng Prvince P. R. China ABSTRACT: The space-time descriptin in Phsics was cmpsed f 3D space
More informationThree charges, all with a charge of 10 C are situated as shown (each grid line is separated by 1 meter).
Three charges, all with a charge f 0 are situated as shwn (each grid line is separated by meter). ) What is the net wrk needed t assemble this charge distributin? a) +0.5 J b) +0.8 J c) 0 J d) -0.8 J e)
More informationCompetition and Invasion in a Microcosmic Setting
University f Tennessee, Knxville Trace: Tennessee Research and Creative Exchange University f Tennessee Hnrs Thesis Prjects University f Tennessee Hnrs Prgram 5-2004 Cmpetitin and Invasin in a Micrcsmic
More informationFlipping Physics Lecture Notes: Simple Harmonic Motion Introduction via a Horizontal Mass-Spring System
Flipping Physics Lecture Ntes: Simple Harmnic Mtin Intrductin via a Hrizntal Mass-Spring System A Hrizntal Mass-Spring System is where a mass is attached t a spring, riented hrizntally, and then placed
More informationMore Tutorial at
Answer each questin in the space prvided; use back f page if extra space is needed. Answer questins s the grader can READILY understand yur wrk; nly wrk n the exam sheet will be cnsidered. Write answers,
More informationSynchronous Motor V-Curves
Synchrnus Mtr V-Curves 1 Synchrnus Mtr V-Curves Intrductin Synchrnus mtrs are used in applicatins such as textile mills where cnstant speed peratin is critical. Mst small synchrnus mtrs cntain squirrel
More informationMaterials Engineering 272-C Fall 2001, Lecture 7 & 8 Fundamentals of Diffusion
Materials Engineering 272-C Fall 2001, Lecture 7 & 8 Fundamentals f Diffusin Diffusin: Transprt in a slid, liquid, r gas driven by a cncentratin gradient (r, in the case f mass transprt, a chemical ptential
More informationComputational modeling techniques
Cmputatinal mdeling techniques Lecture 4: Mdel checing fr ODE mdels In Petre Department f IT, Åb Aademi http://www.users.ab.fi/ipetre/cmpmd/ Cntent Stichimetric matrix Calculating the mass cnservatin relatins
More informationmaking triangle (ie same reference angle) ). This is a standard form that will allow us all to have the X= y=
Intrductin t Vectrs I 21 Intrductin t Vectrs I 22 I. Determine the hrizntal and vertical cmpnents f the resultant vectr by cunting n the grid. X= y= J. Draw a mangle with hrizntal and vertical cmpnents
More informationIntroduction: A Generalized approach for computing the trajectories associated with the Newtonian N Body Problem
A Generalized apprach fr cmputing the trajectries assciated with the Newtnian N Bdy Prblem AbuBar Mehmd, Syed Umer Abbas Shah and Ghulam Shabbir Faculty f Engineering Sciences, GIK Institute f Engineering
More informationWRITING THE REPORT. Organizing the report. Title Page. Table of Contents
WRITING THE REPORT Organizing the reprt Mst reprts shuld be rganized in the fllwing manner. Smetime there is a valid reasn t include extra chapters in within the bdy f the reprt. 1. Title page 2. Executive
More informationElectric Current and Resistance
Electric Current and Resistance Electric Current Electric current is the rate f flw f charge thrugh sme regin f space The SI unit f current is the ampere (A) 1 A = 1 C / s The symbl fr electric current
More informationSPH3U1 Lesson 06 Kinematics
PROJECTILE MOTION LEARNING GOALS Students will: Describe the mtin f an bject thrwn at arbitrary angles thrugh the air. Describe the hrizntal and vertical mtins f a prjectile. Slve prjectile mtin prblems.
More informationand the Doppler frequency rate f R , can be related to the coefficients of this polynomial. The relationships are:
Algrithm fr Estimating R and R - (David Sandwell, SIO, August 4, 2006) Azimith cmpressin invlves the alignment f successive eches t be fcused n a pint target Let s be the slw time alng the satellite track
More informationFlipping Physics Lecture Notes: Simple Harmonic Motion Introduction via a Horizontal Mass-Spring System
Flipping Physics Lecture Ntes: Simple Harmnic Mtin Intrductin via a Hrizntal Mass-Spring System A Hrizntal Mass-Spring System is where a mass is attached t a spring, riented hrizntally, and then placed
More information5.4 Measurement Sampling Rates for Daily Maximum and Minimum Temperatures
5.4 Measurement Sampling Rates fr Daily Maximum and Minimum Temperatures 1 1 2 X. Lin, K. G. Hubbard, and C. B. Baker University f Nebraska, Lincln, Nebraska 2 Natinal Climatic Data Center 1 1. INTRODUCTION
More informationStudy Group Report: Plate-fin Heat Exchangers: AEA Technology
Study Grup Reprt: Plate-fin Heat Exchangers: AEA Technlgy The prblem under study cncerned the apparent discrepancy between a series f experiments using a plate fin heat exchanger and the classical thery
More informationA Polarimetric Survey of Radio Frequency Interference in C- and X-Bands in the Continental United States using WindSat Radiometry
A Plarimetric Survey f Radi Frequency Interference in C- and X-Bands in the Cntinental United States using WindSat Radimetry Steven W. Ellingsn Octber, Cntents Intrductin WindSat Methdlgy Analysis f RFI
More informationCHAPTER 24: INFERENCE IN REGRESSION. Chapter 24: Make inferences about the population from which the sample data came.
MATH 1342 Ch. 24 April 25 and 27, 2013 Page 1 f 5 CHAPTER 24: INFERENCE IN REGRESSION Chapters 4 and 5: Relatinships between tw quantitative variables. Be able t Make a graph (scatterplt) Summarize the
More informationANALYTICAL MODEL FOR PREDICTING STRESS-STRAIN BEHAVIOUR OF BACTERIAL CONCRETE
Internatinal Jurnal f Civil Engineering and Technlgy (IJCIET) Vlume 9, Issue 11, Nvember 018, pp. 383 393, Article ID: IJCIET_09_11_38 Available nline at http://www.iaeme.cm/ijciet/issues.asp?jtype=ijciet&vtype=9&itype=11
More informationFIELD QUALITY IN ACCELERATOR MAGNETS
FIELD QUALITY IN ACCELERATOR MAGNETS S. Russenschuck CERN, 1211 Geneva 23, Switzerland Abstract The field quality in the supercnducting magnets is expressed in terms f the cefficients f the Furier series
More informationDepartment of Economics, University of California, Davis Ecn 200C Micro Theory Professor Giacomo Bonanno. Insurance Markets
Department f Ecnmics, University f alifrnia, Davis Ecn 200 Micr Thery Prfessr Giacm Bnann Insurance Markets nsider an individual wh has an initial wealth f. ith sme prbability p he faces a lss f x (0
More informationThe Electromagnetic Form of the Dirac Electron Theory
0 The Electrmagnetic Frm f the Dirac Electrn Thery Aleander G. Kyriaks Saint-Petersburg State Institute f Technlgy, St. Petersburg, Russia* In the present paper it is shwn that the Dirac electrn thery
More informationCompressibility Effects
Definitin f Cmpressibility All real substances are cmpressible t sme greater r lesser extent; that is, when yu squeeze r press n them, their density will change The amunt by which a substance can be cmpressed
More informationMODULE 1. e x + c. [You can t separate a demominator, but you can divide a single denominator into each numerator term] a + b a(a + b)+1 = a + b
. REVIEW OF SOME BASIC ALGEBRA MODULE () Slving Equatins Yu shuld be able t slve fr x: a + b = c a d + e x + c and get x = e(ba +) b(c a) d(ba +) c Cmmn mistakes and strategies:. a b + c a b + a c, but
More informationRevision: August 19, E Main Suite D Pullman, WA (509) Voice and Fax
.7.4: Direct frequency dmain circuit analysis Revisin: August 9, 00 5 E Main Suite D Pullman, WA 9963 (509) 334 6306 ice and Fax Overview n chapter.7., we determined the steadystate respnse f electrical
More informationWe can see from the graph above that the intersection is, i.e., [ ).
MTH 111 Cllege Algebra Lecture Ntes July 2, 2014 Functin Arithmetic: With nt t much difficulty, we ntice that inputs f functins are numbers, and utputs f functins are numbers. S whatever we can d with
More information1 Course Notes in Introductory Physics Jeffrey Seguritan
Intrductin & Kinematics I Intrductin Quickie Cncepts Units SI is standard system f units used t measure physical quantities. Base units that we use: meter (m) is standard unit f length kilgram (kg) is
More informationSuggested reading: Lackmann (2011), Sections
QG Thery and Applicatins: Apprximatins and Equatins Atms 5110 Synptic Dynamic Meterlgy I Instructr: Jim Steenburgh jim.steenburgh@utah.edu 801-581-8727 Suite 480/Office 488 INSCC Suggested reading: Lackmann
More informationInvestigating the lift force of a toy helicopter
Investigating the lift frce f a ty helicpter I am an active member f my schl s aernautics club. We ccasinally fly gas pwered mdel aircraft and we spend endless hurs at the realistic cntrls f a cmputer
More informationMedium Scale Integrated (MSI) devices [Sections 2.9 and 2.10]
EECS 270, Winter 2017, Lecture 3 Page 1 f 6 Medium Scale Integrated (MSI) devices [Sectins 2.9 and 2.10] As we ve seen, it s smetimes nt reasnable t d all the design wrk at the gate-level smetimes we just
More informationEngineering Approach to Modelling Metal THz Structures
Terahertz Science and Technlgy, ISSN 1941-7411 Vl.4, N.1, March 11 Invited Paper ngineering Apprach t Mdelling Metal THz Structures Stepan Lucyszyn * and Yun Zhu Department f, Imperial Cllege Lndn, xhibitin
More informationA Study on Pullout Strength of Cast-in-place Anchor bolt in Concrete under High Temperature
Transactins f the 7 th Internatinal Cnference n Structural Mechanics in Reactr Technlgy (SMiRT 7) Prague, Czech Republic, August 7 22, 23 Paper #H-2 A Study n Pullut Strength f Cast-in-place Anchr blt
More informationFigure 1a. A planar mechanism.
ME 5 - Machine Design I Fall Semester 0 Name f Student Lab Sectin Number EXAM. OPEN BOOK AND CLOSED NOTES. Mnday, September rd, 0 Write n ne side nly f the paper prvided fr yur slutins. Where necessary,
More informationHomology groups of disks with holes
Hmlgy grups f disks with hles THEOREM. Let p 1,, p k } be a sequence f distinct pints in the interir unit disk D n where n 2, and suppse that fr all j the sets E j Int D n are clsed, pairwise disjint subdisks.
More information22.54 Neutron Interactions and Applications (Spring 2004) Chapter 11 (3/11/04) Neutron Diffusion
.54 Neutrn Interactins and Applicatins (Spring 004) Chapter (3//04) Neutrn Diffusin References -- J. R. Lamarsh, Intrductin t Nuclear Reactr Thery (Addisn-Wesley, Reading, 966) T study neutrn diffusin
More informationPipetting 101 Developed by BSU CityLab
Discver the Micrbes Within: The Wlbachia Prject Pipetting 101 Develped by BSU CityLab Clr Cmparisns Pipetting Exercise #1 STUDENT OBJECTIVES Students will be able t: Chse the crrect size micrpipette fr
More informationHow do scientists measure trees? What is DBH?
Hw d scientists measure trees? What is DBH? Purpse Students develp an understanding f tree size and hw scientists measure trees. Students bserve and measure tree ckies and explre the relatinship between
More informationNovel Three Phase Flux Reversal Machine with Full Pitch Winding
Octber 22-26, 2007 / Exe, Daegu, Krea THD1-1 Nvel Three Phase Flux Reversal Machine with Full Pitch Winding D. S. Mre*, and B. G. Femandes** *Research Schlar, Electrical Engineering Department, Indian
More informationModelling of NOLM Demultiplexers Employing Optical Soliton Control Pulse
Micwave and Optical Technlgy Letters, Vl. 1, N. 3, 1999. pp. 05-08 Mdelling f NOLM Demultiplexers Emplying Optical Slitn Cntrl Pulse Z. Ghassemly, C. Y. Cheung & A. K. Ray Electrnics Research Grup, Schl
More informationCity of Angels School Independent Study Los Angeles Unified School District
City f Angels Schl Independent Study Ls Angeles Unified Schl District INSTRUCTIONAL GUIDE Algebra 1B Curse ID #310302 (CCSS Versin- 06/15) This curse is the secnd semester f Algebra 1, fulfills ne half
More information