Losses of Cigarette Smoke Particles in Oral Cavities

Size: px
Start display at page:

Download "Losses of Cigarette Smoke Particles in Oral Cavities"

Transcription

1 Le f Cgarette Smke Partcle n Oral Cavte O. Prce, B. Agharan, J. Schreter, C. U. Yurter, C. Dcken, and J. McAughey Aled eearch Acate, alegh, NC, USA Brth Amercan Tbacc, G&D BScence Dmetry, Suthamtn, UK

2 Fundng Acknwledgment Fundng fr the tudy wa rvded by Brth Amercan Tbacc.

3 Mtvatn Cgarette mke qute dfferent frm envrnmental PM: Hgh cncentratn f artcle Mxture f var and artcle Hygrcc Mult-cmnent (> 000 cnttuent) Frehly-generated, undergng rad change Unque breathng maneuver Detn redcted by lung detn mdel much lwer than meaured lung detn. Objectve t buld a new mdel that nclude cgarette artcleecfc rerte and mechanm f detn n bth the muth and lung.

4 Smkng Maneuver Drawng n the cgarette flter t generate a ~50 ml uff f mke that fll the ral cavty. Hldng the uff n the muth fr -3 ecnd. Inhalatn f dlutn ar t delver the cgarette mke uff t the lung. Exhalatn eeat Vare between and wthn ndvdual.

5 Mechanm Affectng Partcle Detn Cllgatve effect Hydrdynamc nteractn f artcle wth ther artcle and ar flw (clud effect). Nn-cllgatve effect Cagulatn Exchange f water var and ther cnttuent between the artcle and urrundng ar.

6 Cllgatve Effect Far Aart Lely Packed Clely Packed Clud effect: Partcle behave a a ngle bdy f dtnct denty and vcty. Partcle exerence a reduced hydrdynamc drag frce. Le retance.

7 Nn-Cllgatve Effect Hygrcc Grwth The humd envrnment f the reratry tract allw cndenatn f water mlecule nt the urface f cgarette mke artcle. ate f grwth deend n the ze f the artcle and the amunt f water reent n the envrnment. Phae Change Evaratn r cndenatn f vlatle CSP cmnent (nctne). ate f ze decreae deend n the ze f the artcle and the amunt f nctne reent n the envrnment. Cagulatn Deend n artcle cncentratn. Increae the ze f ndvdual artcle, but decreae artcle cncentratn.

8 Cmnent f Cgarette Smke Partcle Water Nctne Sem-vlatle Inluble Gven fr each cmnent: - Gram mlecular weght - Ma denty - Intal ma fractn Calculate at each tme te: - Cmnent ma fractn - Sze change

9 Cmnent Change Mdel Predctn Cmnent Intal Ma Fractn Water 0.08 Nctne Inluble Sem- Vlatle 0.34

10 Predctn baed n - hygrcc grwth - hae change - cagulatn Partcle Sze Change

11 Puff Smulatn

12 Hythetcal Puff Drawng Scenar Prr t uff, ral cavty cled. Puff f mke enter the ral cavty a a clumn f mke travelng a a free-hear flw. Imact n the back f the muth and dere nt the ral cavty t eventually fll the entre muth. N mxng f the uff wth the urrundng ar untl the uff ht the back f the muth. Partcle may det due t mactn wth the back f the muth r dffun a the mke dere. Addtnal detn may ccur by thermhre, Brwnan dffun, and gravtatnal ettlng.

13 Imactn Detn Fractn

14 Muth-Hld Scenar Puff dere nt the ral cavte and mxe wth the mall amunt f redual ar. Partcle cncentratn reduced due t cagulatn and mxng wth the redual ar n ral cavte. Partcle ze cntnue t change (ncreae) due t cagulatn, hygrcc grwth, and hae change. Partcle det manly by gravtatnal ettlng.

15 Detn Fractn by Thermhre Durng Muth-Hld 0.5 µm artcle

16 Detn Fractn by Gravtatnal Settlng Durng Muth-Hld

17 Clud Effect Mdel after flw thrugh ru meda (Brnkman, 947) Drag frce related t that f Stke drag n ngle hercal artcle makng u the clud: The ceffcent (F c ) related t artcle vlume fractn (cncentratn) and ermeablty. Stk c c D F F V d C d F F ) ( 3 ) ( 3 ) tanh( ) ( c d C F c d d 3 9 8

18 Detn n Oral Cavty Detn redctn ue cmbned mdel ncrratng cmnent change, artcle grwth, and clud effect.

19 Cnclun Tw rmary tental mechanm fr ral detn f CSP were nvetgated: Imactn durng the ntal uff Sedmentatn durng the muth-hld (Effect f thermhre and dffun al cndered) Lttle detn by mactn at the back f the muth redcted due t lack f artcle mmentum. Lttle detn by edmentatn durng muth-hld redcted due t lw ettlng velcte f mall mke artcle. Fr realtc CSP temerature, thermhre ha lttle effect n ral detn. Detn due t mactn and edmentatn enhanced when cllgatve effect (clud-lke rerte) are cndered.

20 Future Drectn Further nvetgate clud effect n artcle drag and ther detn mechanm. Cnduct CFD analy f cgarette uff n the ral cavty durng bth hae f ral detn. Extend the mdel t nclude cgarette artcle detn n the lung.

21

22

23 Partcle Sze Change c hyg cag dt dd dt dd dt dd dt dd cag C dt d d dt dd 3 / 3 ) ( ) / /( ) ( ) ( t t e dt d e C w T d w M w n n n n w w n n w w w w hyg e m m F d M M m M m S Kn Kn Kn T d P M D dt dd T e M P m m F d M M m M m C Kn Kn Kn d D dt dd n T d n n n w w n n n n w w n n n c 4 3 ) (

24 Flw Feld Slutn Analytcal lutn va change f varable: u(r, ) a r '( ) ( ) a ( ) a z ''' '' ' 0 0 : 0 : : 0 ' 0 '

25 Flw Feld Durng Puff uctn Shear-free flw undeterred untl reachng near the back wall. Flw feld fund frm the lutn f ma and mmentum balance equatn: 0 z r u r u z r r r z P z r u z u r u r u r r u r P z u r u u (r,z) u(r, z) r z

26 Partcle Tranrt Durng Puff Suctn Effect f dffun n artcle trajectry: r z Frce actng un artcle: drag, thermhre, and gravty dv CSP m FD Fth Fg dt F D 3 d CSP V VCSP 9 d CSPHT Fth gt Fg mg net r z net t D' D H 6 d CSP 3 4e CSP t D' e CSP D' t k a 4.4 k CSP d CSP k a 8.8 k d CSP

27 Detn Fractn Durng Puff Suctn ral A CSP Flter end ectn A CSP / Prtn mactng n the late L Imactn late (back f muth)

28 artcle dameter: 0.5 µm Puff vlume: 50 ml Oral cavte ntal vlume: 50 ml Suctn tme: ecnd Partcle Trajectry

29 Detn Durng Muth-Hld Wrt cae cenar: Aume the blu frm near the wall unfrmly. Thermhre Gravtatnal Settlng Start f muth hld Tme t

30 Detn Fractn Durng Muth Hld 3 ral g S 3 ral th TD Tt H C 3 D t V V t n V t V t ) ( V t 0 V t V ) ( n n V t n V t V t ) ( V t V n n V t n V t V t ) ( Thermhre Gravtatnal Settlng V t V V t n V t V t ) (

31 Detn Fractn by Thermhre Durng Muth-Hld

32 Detn Fractn by Thermhre Durng Muth-Hld -ecnd muth hld

33 Clud effect n Partcle Detn Inertal mactn Stk F Gravtatnal ettlng V Brwnan dffun F c c 3 3 ( ( a a ) d 36 ) d 8 gc UC S ( d ( d ) ) D KTC ( d ) 3 d F c

Energy & Work

Energy & Work rk Dne by a Cntant Frce 6.-6.4 Energy & rk F N m jule () J rk Dne by a Cntant Frce Example Pullng a Sutcae-n-heel Fnd the wrk dne the rce 45.0-N, the angle 50.0 degree, and the dplacement 75.0 m. 3 ( F

More information

Physic 231 Lecture 33

Physic 231 Lecture 33 Physc 231 Lecture 33 Man pnts f tday s lecture: eat and heat capacty: Q cm Phase transtns and latent heat: Q Lm ( ) eat flw Q k 2 1 t L Examples f heat cnductvty, R values fr nsulatrs Cnvectn R L / k Radatn

More information

BME 5742 Biosystems Modeling and Control

BME 5742 Biosystems Modeling and Control BME 5742 Bsystems Mdeln and Cntrl Cell Electrcal Actvty: In Mvement acrss Cell Membrane and Membrane Ptental Dr. Zv Rth (FAU) 1 References Hppensteadt-Peskn, Ch. 3 Dr. Rbert Farley s lecture ntes Inc Equlbra

More information

_J _J J J J J J J J _. 7 particles in the blue state; 3 particles in the red state: 720 configurations _J J J _J J J J J J J J _

_J _J J J J J J J J _. 7 particles in the blue state; 3 particles in the red state: 720 configurations _J J J _J J J J J J J J _ Dsrder and Suppse I have 10 partcles that can be n ne f tw states ether the blue state r the red state. Hw many dfferent ways can we arrange thse partcles amng the states? All partcles n the blue state:

More information

Si Oxidation. SiO 2. ! A method of forming SiO 2

Si Oxidation. SiO 2. ! A method of forming SiO 2 S Oxatn! A met f frmn SO wc ue a Ma (e.., fr n mplantatn) Oxe n MOSFET Surface pavatn! Frm perfect S-SO nterface S S ( ) ( ) O ( ) ( ) SO ( ) H O SO H ( ) ( ) SO S O Oxant ffue tru te SO flm Reactn tae

More information

Transient Conduction: Spatial Effects and the Role of Analytical Solutions

Transient Conduction: Spatial Effects and the Role of Analytical Solutions Transent Cnductn: Spatal Effects and the Rle f Analytcal Slutns Slutn t the Heat Equatn fr a Plane Wall wth Symmetrcal Cnvectn Cndtns If the lumped capactance apprxmatn can nt be made, cnsderatn must be

More information

Chem 204A, Fall 2004, Mid-term (II)

Chem 204A, Fall 2004, Mid-term (II) Frst tw letters f yur last name Last ame Frst ame McGll ID Chem 204A, Fall 2004, Md-term (II) Read these nstructns carefully befre yu start tal me: 2 hurs 50 mnutes (6:05 PM 8:55 PM) 1. hs exam has ttal

More information

Spring 2002 Lecture #17

Spring 2002 Lecture #17 1443-51 Sprng 22 Lecture #17 r. Jaehn Yu 1. Cndtns fr Equlbrum 2. Center f Gravty 3. Elastc Prpertes f Slds Yung s dulus Shear dulus ulk dulus Tday s Hmewrk Assgnment s the Hmewrk #8!!! 2 nd term eam n

More information

Chapter 3, Solution 1C.

Chapter 3, Solution 1C. COSMOS: Cmplete Onlne Slutns Manual Organzatn System Chapter 3, Slutn C. (a If the lateral surfaces f the rd are nsulated, the heat transfer surface area f the cylndrcal rd s the bttm r the tp surface

More information

Problem #1. Known: All required parameters. Schematic: Find: Depth of freezing as function of time. Strategy:

Problem #1. Known: All required parameters. Schematic: Find: Depth of freezing as function of time. Strategy: BEE 3500 013 Prelm Soluton Problem #1 Known: All requred parameter. Schematc: Fnd: Depth of freezng a functon of tme. Strategy: In thee mplfed analy for freezng tme, a wa done n cla for a lab geometry,

More information

Chapter 6 : Gibbs Free Energy

Chapter 6 : Gibbs Free Energy Wnter 01 Chem 54: ntrductry hermdynamcs Chapter 6 : Gbbs Free Energy... 64 Defntn f G, A... 64 Mawell Relatns... 65 Gbbs Free Energy G(,) (ure substances)... 67 Gbbs Free Energy fr Mtures... 68 ΔG f deal

More information

Conduction Heat Transfer

Conduction Heat Transfer Cnductn Heat Transfer Practce prblems A steel ppe f cnductvty 5 W/m-K has nsde and utsde surface temperature f C and 6 C respectvely Fnd the heat flw rate per unt ppe length and flux per unt nsde and per

More information

A/2 l,k. Problem 1 STRATEGY. KNOWN Resistance of a complete spherical shell: r rk. Inner and outer radii

A/2 l,k. Problem 1 STRATEGY. KNOWN Resistance of a complete spherical shell: r rk. Inner and outer radii Prblem 1 STRATEGY KNOWN Resstance f a cmplete sphercal shell: R ( r r / (4 π r rk sphere Inner an uter ra r an r, SOLUTION Part 1: Resstance f a hemsphercal shell: T calculate the resstance f the hemsphere,

More information

Physics 181. Particle Systems

Physics 181. Particle Systems Physcs 181 Partcle Systems Overvew In these notes we dscuss the varables approprate to the descrpton of systems of partcles, ther defntons, ther relatons, and ther conservatons laws. We consder a system

More information

6. ELUTRIATION OF PARTICLES FROM FLUIDIZED BEDS

6. ELUTRIATION OF PARTICLES FROM FLUIDIZED BEDS 6. ELUTRIATION OF PARTICLES FROM FLUIDIZED BEDS Elutratn s the prcess n whch fne partcles are carred ut f a fludzed bed due t the flud flw rate passng thrugh the bed. Typcally, fne partcles are elutrated

More information

Lecture 12. Heat Exchangers. Heat Exchangers Chee 318 1

Lecture 12. Heat Exchangers. Heat Exchangers Chee 318 1 Lecture 2 Heat Exchangers Heat Exchangers Chee 38 Heat Exchangers A heat exchanger s used t exchange heat between tw fluds f dfferent temperatures whch are separated by a sld wall. Heat exchangers are

More information

Approach: (Equilibrium) TD analysis, i.e., conservation eqns., state equations Issues: how to deal with

Approach: (Equilibrium) TD analysis, i.e., conservation eqns., state equations Issues: how to deal with Schl f Aerspace Chemcal D: Mtvatn Prevus D Analyss cnsdered systems where cmpstn f flud was frzen fxed chemcal cmpstn Chemcally eactng Flw but there are numerus stuatns n prpulsn systems where chemcal

More information

Chapter 7. Systems 7.1 INTRODUCTION 7.2 MATHEMATICAL MODELING OF LIQUID LEVEL SYSTEMS. Steady State Flow. A. Bazoune

Chapter 7. Systems 7.1 INTRODUCTION 7.2 MATHEMATICAL MODELING OF LIQUID LEVEL SYSTEMS. Steady State Flow. A. Bazoune Chapter 7 Flud Systems and Thermal Systems 7.1 INTODUCTION A. Bazune A flud system uses ne r mre fluds t acheve ts purpse. Dampers and shck absrbers are eamples f flud systems because they depend n the

More information

CTN 2/23/16. EE 247B/ME 218: Introduction to MEMS Design Lecture 11m2: Mechanics of Materials. Copyright 2016 Regents of the University of California

CTN 2/23/16. EE 247B/ME 218: Introduction to MEMS Design Lecture 11m2: Mechanics of Materials. Copyright 2016 Regents of the University of California Vlume Change fr a Unaxal Stress Istrpc lastcty n 3D Istrpc = same n all drectns The cmplete stress-stran relatns fr an strpc elastc Stresses actng n a dfferental vlume element sld n 3D: (.e., a generalzed

More information

Final Exam Spring 2014 SOLUTION

Final Exam Spring 2014 SOLUTION Appled Opts H-464/564 C 594 rtland State nverst A. La Rsa Fnal am Sprng 14 SOLTION Name There are tw questns 1%) plus an ptnal bnus questn 1%) 1. Quarter wave plates and half wave plates The fgures belw

More information

Thermodynamics of Materials

Thermodynamics of Materials Thermdynamcs f Materals 14th Lecture 007. 4. 8 (Mnday) FUGACITY dg = Vd SdT dg = Vd at cnstant T Fr an deal gas dg = (RT/)d = RT dln Ths s true fr deal gases nly, but t wuld be nce t have a smlar frm fr

More information

CIRCLE YOUR DIVISION: Div. 1 (9:30 am) Div. 2 (11:30 am) Div. 3 (2:30 pm) Prof. Ruan Prof. Naik Mr. Singh

CIRCLE YOUR DIVISION: Div. 1 (9:30 am) Div. 2 (11:30 am) Div. 3 (2:30 pm) Prof. Ruan Prof. Naik Mr. Singh Frst CIRCLE YOUR DIVISION: Dv. 1 (9:30 am) Dv. (11:30 am) Dv. 3 (:30 m) Prf. Ruan Prf. Na Mr. Sngh Schl f Mechancal Engneerng Purdue Unversty ME315 Heat and Mass ransfer Eam #3 Wednesday Nvember 17 010

More information

HANSEN SOLUBILITY PARAMETERS IN CHROMATOGRAPHIC SCIENCES ADAM VOELKEL, K. ADAMSKA POZNAŃ UNIVERSITY OF TECHNOLOGY, POLAND

HANSEN SOLUBILITY PARAMETERS IN CHROMATOGRAPHIC SCIENCES ADAM VOELKEL, K. ADAMSKA POZNAŃ UNIVERSITY OF TECHNOLOGY, POLAND HANSN SOLUBILITY PARAMTRS IN CHROMATOGRAPHIC SCINCS ADAM OLKL, K. ADAMSKA POZNAŃ UNIRSITY OF TCHNOLOGY, POLAND SOLUBILITY PARAMTR THORY nergy f varzatn g l U ar U T d Chesve energy densty c c ch H w RT

More information

CHAPTER 3 ANALYSIS OF KY BOOST CONVERTER

CHAPTER 3 ANALYSIS OF KY BOOST CONVERTER 70 CHAPTER 3 ANALYSIS OF KY BOOST CONERTER 3.1 Intrductn The KY Bst Cnverter s a recent nventn made by K.I.Hwu et. al., (2007), (2009a), (2009b), (2009c), (2010) n the nn-slated DC DC cnverter segment,

More information

Section 3: Detailed Solutions of Word Problems Unit 1: Solving Word Problems by Modeling with Formulas

Section 3: Detailed Solutions of Word Problems Unit 1: Solving Word Problems by Modeling with Formulas Sectn : Detaled Slutns f Wrd Prblems Unt : Slvng Wrd Prblems by Mdelng wth Frmulas Example : The factry nvce fr a mnvan shws that the dealer pad $,5 fr the vehcle. If the stcker prce f the van s $5,, hw

More information

Analysis The characteristic length of the junction and the Biot number are

Analysis The characteristic length of the junction and the Biot number are -4 4 The temerature f a gas stream s t be measured by a thermule. The tme t taes t regster 99 erent f the ntal ΔT s t be determned. Assumtns The juntn s sheral n shae wth a dameter f D 0.00 m. The thermal

More information

Wp/Lmin. Wn/Lmin 2.5V

Wp/Lmin. Wn/Lmin 2.5V UNIVERITY OF CALIFORNIA Cllege f Engneerng Department f Electrcal Engneerng and Cmputer cences Andre Vladmrescu Hmewrk #7 EEC Due Frday, Aprl 8 th, pm @ 0 Cry Prblem #.5V Wp/Lmn 0.0V Wp/Lmn n ut Wn/Lmn.5V

More information

Chapter 9 Compressible Flow 667

Chapter 9 Compressible Flow 667 Chapter 9 Cmpreible Flw 667 9.57 Air flw frm a tank thrugh a nzzle int the tandard atmphere, a in Fig. P9.57. A nrmal hck tand in the exit f the nzzle, a hwn. Etimate (a) the tank preure; and (b) the ma

More information

8 Waves in Uniform Magnetized Media

8 Waves in Uniform Magnetized Media 8 Wave n Unform Magnetzed Meda 81 Suceptblte The frt order current can be wrtten j = j = q d 3 p v f 1 ( r, p, t) = ɛ 0 χ E For Maxwellan dtrbuton Y n (λ) = f 0 (v, v ) = 1 πvth exp (v V ) v th 1 πv th

More information

Part III Lectures Field-Effect Transistors (FETs) and Circuits

Part III Lectures Field-Effect Transistors (FETs) and Circuits Part III Lecture 5-8 Feld-Effect Trantr (FET) and Crcut Unverty f Technlgy Feld-Effect Trantr (FET) Electrcal and Electrnc Engneerng epartment Lecture Ffteen - Page f 8 ecnd Year, Electrnc I, 2009-200

More information

"NEET / AIIMS " SOLUTION (6) Avail Video Lectures of Experienced Faculty.

NEET / AIIMS  SOLUTION (6) Avail Video Lectures of Experienced Faculty. 07 NEET EXAMINATION SOLUTION (6) Avail Vide Lectures f Exerienced Faculty Page Sl. The lean exressin which satisfies the utut f this lgic gate is C = A., Whichindicates fr AND gate. We can see, utut C

More information

Work is the change in energy of a system (neglecting heat transfer). To examine what could

Work is the change in energy of a system (neglecting heat transfer). To examine what could Work Work s the change n energy o a system (neglectng heat transer). To eamne what could cause work, let s look at the dmensons o energy: L ML E M L F L so T T dmensonally energy s equal to a orce tmes

More information

GASES. PV = nrt N 2 CH 4 CO 2 O 2 HCN N 2 O NO 2. Pressure & Boyle s Law Temperature & Charles s Law Avogadro s Law IDEAL GAS LAW

GASES. PV = nrt N 2 CH 4 CO 2 O 2 HCN N 2 O NO 2. Pressure & Boyle s Law Temperature & Charles s Law Avogadro s Law IDEAL GAS LAW GASES Pressure & Byle s Law Temperature & Charles s Law Avgadr s Law IDEAL GAS LAW PV = nrt N 2 CH 4 CO 2 O 2 HCN N 2 O NO 2 Earth s atmsphere: 78% N 2 21% O 2 sme Ar, CO 2 Sme Cmmn Gasses Frmula Name

More information

SIMULATION OF THREE PHASE THREE LEG TRANSFORMER BEHAVIOR UNDER DIFFERENT VOLTAGE SAG TYPES

SIMULATION OF THREE PHASE THREE LEG TRANSFORMER BEHAVIOR UNDER DIFFERENT VOLTAGE SAG TYPES SIMULATION OF THREE PHASE THREE LEG TRANSFORMER BEHAVIOR UNDER DIFFERENT VOLTAGE SAG TYPES Mhammadreza Dlatan Alreza Jallan Department f Electrcal Engneerng, Iran Unversty f scence & Technlgy (IUST) e-mal:

More information

Physics 207: Lecture 20. Today s Agenda Homework for Monday

Physics 207: Lecture 20. Today s Agenda Homework for Monday Physcs 207: Lecture 20 Today s Agenda Homework for Monday Recap: Systems of Partcles Center of mass Velocty and acceleraton of the center of mass Dynamcs of the center of mass Lnear Momentum Example problems

More information

EECE 301 Signals & Systems Prof. Mark Fowler

EECE 301 Signals & Systems Prof. Mark Fowler -T Sytem: Ung Bode Plot EEE 30 Sgnal & Sytem Pro. Mark Fowler Note Set #37 /3 Bode Plot Idea an Help Vualze What rcut Do Lowpa Flter Break Pont = / H ( ) j /3 Hghpa Flter c = / L Bandpa Flter n nn ( a)

More information

Let s start from a first-order low pass filter we already discussed.

Let s start from a first-order low pass filter we already discussed. EEE0 Netrk Analy II Dr. harle Km Nte09: Actve Flter ---Part. gher-order Actve Flter The rt-rder lter d nt harply dvde the pa band and the tp band. One apprach t btan a harper trantn beteen the pa band

More information

Dr. Shalabh Department of Mathematics and Statistics Indian Institute of Technology Kanpur

Dr. Shalabh Department of Mathematics and Statistics Indian Institute of Technology Kanpur Analyss of Varance and Desgn of Exerments-I MODULE III LECTURE - 2 EXPERIMENTAL DESIGN MODELS Dr. Shalabh Deartment of Mathematcs and Statstcs Indan Insttute of Technology Kanur 2 We consder the models

More information

Out-of-plane orbital maneuvers using swing-bys with the Moon

Out-of-plane orbital maneuvers using swing-bys with the Moon Jurnal f Physcs: Cnference Seres PAPER OPEN ACCESS Out-f-plane rbtal maneuvers usng swng-bys wth the Mn Related cntent - Pwered Swng-By Maneuvers arund the Mn A F Slva, A F B A Prad and O C Wnter cte ths

More information

Physics 141. Lecture 14. Frank L. H. Wolfs Department of Physics and Astronomy, University of Rochester, Lecture 14, Page 1

Physics 141. Lecture 14. Frank L. H. Wolfs Department of Physics and Astronomy, University of Rochester, Lecture 14, Page 1 Physcs 141. Lecture 14. Frank L. H. Wolfs Department of Physcs and Astronomy, Unversty of Rochester, Lecture 14, Page 1 Physcs 141. Lecture 14. Course Informaton: Lab report # 3. Exam # 2. Mult-Partcle

More information

Grade 12 Physics Exam Review

Grade 12 Physics Exam Review Grade 12 Physcs Exam Revew 1. A 40 kg wagn s pulled wth an appled frce f 50 N [E 37 degrees abve the hrzntal. The wagn mves 8 m [E] hrzntally whle 5 N f frctn act. Fnd the wrk dne n the wagn by the...

More information

Effects of high RH on α-pinene SOA phase partitioning

Effects of high RH on α-pinene SOA phase partitioning Effets f hgh RH n α-pnene SA phase parttnng Götebrg summer shl 26/06/2008 Nenne Prsle PhD student Chemstry, CCAR, Unv. Cpenhagen, Denmark nlp@kem.ku.dk 26/06/2008 Götebrg, Nenne Prsle 1 Mtvatn Current

More information

ELABORATING AND ANALYSING THE REAL BALANCE OF HEAT FOR THE STEAM GENERATOR RGL10/D-D

ELABORATING AND ANALYSING THE REAL BALANCE OF HEAT FOR THE STEAM GENERATOR RGL10/D-D Annals f te Unversty f Petrşan, Mecancal Engneerng, 10 (2008), 155-160 155 ELABORATING AND ANALYSING THE REAL BALANCE OF HEAT FOR THE STEAM GENERATOR RGL10/D-D DAN CODRUŢ PETRILEAN 1 Abstract: Te real

More information

The metal-oxide-semiconductor field-effect transistor consists of two p-n junctions either side of a MOS diode which acts as the gate.

The metal-oxide-semiconductor field-effect transistor consists of two p-n junctions either side of a MOS diode which acts as the gate. Intructn The metal-xe-emcnuctr fel-effect trantr cnt f tw -n junctn ether e f a MOS e whch act a the gate. MOSFET evce make u arun 90% f the electrnc nutry ue t ther lw wer an ther mall ze (cmare wth blar

More information

Waveshapping Circuits and Data Converters. Lesson #17 Comparators and Schmitt Triggers Section BME 373 Electronics II J.

Waveshapping Circuits and Data Converters. Lesson #17 Comparators and Schmitt Triggers Section BME 373 Electronics II J. Waeshappg Crcuts and Data Cnerters Lessn #7 Cmparatrs and Schmtt Trggers Sectn. BME 7 Electrncs II 0 Waeshappg Crcuts and Data Cnerters Cmparatrs and Schmtt Trggers Astable Multbratrs and Tmers ectfers,

More information

4. The material balances for isothermal ideal reactor models

4. The material balances for isothermal ideal reactor models Summay Geneal mateal balane f eatng system Bath eat Cntnuus-flw eats: CST (Cntnuus Sted Tank eat) P (Plug lw eat) Steady state f CST and P Desgn tasks : utlet (fnal nvesn), gven vlume f eat x vlume f eat,

More information

NOTES. Name: Date: Topic: Periodic Table & Atoms Notes. Period: Matter

NOTES. Name: Date: Topic: Periodic Table & Atoms Notes. Period: Matter NOTES Unit: Tpic: Peridic Table & Atms Ntes Name: Date: Perid: Matter Atmic Structure The term matter describes all f the physical substances arund us. Matter is anything that has mass and takes up space.

More information

V. Electrostatics Lecture 27a: Diffuse charge at electrodes

V. Electrostatics Lecture 27a: Diffuse charge at electrodes V. Electrstatcs Lecture 27a: Dffuse charge at electrdes Ntes by MIT tudent We have talked abut the electrc duble structures and crrespndng mdels descrbng the n and ptental dstrbutn n the duble layer. Nw

More information

O C S polar - greater force. H polar greater force. H polar. polar H-bond

O C S polar - greater force. H polar greater force. H polar. polar H-bond hapter 10 : 29, 30, 31, 33, 36, 40, 46, 48, 50, 72, 87, 91, 93, 110 29. a. Lndn e. Lndn b. diple-diple f. diple-diple c. -bnding g. in-in d. in-in 30. a. in-in e. -bnding b. Lndn f. diple-diple c. Lndn

More information

ES201 - Examination 2 Winter Adams and Richards NAME BOX NUMBER

ES201 - Examination 2 Winter Adams and Richards NAME BOX NUMBER ES201 - Examinatin 2 Winter 2003-2004 Adams and Richards NAME BOX NUMBER Please Circle One : Richards (Perid 4) ES201-01 Adams (Perid 4) ES201-02 Adams (Perid 6) ES201-03 Prblem 1 ( 12 ) Prblem 2 ( 24

More information

ELG4139: Op Amp-based Active Filters

ELG4139: Op Amp-based Active Filters ELG439: Op Amp-baed Actve Flter Advantage: educed ze and weght, and therere paratc. Increaed relablty and mprved perrmance. Smpler degn than r pave lter and can realze a wder range unctn a well a prvdng

More information

Lucas Imperfect Information Model

Lucas Imperfect Information Model Lucas Imerfect Infrmatn Mdel 93 Lucas Imerfect Infrmatn Mdel The Lucas mdel was the frst f the mdern, mcrfundatns mdels f aggregate suly and macrecnmcs It bult drectly n the Fredman-Phels analyss f the

More information

Not at Steady State! Yes! Only if reactions occur! Yes! Ideal Gas, change in temperature or pressure. Yes! Class 15. Is the following possible?

Not at Steady State! Yes! Only if reactions occur! Yes! Ideal Gas, change in temperature or pressure. Yes! Class 15. Is the following possible? Chapter 5-6 (where we are gong) Ideal gae and lqud (today) Dente Partal preure Non-deal gae (next tme) Eqn. of tate Reduced preure and temperature Compreblty chart (z) Vapor-lqud ytem (Ch. 6) Vapor preure

More information

Thermodynamics and Equilibrium

Thermodynamics and Equilibrium Thermdynamics and Equilibrium Thermdynamics Thermdynamics is the study f the relatinship between heat and ther frms f energy in a chemical r physical prcess. We intrduced the thermdynamic prperty f enthalpy,

More information

A Note on the Linear Programming Sensitivity. Analysis of Specification Constraints. in Blending Problems

A Note on the Linear Programming Sensitivity. Analysis of Specification Constraints. in Blending Problems Aled Mathematcal Scences, Vl. 2, 2008, n. 5, 241-248 A Nte n the Lnear Prgrammng Senstvty Analyss f Secfcatn Cnstrants n Blendng Prblems Umt Anc Callway Schl f Busness and Accuntancy Wae Frest Unversty,

More information

Q x = cos 1 30 = 53.1 South

Q x = cos 1 30 = 53.1 South Crdinatr: Dr. G. Khattak Thursday, August 0, 01 Page 1 Q1. A particle mves in ne dimensin such that its psitin x(t) as a functin f time t is given by x(t) =.0 + 7 t t, where t is in secnds and x(t) is

More information

Compressibility Effects

Compressibility 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 information

No! Yes! Only if reactions occur! Yes! Ideal Gas, change in temperature or pressure. Survey Results. Class 15. Is the following possible?

No! Yes! Only if reactions occur! Yes! Ideal Gas, change in temperature or pressure. Survey Results. Class 15. Is the following possible? Survey Reult Chapter 5-6 (where we are gong) % of Student 45% 40% 35% 30% 25% 20% 15% 10% 5% 0% Hour Spent on ChE 273 1-2 3-4 5-6 7-8 9-10 11+ Hour/Week 2008 2009 2010 2011 2012 2013 2014 2015 2017 F17

More information

, where. This is a highpass filter. The frequency response is the same as that for P.P.14.1 RC. Thus, the sketches of H and φ are shown below.

, where. This is a highpass filter. The frequency response is the same as that for P.P.14.1 RC. Thus, the sketches of H and φ are shown below. hapter 4, Slutn. H ( H(, where H π H ( φ H ( tan - ( Th a hghpa lter. The requency repne the ame a that r P.P.4. except that. Thu, the ketche H and φ are hwn belw. H.77 / φ 9 45 / hapter 4, Slutn. H(,

More information

Introduction to Electronic circuits.

Introduction to Electronic circuits. Intrductn t Electrnc crcuts. Passve and Actve crcut elements. Capactrs, esstrs and Inductrs n AC crcuts. Vltage and current dvders. Vltage and current surces. Amplfers, and ther transfer characterstc.

More information

CHAPTER X PHASE-CHANGE PROBLEMS

CHAPTER X PHASE-CHANGE PROBLEMS Chapter X Phae-Change Problem December 3, 18 917 CHAPER X PHASE-CHANGE PROBLEMS X.1 Introducton Clacal Stefan Problem Geometry of Phae Change Problem Interface Condton X. Analytcal Soluton for Soldfcaton

More information

Projectile Motion. What is projectile? Projectile -Any object which projected by some means and continues to move due to its own inertia (mass).

Projectile Motion. What is projectile? Projectile -Any object which projected by some means and continues to move due to its own inertia (mass). Prjectile Mtin AP Phyic B What i prjectile? Prjectile -Any bject which prjected by me mean and cntinue t me due t it wn inertia (ma). 1 Prjectile me in TWO dimenin Since a prjectile me in - dimenin, it

More information

QCE Chemistry. Year 2015 Mark 0.00 Pages 20 Published Jan 31, Chemistry: Revision Notes. By Sophie (1 ATAR)

QCE Chemistry. Year 2015 Mark 0.00 Pages 20 Published Jan 31, Chemistry: Revision Notes. By Sophie (1 ATAR) QCE Chemistry Year 2015 Mark 0.00 Pages 20 Published Jan 31, 2017 11 Chemistry: Revisin Ntes By Sphie (1 ATAR) Pwered by TCPDF (www.tcpdf.rg) Yur ntes authr, Sphie. Sphie achieved an ATAR f 1 in 2016 while

More information

Variable Structure Control ~ Basics

Variable Structure Control ~ Basics Varable Structure Control ~ Bac Harry G. Kwatny Department of Mechancal Engneerng & Mechanc Drexel Unverty Outlne A prelmnary example VS ytem, ldng mode, reachng Bac of dcontnuou ytem Example: underea

More information

AP Statistics Ch 3 Examining Relationships

AP Statistics Ch 3 Examining Relationships Introducton To tud relatonhp between varable, we mut meaure the varable on the ame group of ndvdual. If we thnk a varable ma eplan or even caue change n another varable, then the eplanator varable and

More information

Big Data Analytics! Special Topics for Computer Science CSE CSE Mar 31

Big Data Analytics! Special Topics for Computer Science CSE CSE Mar 31 Bg Data Analytcs! Specal Tpcs fr Cmputer Scence CSE 4095-001 CSE 5095-005! Mar 31 Fe Wang Asscate Prfessr Department f Cmputer Scence and Engneerng fe_wang@ucnn.edu Intrductn t Deep Learnng Perceptrn In

More information

A Proposal of Heating Load Calculation considering Stack Effect in High-rise Buildings

A Proposal of Heating Load Calculation considering Stack Effect in High-rise Buildings A Prpsal f Heatng Lad Calculatn cnsderng Stack Effect n Hgh-rse Buldngs *Dsam Sng 1) and Tae-Hyuk Kang 2) 1) Department f Archtectural Engneerng, Sungkyunkwan Unversty, 2066 Sebu-r, Jangan-gu, Suwn, 440-746,

More information

Edexcel GCSE Physics

Edexcel GCSE Physics Edexcel GCSE Physics Tpic 10: Electricity and circuits Ntes (Cntent in bld is fr Higher Tier nly) www.pmt.educatin The Structure f the Atm Psitively charged nucleus surrunded by negatively charged electrns

More information

Ensemble Methods: Boosting

Ensemble Methods: Boosting Ensemble Methods: Boostng Ncholas Ruozz Unversty of Texas at Dallas Based on the sldes of Vbhav Gogate and Rob Schapre Last Tme Varance reducton va baggng Generate new tranng data sets by samplng wth replacement

More information

Nonisothermal Chemical Reactors

Nonisothermal Chemical Reactors he 471 Fall 2014 LEUE 7a Nnithermal hemical eactr S far we have dealt with ithermal chemical reactr and were able, by ug nly a many pecie ma balance a there are dependent react t relate reactr ize, let

More information

CHAPTER 11. Solutions for Exercises. (b) An inverting amplifier has negative gain. Thus L

CHAPTER 11. Solutions for Exercises. (b) An inverting amplifier has negative gain. Thus L CHPTE Slutn fr Exerce E. (a nnnertng amplfer ha pte gan. Thu ( t ( t 50 ( t 5.0 n(000πt (b n nertng amplfer ha negate gan. Thu ( t ( t 50 ( t 5.0 n(000πt E. V V 75 500 + 5+ 75 c 75 V 000 75 500 V + + 500

More information

CONVECTIVE HEAT TRANSFER OF NANOFLUIDS IN MINICHANNEL UNDER LAMINAR FLOW CONDITIONS

CONVECTIVE HEAT TRANSFER OF NANOFLUIDS IN MINICHANNEL UNDER LAMINAR FLOW CONDITIONS Prceedngs f te Internatnal Cerence n Mecancal Engneerng 007 (ICME007) 9-31 December 007, Daka, Banglades ICME07-FL-7 CONVECTIVE HEAT TRANSFER OF NANOFLUIDS IN MINICHANNEL UNDER LAMINAR FLOW CONDITIONS

More information

Chem 111 Summer 2013 Key III Whelan

Chem 111 Summer 2013 Key III Whelan Chem 111 Summer 2013 Key III Whelan Questin 1 6 Pints Classify each f the fllwing mlecules as plar r nnplar? a) NO + : c) CH 2 Cl 2 : b) XeF 4 : Questin 2 The hypthetical mlecule PY 3 Z 2 has the general

More information

Name Student ID. A student uses a voltmeter to measure the electric potential difference across the three boxes.

Name Student ID. A student uses a voltmeter to measure the electric potential difference across the three boxes. Name Student ID II. [25 pt] Thi quetin cnit f tw unrelated part. Part 1. In the circuit belw, bulb 1-5 are identical, and the batterie are identical and ideal. Bxe,, and cntain unknwn arrangement f linear

More information

Phys101 Final Code: 1 Term: 132 Wednesday, May 21, 2014 Page: 1

Phys101 Final Code: 1 Term: 132 Wednesday, May 21, 2014 Page: 1 Phys101 Final Cde: 1 Term: 1 Wednesday, May 1, 014 Page: 1 Q1. A car accelerates at.0 m/s alng a straight rad. It passes tw marks that are 0 m apart at times t = 4.0 s and t = 5.0 s. Find the car s velcity

More information

4.8 Degradation of Elastomers by Heat and/or Radiation

4.8 Degradation of Elastomers by Heat and/or Radiation 4.8 Degradatn f Elastmers by Heat and/r Radatn M.It Japan Atmc Energy Research Insttute, Nuclear Educatn Center 2-28-49, Hnkmagme, Bunkyu-ku Tky, 113, JAPAN Abstract Ths artcle studed sme prblems n the

More information

Turbulent Flow. Turbulent Flow

Turbulent Flow. Turbulent Flow http://www.youtube.com/watch?v=xoll2kedog&feature=related http://br.youtube.com/watch?v=7kkftgx2any http://br.youtube.com/watch?v=vqhxihpvcvu 1. Caothc fluctuatons wth a wde range of frequences and

More information

PHY2053 Summer 2012 Exam 2 Solutions N F o f k

PHY2053 Summer 2012 Exam 2 Solutions N F o f k HY0 Suer 0 Ea Slutns. he ree-bdy dagra r the blck s N F 7 k F g Usng Newtn s secnd law r the -cnents F a F F cs7 k 0 k F F cs7 (0 N ( Ncs7 N he wrk dne by knetc rctn k r csθ ( N(6 cs80 0 N. Mechancal energy

More information

Analytical Modeling of Natural Convection in Horizontal Annuli

Analytical Modeling of Natural Convection in Horizontal Annuli Analytcal Mdelng f Natural Cnvectn n Hrzntal Annul Peter Teertstra, M. Mchael Yvanvch, J. Rchard Culham Mcrelectrncs Heat Transfer Labratry Department f Mechancal Engneerng Unversty f Waterl Waterl, Ontar,

More information

Department of Civil Engineering & Applied Mechanics McGill University, Montreal, Quebec Canada

Department of Civil Engineering & Applied Mechanics McGill University, Montreal, Quebec Canada Department f Cvl Engneerng & Appled Mechancs McGll Unversty, Mntreal, Quebec Canada CIVE 90 THEMODYNAMICS & HEAT TANSFE Assgnment #6 SOUTIONS. Cnsder a.-m hgh and -m-wde duble-pane wndw cnsstng f tw 3-mmthck

More information

Problem 1. Refracting Surface (Modified from Pedrotti 2-2)

Problem 1. Refracting Surface (Modified from Pedrotti 2-2) .70 Optc Hmewrk # February 8, 04 Prblem. Reractng Surace (Me rm Pertt -) Part (a) Fermat prncple requre that every ray that emanate rm the bject an pae thrugh the mage pnt mut be chrnu (.e., have equal

More information

A) 0.77 N B) 0.24 N C) 0.63 N D) 0.31 N E) 0.86 N. v = ω k = 80 = 32 m/s. Ans: (32) 2 = 0.77 N

A) 0.77 N B) 0.24 N C) 0.63 N D) 0.31 N E) 0.86 N. v = ω k = 80 = 32 m/s. Ans: (32) 2 = 0.77 N Q1. A transverse sinusidal wave travelling n a string is given by: y (x,t) = 0.20 sin (2.5 x 80 t) (SI units). The length f the string is 2.0 m and its mass is 1.5 g. What is the magnitude f the tensin

More information

Projectile Motion. Parabolic Motion curved motion in the shape of a parabola. In the y direction, the equation of motion has a t 2.

Projectile Motion. Parabolic Motion curved motion in the shape of a parabola. In the y direction, the equation of motion has a t 2. Projectle Moton Phc Inentor Parabolc Moton cured oton n the hape of a parabola. In the drecton, the equaton of oton ha a t ter Projectle Moton the parabolc oton of an object, where the horzontal coponent

More information

Exploiting vector space properties for the global optimization of process networks

Exploiting vector space properties for the global optimization of process networks Exptng vectr space prpertes fr the gbal ptmzatn f prcess netwrks Juan ab Ruz Ignac Grssmann Enterprse Wde Optmzatn Meetng March 00 Mtvatn - The ptmzatn f prcess netwrks s ne f the mst frequent prblems

More information

Matter Content from State Frameworks and Other State Documents

Matter Content from State Frameworks and Other State Documents Atms and Mlecules Mlecules are made f smaller entities (atms) which are bnded tgether. Therefre mlecules are divisible. Miscnceptin: Element and atm are synnyms. Prper cnceptin: Elements are atms with

More information

Short notes for Heat transfer

Short notes for Heat transfer Furier s Law f Heat Cnductin Shrt ntes fr Heat transfer Q = Heat transfer in given directin. A = Crss-sectinal area perpendicular t heat flw directin. dt = Temperature difference between tw ends f a blck

More information

EE 204 Lecture 25 More Examples on Power Factor and the Reactive Power

EE 204 Lecture 25 More Examples on Power Factor and the Reactive Power EE 204 Lecture 25 Mre Examples n Pwer Factr and the Reactve Pwer The pwer factr has been defned n the prevus lecture wth an example n pwer factr calculatn. We present tw mre examples n ths lecture. Example

More information

Work, Energy, and Power

Work, Energy, and Power rk, Energy, and Pwer Physics 1 There are many different TYPES f Energy. Energy is expressed in JOULES (J 419J 4.19 1 calrie Energy can be expressed mre specifically by using the term ORK( rk The Scalar

More information

Lecture Notes for STATISTICAL METHODS FOR BUSINESS II BMGT 212. Chapters 14, 15 & 16. Professor Ahmadi, Ph.D. Department of Management

Lecture Notes for STATISTICAL METHODS FOR BUSINESS II BMGT 212. Chapters 14, 15 & 16. Professor Ahmadi, Ph.D. Department of Management Lecture Notes for STATISTICAL METHODS FOR BUSINESS II BMGT 1 Chapters 14, 15 & 16 Professor Ahmad, Ph.D. Department of Management Revsed August 005 Chapter 14 Formulas Smple Lnear Regresson Model: y =

More information

To get you thinking...

To get you thinking... T get yu thinking... 1.) What is an element? Give at least 4 examples f elements. 2.) What is the atmic number f hydrgen? What des a neutral hydrgen atm cnsist f? Describe its "mtin". 3.) Hw des an atm

More information

Comparison of Building Codes and Insulation in China and Iceland

Comparison of Building Codes and Insulation in China and Iceland Prceedngs Wrld Gethermal Cngress 00 Bal, Indnesa, 5-9 prl 00 Cmparsn f Buldng Cdes and Insulatn n Chna and Iceland Hayan Le and Pall Valdmarssn Tanjn Gethermal esearch & Tranng Centre, Tanjn Unversty,

More information

EE247B/ME218: Introduction to MEMS Design Lecture 7m1: Lithography, Etching, & Doping CTN 2/6/18

EE247B/ME218: Introduction to MEMS Design Lecture 7m1: Lithography, Etching, & Doping CTN 2/6/18 EE247B/ME218 Intrductin t MEMS Design Lecture 7m1 Lithgraphy, Etching, & Dping Dping f Semicnductrs Semicnductr Dping Semicnductrs are nt intrinsically cnductive T make them cnductive, replace silicn atms

More information

Gasometric Determination of NaHCO 3 in a Mixture

Gasometric Determination of NaHCO 3 in a Mixture 60 50 40 0 0 5 15 25 35 40 Temperature ( o C) 9/28/16 Gasometrc Determnaton of NaHCO 3 n a Mxture apor Pressure (mm Hg) apor Pressure of Water 1 NaHCO 3 (s) + H + (aq) Na + (aq) + H 2 O (l) + CO 2 (g)

More information

Physics for Scientists and Engineers. Chapter 9 Impulse and Momentum

Physics for Scientists and Engineers. Chapter 9 Impulse and Momentum Physcs or Scentsts and Engneers Chapter 9 Impulse and Momentum Sprng, 008 Ho Jung Pak Lnear Momentum Lnear momentum o an object o mass m movng wth a velocty v s dened to be p mv Momentum and lnear momentum

More information

How can standard heats of formation be used to calculate the heat of a reaction?

How can standard heats of formation be used to calculate the heat of a reaction? Answer Key ALE 28. ess s Law and Standard Enthalpies Frmatin (Reerence: Chapter 6 - Silberberg 4 th editin) Imprtant!! Fr answers that invlve a calculatin yu must shw yur wrk neatly using dimensinal analysis

More information

Chapter 07: Kinetic Energy and Work

Chapter 07: Kinetic Energy and Work Chapter 07: Knetc Energy and Work Conservaton o Energy s one o Nature s undamental laws that s not volated. Energy can take on derent orms n a gven system. Ths chapter we wll dscuss work and knetc energy.

More information

Trimester 2 Exam 3 Study Guide Honors Chemistry. Honors Chemistry Exam 3 Review

Trimester 2 Exam 3 Study Guide Honors Chemistry. Honors Chemistry Exam 3 Review Trimester 2 Exam 3 Study Guide Hnrs Chemistry BOND POLARITY Hnrs Chemistry Exam 3 Review Identify whether a bnd is plar r nnplar based ff difference in electrnegativity btwn 2 atms (electrnegativity values

More information

Phys 344 Ch 5 Lect 4 Feb 28 th,

Phys 344 Ch 5 Lect 4 Feb 28 th, hys 44 Ch 5 Lect 4 Feb 8 th, 009 1 Wed /4 Fr /6 Mn /9 Wed /11 Fr / 1 55 Dlute Slutn 56 Chemcal Equlbrum Revew Exam (C 107 S 60, 61 Bltzmann Statstcs Bnus: hys Sr hess resentatns @ 4pm HW17: 7,76,8 HW18:8,84,86,88,89,91

More information

WYSE Academic Challenge 2014 Sectional Physics Exam SOLUTION SET. [ F][ d] [ t] [ E]

WYSE Academic Challenge 2014 Sectional Physics Exam SOLUTION SET. [ F][ d] [ t] [ E] WYSE Aaem Challenge 0 Setnal hss Exam SOLUTION SET. Crret answer: E Unts Trque / unts pwer: [ r ][ ] [ E] [ t] [ r ][ ][ t] [ E] [ r ][ ][ t] [ ][ ] [ r ][ t] [ ] m s m s. Crret answer: D The net external

More information

ENGI 4421 Probability & Statistics

ENGI 4421 Probability & Statistics Lecture Ntes fr ENGI 441 Prbablty & Statstcs by Dr. G.H. Gerge Asscate Prfessr, Faculty f Engneerng and Appled Scence Seventh Edtn, reprnted 018 Sprng http://www.engr.mun.ca/~ggerge/441/ Table f Cntents

More information