The maximum heat transfer rate is for an infinite area counter flow heat exchanger.
|
|
|
- Suzanna Lindsey
- 5 years ago
- Views:
Transcription
1 IAM Heat Exangers 9. Aendix Illustratin f se nets in eat exangers 9.. Heat Exanger Effetiveness is is defined as: Atual Heat ransfer ate Maxiu Pssible Heat ransfer ate q q ax e axiu eat transfer rate is fr an infinite area unter flw eat exanger. q ax ( q ( i i ax i i i.e. in general: q & ( i ax ( in In a real eat exanger q ( ( i i i ( i ( & ( in i i ( & ( in i ( i i S: ( i & i if ( in and if ( & in ( i i ( i i ( 9.. ransfer Unit nsider a unter flw eat exanger: dq d d ake & < d d > nstant (s PDF reated wit FinePrint dffatr trial versin tt: 7
2 IAM Heat Exangers e erating line is a lt f te rresnding values f against in te exanger (wit sle s > fr & <. is is ared wit te equilibriu line wi is drawn su tat (sle. Sle f erating line: s & i i In tis situatin s ( & ( & in ax Fr tis ase: ( & i < and i i UA NU is a nn-diensinal exressin f te eat exanger size. ( in e greater te nuber f transfer units, te lser te erating line araes t te equilibriu line. 9.. arisn between LMD fatr and NU-effetiveness araes are tw exangers: [] Perfet unter flw (as referene [] eal exanger Ea as te sae q, U,,,,,, but teir areas are different. i i Aunterflw en F t and A atual (NU unterflw F t fr te sae value f (NU atual Als te araeter S fr ( in S fr ( in araeter ( & in ( & ax eiter r ( & ( & ax in i.e. a ne-t-ne rresndene exists between te tw sets f araeters. PDF reated wit FinePrint dffatr trial versin tt: 8
3 IAM Heat Exangers 9.4. eerature rss in a sell and tube eat exanger nsider a ne sell-ass, tw tube-ass eat exanger: A teerature rss is iinent wen: ( i but ( & ( in i i r ( & ( in i ( i i In te abve ase & < i i..(9.4. i i i + i i i + i i But if tere is a teerature rss: & and if ( in & ten ( & ( & in ax i i Substituting fr in Equatin 9.4.: + is an be drawn n te arriate NU lt t illustrate te urrene f te teerature rss. PDF reated wit FinePrint dffatr trial versin tt: 9
4 IAM Heat Exangers eerature distributin in a (, sell and tube eat exanger e detailed teerature distributin deends n te relative ats taken b te sell and tube fluids Graial reresentatin f Heat Exangers in Series ake & & in ( s sle > Overall effetiveness: Fr te diagra, Siilarl: us i i i i ( 4 4 i i i 4 4 PDF reated wit FinePrint dffatr trial versin tt:
5 IAM Heat Exangers In general, fr n asses: Inverting: n i i i n i i i (9.6. Slving fr, i n n i i i i i If all te units are idential ( n {( ( } n {( ( } r inverting: n {( ( } n {( ( } i and we ut (aait ati...(9.6. Seial ase f Fr te abve exressin, fr te seial ase f, is undefined. e diagra n te left a be used t investigate te situatin. In tis ase te erating line as a sle f unit. We nsider n idential exangers in series. e stri AXZ' reresents te first f tese. Fr te first exanger : XY XZ but ZZ but XY AX n is silifies t : n As befre: { n } { n} n + ( n ( n n DE DF n sine tere are"n"stris and XY (ZZ PDF reated wit FinePrint dffatr trial versin tt:
6 IAM Heat Exangers Heat exangers in Series-Parallel nfiguratin In general fr n asses: n i i i Fr te seial ase were 0, ten n { i} and { i} i n i us, fr 0, te teerature f te sendar fluid reains nstant and s te situatin alies t an te f exanger and an te f nnetin fr te sendar fluid (series, arallel r binatins f te tw. 0. eferene Bks. JANNA, Willia S, Engineering Heat ransfer, Van-Nstrand einld Internatinal. HOLMAN, J P, Heat ransfer, MGraw-Hill. KEIH, F, ransissin de la aleur (ranslatin f Priniles f Heat ransfer, Massn et ie. 4. KAYS, W M and LONDON, A L, at Heat Exangers, MGraw-Hill 5. SAADUA, J F, Initiatin aux ransferts eriques, enique et Duentatin. 6. SHAMSUNDA, N, A rert f te lg-ean teerature-differene rretin fatr, Meanial Engineering News, 9(, 4-5, LIENHAD, J (iv and LIENHAD, J (v, A Heat ransfer extbk, rd editin (August 00. Available fr dwnlad n te Internet at: tt:web.it.edulienardwwwatt.tl PDF reated wit FinePrint dffatr trial versin tt:
7 IAM Heat Exangers. ables f eretial elatinsis fr Heat Exangers.. Heat exanger effetiveness relatins N NU ( in ( in ( ax UA & effetiveness Flw geetr elatin Duble ie: Parallel-flw { ex[ N( + ]} ( + unter-flw ex[ N( ] ex[ N( ] rss flw: unter-flw ( N ( N + Bt fluids unixed ex( Nn ex were n n N 0. Bt fluids ixed + ex( N ex( N N ( ax ixed, ( in unixed ( { ex[ ( ex( N ]} ( ax unixed, ( in Sell and tube: ixed ex{ ( [ ex( N ]} One sell ass,, 4, 6 tube asses + + ( + + ex ex { N( + } { ( N + } All exangers wit 0: ex( N PDF reated wit FinePrint dffatr trial versin tt:
8 IAM Heat Exangers.. NU relatins fr eat exangers ( in ( ax effetiveness N NU UA ( in Flw geetr Duble ie: elatin Parallel-flw lg { ( + } N e ( + unter-flw ( - N lge unter-flw ( N (- rss flw: ( ax ixed, ( in unixed N lg [ + ( lg ( ] e e ( ax unixed, ( in Sell and tube: ixed N ( lg [ + lg ( ] e e One sell ass,, 4, 6 tube asses N ( + lg e ( ( ( + + ( + All exangers wit 0: N lg ( e PDF reated wit FinePrint dffatr trial versin tt: 4
9 IAM Heat Exangers. arts.. Sell and ube Heat Exanger.. rretin Fatr Plt fr (, Sell and ube Heat Exanger PDF reated wit FinePrint dffatr trial versin tt: 5
10 IAM Heat Exangers.. en Brek lt fr utlet teerature f a (, Sell and ube Heat Exanger.4. &.5. Effetiveness-NU lts fr (a Duble ie; (b (, Sell and ube Exangers PDF reated wit FinePrint dffatr trial versin tt: 6
11 IAM Heat Exangers.6. rretin Fatr Plt fr rssflw Heat Exanger wit Bt Fluids Unixed.7. Effetiveness-NU Plt fr rssflw Heat Exanger wit Bt Fluids Unixed PDF reated wit FinePrint dffatr trial versin tt: 7
12 IAM Heat Exangers.8. rretin Fatr Plt fr rssflw Heat Exanger wit One Fluid Mixed.9. Effetiveness-NU Plt fr rssflw Heat Exanger wit One Fluid Mixed PDF reated wit FinePrint dffatr trial versin tt: 8
13 IAM Heat Exangers.0. rretin Fatr Plt fr rssflw Heat Exanger wit Bt Fluids Mixed.. Effetiveness-NU Plt fr rssflw Heat Exanger wit Bt Fluids Mixed PDF reated wit FinePrint dffatr trial versin tt: 9
Lecture 3 Heat Exchangers
L3 Leture 3 Heat Exangers Heat Exangers. Heat Exangers Transfer eat from one fluid to anoter. Want to imise neessary ardware. Examples: boilers, ondensors, ar radiator, air-onditioning oils, uman body.
Heat exchanger. Heat exchanger
s are deves n w eat s transferred between tw fluds at dfferent teperatures wtut any xng f fluds. type. Dret eat transfer type 2. Strage type 3. Dret ntat type ttps://www.faebk./0000085304058/vdes/96230780490756/.
The Second Law implies:
e Send Law ilie: ) Heat Engine η W in H H L H L H, H H ) Ablute eerature H H L L Sale, L L W ) Fr a yle H H L L H 4) Fr an Ideal Ga Cyle H H L L L δ reerible ree d Claiu Inequality δ eerible Cyle fr a
Outline. Heat Exchangers. Heat Exchangers. Compact Heat Exchangers. Compact Heat Exchangers II. Heat Exchangers April 18, ME 375 Heat Transfer 1
Hat Exangr April 8, 007 Hat Exangr Larry artt Manial Engrg 375 Hat ranfr April 8, 007 Outl Bai ida f at xangr Ovrall at tranfr ffiint Lg-man tmpratur diffrn mtd Efftivn NU mtd ratial nidratin Hat Exangr
Module 7: Solved Problems
Mdule 7: Slved Prblems 1 A tn-walled nentr tube eat exanger f 019-m lengt s t be used t eat denzed water frm 40 t 60 at a flw rate f 5 kg/s te denzed water flws trug te nner tube f 30-mm dameter wle t
Earlier Lecture. This gas tube is called as Pulse Tube and this phenomenon is called as Pulse Tube action.
31 1 Earlier Leture In te earlier leture, we ave seen a Pulse Tube (PT) ryoooler in wi te meanial displaer is removed and an osillating gas flow in te tin walled tube produes ooling. Tis gas tube is alled
Journal of Theoretics
Jurnal f Teretis Vlue 6-1, Feb-Mar 00 Te Pssibility f Neutrins Deteted as Tayns Takaaki Musa usa@jda-trdi.g.j usa@jg.ejnet.ne.j M.R.I., 3-11-7-601, Naiki, Kanazawa-ku Ykaa, 36-0005, Jaan Abstrat: Reent
Given: Hot fluid oil, Cold fluid - water (T 1, T 2 ) (t 1, t 2 ) Water
. In a counter flow double pipe eat excanger, oil is cooled fro 85 to 55 by water entering at 5. Te ass flow rate of oil is 9,800 kg/ and specific eat f oil is 000 J/kg K. Te ass flow rate of water is
Math Spring 2013 Solutions to Assignment # 3 Completion Date: Wednesday May 15, (1/z) 2 (1/z 1) 2 = lim
Mat 311 - Spring 013 Solutions to Assignment # 3 Completion Date: Wednesday May 15, 013 Question 1. [p 56, #10 (a)] 4z Use te teorem of Sec. 17 to sow tat z (z 1) = 4. We ave z 4z (z 1) = z 0 4 (1/z) (1/z
1. (2.5.1) So, the number of moles, n, contained in a sample of any substance is equal N n, (2.5.2)
Lecture.5. Ideal gas law We have already discussed general rinciles of classical therodynaics. Classical therodynaics is a acroscoic science which describes hysical systes by eans of acroscoic variables,
Heat Transfer and Friction Characteristics of Heat Exchanger Under Lignite Fly-Ash
The 20th Cnferene f Mehanial Engineering Netwrk f Thailand 18-20 Otber 2006, Nakhn Rathasima, Thailand Heat Transfer and Fritin Charateristis f Heat Exhanger Under ignite Fly-Ash Pipat Juangjandee 1*,
Maximum work for Carnot-like heat engines with infinite heat source
Maximum work for arnot-like eat engines wit infinite eat soure Rui Long and Wei Liu* Sool of Energy and Power Engineering, Huazong University of Siene and enology, Wuan 4374, ina orresponding autor: Wei
4. The slope of the line 2x 7y = 8 is (a) 2/7 (b) 7/2 (c) 2 (d) 2/7 (e) None of these.
Mat 11. Test Form N Fall 016 Name. Instructions. Te first eleven problems are wort points eac. Te last six problems are wort 5 points eac. For te last six problems, you must use relevant metods of algebra
1 Proving the Fundamental Theorem of Statistical Learning
THEORETICAL MACHINE LEARNING COS 5 LECTURE #7 APRIL 5, 6 LECTURER: ELAD HAZAN NAME: FERMI MA ANDDANIEL SUO oving te Fundaental Teore of Statistical Learning In tis section, we prove te following: Teore.
NAME Borough of Manhattan Community College Course Physics 110 Sec 721 Instructor: Dr. Hulan E. Jack Jr. Date December 19, 2006
Brug f Manattan unity llege urse Pysics 110 Sec 721 nstructr: Dr. Hulan E. Jack Jr. Date Deceber 19, 2006 inal Exa NSTRUTONS - D 7 prbles : D Prble 1, 2 fr Prble 2,3 and 4, 2 fr Prbles 5,6 and 7, 2 fr
Heat Transfer/Heat Exchanger
Heat ransfer/heat Excanger How is te eat transfer? Mecanism of Convection Applications. Mean fluid Velocity and Boundary and teir effect on te rate of eat transfer. Fundamental equation of eat transfer
(b) The heat transfer can be determined from an energy balance on the system
8-5 Heat is transferred to a iston-cylinder device wit a set of stos. e work done, te eat transfer, te exergy destroyed, and te second-law efficiency are to be deterined. Assutions e device is stationary
BASIC DIRECT-CURRENT MEASUREMENTS
Brwn University Physics 0040 Intrductin BASIC DIRECT-CURRENT MEASUREMENTS The measurements described here illustrate the peratin f resistrs and capacitrs in electric circuits, and the use f sme standard
CFD Investigation of Clearance on Pressure Distribution and Fluid Film Thickness in Hydrodynamic Journal Bearing
Vlue 4, Issue (016) 571-575 ISS 47-58 Internatinal Jurnal f Advane Resear and Innvatin CFD Investigatin f Clearane n Pressure Distributin and Fluid Fil Tikness in Hydrdynai Jurnal Bearing Ait Maaan 1,
Question 2-1. Solution 2-1 CHAPTER 2 HYDROSTATICS
CHAPTER HYDROSTATICS. INTRODUCTION Hydraulic engineers have any engineering applicatins in hich they have t cpute the frce being exerted n suberged surfaces. The hydrstatic frce n any suberged plane surface
(b) Using the ideal gas equation of state, and noting that the total mass of gas occupies the same total volume at the final state as initially: where
6.55 Given: An inulated cylinder i initially divided int halve y a itn. On either ide the itn i a ga at a knwn tate. The itn i releaed and equiliriu i attained. Find: Deterine the inal reure, inal teerature,
Physics 231 Lecture 35
ysis 1 Leture 5 Main points of last leture: Heat engines and effiieny: eng e 1 Carnot yle and Carnot engine. eng e 1 is in Kelvin. Refrigerators CO eng Ideal refrigerator CO rev reversible Entropy ΔS Computation
Chapter 4: Numerical Methods for Common Mathematical Problems
1 Capter 4: Numerical Metods for Common Matematical Problems Interpolation Problem: Suppose we ave data defined at a discrete set of points (x i, y i ), i = 0, 1,..., N. Often it is useful to ave a smoot
5.1 The derivative or the gradient of a curve. Definition and finding the gradient from first principles
Capter 5: Dierentiation In tis capter, we will study: 51 e derivative or te gradient o a curve Deinition and inding te gradient ro irst principles 5 Forulas or derivatives 5 e equation o te tangent line
Exponentials and Logarithms Review Part 2: Exponentials
Eponentials and Logaritms Review Part : Eponentials Notice te difference etween te functions: g( ) and f ( ) In te function g( ), te variale is te ase and te eponent is a constant. Tis is called a power
ESCI 341 Atmospheric Thermodynamics Lesson 11 The Second Law of Thermodynamics
ESCI 341 Atmosperi ermodynamis Lesson 11 e Seond Law of ermodynamis Referenes: Pysial Cemistry (4 t edition), Levine ermodynamis and an Introdution to ermostatistis, Callen HE SECOND LAW OF HERMODYNAMICS
Precalculus Notes: Unit 6 Law of Sines & Cosines, Vectors, & Complex Numbers. A can be rewritten as B
Date: 6.1 Law of Sines Syllaus Ojetie: 3.5 Te student will sole appliation prolems inoling triangles (Law of Sines). Deriing te Law of Sines: Consider te two triangles. a C In te aute triangle, sin and
Math 31A Discussion Notes Week 4 October 20 and October 22, 2015
Mat 3A Discussion Notes Week 4 October 20 and October 22, 205 To prepare for te first midterm, we ll spend tis week working eamples resembling te various problems you ve seen so far tis term. In tese notes
SS1 QUESTIONS FOR 2018 MATHSCHAMP
SS QUESTIONS FOR 08 MATHSCHAMP. A student exressed the nuber 67098 correct to 6700. Which of the following correctly describes the degree of aroxiation ade? I. 4 significant figures II. nearest ten III.
This document is published in: Economics Letters (2001), 72(3), DOI: /S (01) Elsevier Science B.V.
Tis document is publised in: Economics Letters (2001), 72(3), 303-307. DOI: 10.1016/S0165-1765(01)00445-1 2001 Elsevier Science B.V. Extending communication-proof equilibrium to infinit games José Luis
Chapter 3. Problem Solutions
Capter. Proble Solutions. A poton and a partile ave te sae wavelengt. Can anyting be said about ow teir linear oenta opare? About ow te poton's energy opares wit te partile's total energy? About ow te
MATH 1A Midterm Practice September 29, 2014
MATH A Midterm Practice September 9, 04 Name: Problem. (True/False) If a function f : R R is injective, ten f as an inverse. Solution: True. If f is injective, ten it as an inverse since tere does not
1 Calculus. 1.1 Gradients and the Derivative. Q f(x+h) f(x)
Calculus. Gradients and te Derivative Q f(x+) δy P T δx R f(x) 0 x x+ Let P (x, f(x)) and Q(x+, f(x+)) denote two points on te curve of te function y = f(x) and let R denote te point of intersection of
LIMITS AND DERIVATIVES CONDITIONS FOR THE EXISTENCE OF A LIMIT
LIMITS AND DERIVATIVES Te limit of a function is defined as te value of y tat te curve approaces, as x approaces a particular value. Te limit of f (x) as x approaces a is written as f (x) approaces, as
Tangent Lines-1. Tangent Lines
Tangent Lines- Tangent Lines In geometry, te tangent line to a circle wit centre O at a point A on te circle is defined to be te perpendicular line at A to te line OA. Te tangent lines ave te special property
Physics 321 Solutions for Final Exam
Page f 8 Physics 3 Slutins fr inal Exa ) A sall blb f clay with ass is drpped fr a height h abve a thin rd f length L and ass M which can pivt frictinlessly abut its center. The initial situatin is shwn
Lecture 21. Numerical differentiation. f ( x+h) f ( x) h h
Lecture Numerical differentiation Introduction We can analytically calculate te derivative of any elementary function, so tere migt seem to be no motivation for calculating derivatives numerically. However
3.1 Extreme Values of a Function
.1 Etreme Values of a Function Section.1 Notes Page 1 One application of te derivative is finding minimum and maimum values off a grap. In precalculus we were only able to do tis wit quadratics by find
These errors are made from replacing an infinite process by finite one.
Introduction :- Tis course examines problems tat can be solved by metods of approximation, tecniques we call numerical metods. We begin by considering some of te matematical and computational topics tat
HCB-3 Edition. Solutions Chapter 12 Problems. SOLUTION: Refer to saturated steam table (Table A3-SI) and superheated steam table (Table A4-SI)
HCB- Editin 12.1 Slutins Chapter 12 Prbles GIVEN: Fllwing table fr water: T (C p (kpa v ( /kg Phase 60 (1.25 (2 ( 175 (4 Saturated vapr 00 00 (5 (6 100 10 (7 (8 (9 (10 0.001097 Saturated vapr 1000 10 (11
Mock Exam 4 Paper 1. 1 Achiever. Section A(1) ab = ab. = a b. by (a), we have x < 46 (3) 25. \ The range of the values of x is x 7 3.
Mock Exa Mock Exa aper Section A().. 6 ( ) 0 a b 0 ( ) a b 9 6 9 6 a b n n n n. (a) 9a b ( a) ( b) ( a b)( a + b) 0 + 7x 6. (a) < 6x 0 + 7x < 66 8x 7x + 8x < 66 0 x < 6 6 x < For 7 - x 0, 7 x 0 + 7x For
Section 3.1: Derivatives of Polynomials and Exponential Functions
Section 3.1: Derivatives of Polynomials and Exponential Functions In previous sections we developed te concept of te derivative and derivative function. Te only issue wit our definition owever is tat it
Chemical Engineering 170 October 16, 2003 Midterm Exam Closed Book and Closed Notes One 8.5 x 11 in. page of notes allowed
Cheical ngineering 70 Octber 6, 00 Mier xa Clsed B and Clsed Ntes One 8.5 x in. page f ntes allwed ectin. hrt Answers. Nae fur interactins invlved in aintaining the tertiary structure f prteins. Hydrgen
WYSE Academic Challenge 2004 State Finals Mathematics Solution Set
WYSE Academic Callenge 00 State Finals Matematics Solution Set. Answer: c. We ave a sstem of tree equations and tree unknowns. We ave te equations: x + + z 0, x + 6 + 7z 9600, and 7x + + z 90. Wen we solve,
Part 2: Introduction to Open-Channel Flow SPRING 2005
Part : Introduction to Open-Cannel Flow SPRING 005. Te Froude number. Total ead and specific energy 3. Hydraulic jump. Te Froude Number Te main caracteristics of flows in open cannels are tat: tere is
(4.2) -Richardson Extrapolation
(.) -Ricardson Extrapolation. Small-O Notation: Recall tat te big-o notation used to define te rate of convergence in Section.: Suppose tat lim G 0 and lim F L. Te function F is said to converge to L as
1 2 x Solution. The function f x is only defined when x 0, so we will assume that x 0 for the remainder of the solution. f x. f x h f x.
Problem. Let f x x. Using te definition of te derivative prove tat f x x Solution. Te function f x is only defined wen x 0, so we will assume tat x 0 for te remainder of te solution. By te definition of
Chapter 1 Functions and Graphs. Section 1.5 = = = 4. Check Point Exercises The slope of the line y = 3x+ 1 is 3.
Capter Functions and Graps Section. Ceck Point Exercises. Te slope of te line y x+ is. y y m( x x y ( x ( y ( x+ point-slope y x+ 6 y x+ slope-intercept. a. Write te equation in slope-intercept form: x+
Y.J. Cho **, Hazim Awbi** & Taghi Karimipanah* *) Fresh AB, SWEDEN **) University of Reading, UK
The Characteristics f Wall Cnfluent Jets fr Ventilated Enclsures 9 th Internatinal Cnference n Air Distributin in Rs niversity f Cibra PORTGAL Y.J. Ch **, Hazi Awbi** & Taghi Kariipanah* *) Fresh AB, SWEDEN
CONVECTION IN MICROCHANNELS
CAPER. Intrductin CONVECION IN MICROCANNELS.. Cntinuu and hernaic ythei. Previu chater are baed n tw fundaental autin: () Cntinuu: Navier-Stke equatin, and the energy equatin are alicable () hernaic equilibriu:
- Prefixes 'mono', 'uni', 'bi' and 'du' - Why are there no asprins in the jungle? Because the parrots ate them all.
- Prfs '', '', 'b' a '' - Na: Wrsar 27 Dat: W ar tr asrs t? Bas t arrts at t a. At t btt f t a s a st f wrs. Ts wrs ar t. T wrs av b a rta (ra arss), vrta (ra w) r aa (fr rr t rr). W f a wr, raw a at r
Section 2.1 The Definition of the Derivative. We are interested in finding the slope of the tangent line at a specific point.
Popper 6: Review of skills: Find tis difference quotient. f ( x ) f ( x) if f ( x) x Answer coices given in audio on te video. Section.1 Te Definition of te Derivative We are interested in finding te slope
SECTION 1.10: DIFFERENCE QUOTIENTS LEARNING OBJECTIVES
(Section.0: Difference Quotients).0. SECTION.0: DIFFERENCE QUOTIENTS LEARNING OBJECTIVES Define average rate of cange (and average velocity) algebraically and grapically. Be able to identify, construct,
Physics I Keystone Institute of Technology & Management, Surajgarh Unit V. Postulates of Einstein s special theory of relativity
Physis I Keystne Institte f Tehnlgy & Manageent, Srajgarh Unit V Pstlates f Einstein s speial thery f relativity. Priniple f Physial Eqivalene The laws f physis, (bth ehanis and eletrdynais) epressed in
THERMODYNAMICS Lecture 15: Heat exchangers
HERMODYNAMICS Leture 5: Heat exangers Pierwsza strona Introdution to Heat Exangers Wat Are Heat Exangers? Heat exangers are units designed to transfer eat from a ot flowing stream to a old flowing stream
Lecture 27: Entropy and Information Prof. WAN, Xin
General Pysis I Leture 27: Entropy and Information Prof. WAN, Xin xinwan@zju.edu.n ttp://zimp.zju.edu.n/~xinwan/ 1st & 2nd Laws of ermodynamis e 1st law speifies tat we annot get more energy out of a yli
MVT and Rolle s Theorem
AP Calculus CHAPTER 4 WORKSHEET APPLICATIONS OF DIFFERENTIATION MVT and Rolle s Teorem Name Seat # Date UNLESS INDICATED, DO NOT USE YOUR CALCULATOR FOR ANY OF THESE QUESTIONS In problems 1 and, state
Lecture 10: Carnot theorem
ecture 0: Carnot teorem Feb 7, 005 Equivalence of Kelvin and Clausius formulations ast time we learned tat te Second aw can be formulated in two ways. e Kelvin formulation: No process is possible wose
Basic Thermodynamic Relations
Basic herodynaic Relations Isolated syste: this is a syste that does not exchange energy with the surrounding edia. First Postulate (equilibriu theore) : Isolated syste always reaches the equilibriu state
Time varying fields and Maxwell's equations Chapter 9
Tie varying fields and Maxwell's equatins hapter 9 Dr. Naser Abu-Zaid Page 9/7/202 FARADAY LAW OF ELETROMAGNETI INDUTION A tie varying agnetic field prduces (induces) a current in a clsed lp f wire. The
5.1 We will begin this section with the definition of a rational expression. We
Basic Properties and Reducing to Lowest Terms 5.1 We will begin tis section wit te definition of a rational epression. We will ten state te two basic properties associated wit rational epressions and go
Similar Right Triangles
9.3 EX EENIL KNOWLEGE N KILL G.8. G.8. imilar igt riangles Essential Question How are altitudes and geometric means of rigt triangles related? Writing a onjecture Work wit a partner. a. Use dnamic geometr
Determination of heat transfer intensity between free streaming water film and rigid surface using thermography
Determination of eat transfer intensity between free ing water film and rigid surfae using termograpy Faulty of meanial engineering and naval ariteture University of Zagreb, Croatia Abstrat by S. Švaić,
Homework 1. Problem 1 Browse the 331 website to answer: When you should use data symbols on a graph. (Hint check out lab reports...
Homework 1 Problem 1 Browse te 331 website to answer: Wen you sould use data symbols on a grap. (Hint ceck out lab reports...) Solution 1 Use data symbols to sow data points unless tere is so muc data
3.4 Worksheet: Proof of the Chain Rule NAME
Mat 1170 3.4 Workseet: Proof of te Cain Rule NAME Te Cain Rule So far we are able to differentiate all types of functions. For example: polynomials, rational, root, and trigonometric functions. We are
PHYSICS 151 Notes for Online Lecture #23
PHYSICS 5 Ntes fr Online Lecture #3 Peridicity Peridic eans that sething repeats itself. r exaple, eery twenty-fur hurs, the Earth aes a cplete rtatin. Heartbeats are an exaple f peridic behair. If yu
10 Derivatives ( )
Instructor: Micael Medvinsky 0 Derivatives (.6-.8) Te tangent line to te curve yf() at te point (a,f(a)) is te line l m + b troug tis point wit slope Alternatively one can epress te slope as f f a m lim
. Compute the following limits.
Today: Tangent Lines and te Derivative at a Point Warmup:. Let f(x) =x. Compute te following limits. f( + ) f() (a) lim f( +) f( ) (b) lim. Let g(x) = x. Compute te following limits. g(3 + ) g(3) (a) lim
ALGEBRA AND TRIGONOMETRY REVIEW by Dr TEBOU, FIU. A. Fundamental identities Throughout this section, a and b denotes arbitrary real numbers.
ALGEBRA AND TRIGONOMETRY REVIEW by Dr TEBOU, FIU A. Fundamental identities Trougout tis section, a and b denotes arbitrary real numbers. i) Square of a sum: (a+b) =a +ab+b ii) Square of a difference: (a-b)
3B SCIENTIFIC PHYSICS
3B SCIENTIFIC PHYSICS Peltier Heat Pump 0076 Instrution manual 05/7 TL/JS Transport ase Semati view 3 Stirrer unit 4 Connetor for stirrer unit 5 Connetor for power supply 6 Stirring rod old side 7 Peltier
3 Thermodynamics and Statistical mechanics
Therodynaics and Statistical echanics. Syste and environent The syste is soe ortion of atter that we searate using real walls or only in our ine, fro the other art of the universe. Everything outside the
TUTORIAL 1 SIMPLE HARMONIC MOTION. Instructor: Kazumi Tolich
TUTORIAL 1 SIMPLE HARMONIC MOTION Instructor: Kazui Tolich About tutorials 2 Tutorials are conceptual exercises that should be worked on in groups. Each slide will consist of a series of questions that
Chapter 5 Differentiation
Capter 5 Differentiation Course Title: Real Analsis 1 Course Code: MTH31 Course instrutor: Dr Atiq ur Reman Class: MS-II Course URL: wwwmatitorg/atiq/fa15-mt31 Derivative of a funtion: Let f be defined
Solutions to Homework #05 MATH ln z 2 + x 2 1 = 2x2 z 2 + x 2 + ln z2 + x 2. = x. ln z 2 + x 2 2z z 2 + x 2 = 2xz
Solutions to Homeork #05 MATH Kaai Section. (I) Exercise #. g x and g z : Product Rule: g x = x @ ln z + x + ln z + x @ [x] = x x z + x + ln z + x = x z + x + ln z + x x is eld constant. g z = x @ ln z
1. Consider the trigonometric function f(t) whose graph is shown below. Write down a possible formula for f(t).
. Consider te trigonometric function f(t) wose grap is sown below. Write down a possible formula for f(t). Tis function appears to be an odd, periodic function tat as been sifted upwards, so we will use
Outline. Steady Heat Transfer with Conduction and Convection. Review Steady, 1-D, Review Heat Generation. Review Heat Generation II
Steady Heat ansfe ebuay, 7 Steady Heat ansfe wit Cnductin and Cnvectin ay Caett Mecanical Engineeing 375 Heat ansfe ebuay, 7 Outline eview last lectue Equivalent cicuit analyses eview basic cncept pplicatin
rcrit (r C + t m ) 2 ] crit + t o crit The critical radius is evaluated at a given axial location z from the equation + (1 , and D = 4D = 555.
![rcrit (r C + t m ) 2 ] crit + t o crit The critical radius is evaluated at a given axial location z from the equation + (1 , and D = 4D = 555.](/thumbs/71/66154865.jpg "rcrit (r C + t m ) 2 ] crit + t o crit The critical radius is evaluated at a given axial location z from the equation + (1 , and D = 4D = 555.")
hapter 1 c) When the average bld velcity in the capillary is reduced by a factr f 10, the delivery f the slute t the capillary is liited s that the slute cncentratin after crit 0.018 c is equal t er at
Continuity and Differentiability Worksheet
Continuity and Differentiability Workseet (Be sure tat you can also do te grapical eercises from te tet- Tese were not included below! Typical problems are like problems -3, p. 6; -3, p. 7; 33-34, p. 7;
The Derivative The rate of change
Calculus Lia Vas Te Derivative Te rate of cange Knowing and understanding te concept of derivative will enable you to answer te following questions. Let us consider a quantity wose size is described by
Natural Convection Experiment Measurements from a Vertical Surface
OBJECTIVE Natural Convetion Experiment Measurements from a Vertial Surfae 1. To demonstrate te basi priniples of natural onvetion eat transfer inluding determination of te onvetive eat transfer oeffiient.
4.2 - Richardson Extrapolation
. - Ricardson Extrapolation. Small-O Notation: Recall tat te big-o notation used to define te rate of convergence in Section.: Definition Let x n n converge to a number x. Suppose tat n n is a sequence
Chapter 4 The debroglie hypothesis
Capter 4 Te debrglie yptesis In 194, te Frenc pysicist Luis de Brglie after lking deeply int te special tery f relatiity and ptn yptesis,suggested tat tere was a mre fundamental relatin between waes and
232 Calculus and Structures
3 Calculus and Structures CHAPTER 17 JUSTIFICATION OF THE AREA AND SLOPE METHODS FOR EVALUATING BEAMS Calculus and Structures 33 Copyrigt Capter 17 JUSTIFICATION OF THE AREA AND SLOPE METHODS 17.1 THE
1.5 Functions and Their Rates of Change
66_cpp-75.qd /6/8 4:8 PM Page 56 56 CHAPTER Introduction to Functions and Graps.5 Functions and Teir Rates of Cange Identif were a function is increasing or decreasing Use interval notation Use and interpret
The Derivative as a Function
Section 2.2 Te Derivative as a Function 200 Kiryl Tsiscanka Te Derivative as a Function DEFINITION: Te derivative of a function f at a number a, denoted by f (a), is if tis limit exists. f (a) f(a + )
Exam 1 Review Solutions
Exam Review Solutions Please also review te old quizzes, and be sure tat you understand te omework problems. General notes: () Always give an algebraic reason for your answer (graps are not sufficient),
MAT 1275: Introduction to Mathematical Analysis
1 MT 1275: Intrdutin t Mtemtil nlysis Dr Rzenlyum Slving Olique Tringles Lw f Sines Olique tringles tringles tt re nt neessry rigt tringles We re ging t slve tem It mens t find its si elements sides nd
We name Functions f (x) or g(x) etc.
Section 2 1B: Function Notation Bot of te equations y 2x +1 and y 3x 2 are functions. It is common to ave two or more functions in terms of x in te same problem. If I ask you wat is te value for y if x
Lecture 17. Dielectric Materials
Lecture 17 Dielectric Materials 3/ 3 3 3/ 3/ 4 4 exp = = = e R R B B e B v c B g v c e k k k k E π π π Dielectric aterials play a large rle in electrnics. One exaple was te xide in te MOS structures. Als
SCHMIDT THEORY FOR STIRLING ENGINES
SHMIDT THOY FO STILING NGINS KOIHI HIATA Musashin-jjutaku 6-10, Gakuen -6-1, Musashimurayama, Tky 08, Japan Phne & Fax: +81-45-67-0086 e-mail: khirata@gem.bekkame.ne.jp url: http://www.bekkame.ne.jp/~khirata
, 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
Lecture 10 Adiabatic Processes
ASME231 Atmsheri hermdynamis NC A& State U Deartment f Physis Dr. Yuh-Lang Lin htt://meslab.rg ylin@nat.edu Leture 10 Adiabati Presses (Se.3.5 f Hess) [Classial equatin editr: 0 dq ] Definitin: If a thermdynami
Higher Derivatives. Differentiable Functions
Calculus 1 Lia Vas Higer Derivatives. Differentiable Functions Te second derivative. Te derivative itself can be considered as a function. Te instantaneous rate of cange of tis function is te second derivative.
Electrochemistry. Reduction: the gaining of electrons. Reducing agent (reductant): species that donates electrons to reduce another reagent.
Electrchemistry Review: Reductin: the gaining f electrns Oxidatin: the lss f electrns Reducing agent (reductant): species that dnates electrns t reduce anther reagent. Oxidizing agent (xidant): species
Observations on harmonic Progressions *
Oservations on armoni Progressions * Leonard Euler Under te name of armoni progressions all series of frations are understood, wose numerators are equal to ea oter, ut wose denominators on te oter onstitute
AVL trees. AVL trees
Dnamic set DT dnamic set DT is a structure tat stores a set of elements. Eac element as a (unique) ke and satellite data. Te structure supports te following operations. Searc(S, k) Return te element wose
CHAPTER 2 THERMODYNAMICS
CHAPER 2 HERMODYNAMICS 2.1 INRODUCION herodynaics is the study of the behavior of systes of atter under the action of external fields such as teerature and ressure. It is used in articular to describe
Physics Teach Yourself Series Topic 15: Wavelike nature of matter (Unit 4)
Pysics Teac Yourself Series Topic 15: Wavelie nature of atter (Unit 4) A: Level 14, 474 Flinders Street Melbourne VIC 3000 T: 1300 134 518 W: tss.co.au E: info@tss.co.au TSSM 2017 Page 1 of 8 Contents
Section 12. Afocal Systems
OPTI-0/0 Geoetrical and Instruental Optics Copyrigt 08 Jon E. Greivenkap - Section Aocal Systes Gaussian Optics Teores In te initial discussion o Gaussian optics, one o te teores deined te two dierent
Heat exchangers: Heat exchanger types:
Heat exhangers: he proess of heat exhange between two fluids that are at different temperatures and separated by a solid wall ours in many engineering appliations. he devie used to implement this exhange