The Governing Equations
|
|
- Kimberly Hudson
- 5 years ago
- Views:
Transcription
1 The Governng Equatons L. Goodman General Physcal Oceanography MAR 555 School for Marne Scences and Technology Umass-Dartmouth
2 Dynamcs of Oceanography The Governng Equatons- (IPO-7) Mass Conservaton and Momentum Equaton Conservaton of Mass Flow Water s approxmately ncompressble Volume flow of water gong n = Volume flow of water gong out.
3 Text: IPO- Introducton to Physcal Oceanography by Bob Stewart Download pdf fle verson for complete notes and/or use the on lne verson for summary. Introducton to Physcal Oceanography by Bob Stewart, Texas A&M
4 Mass Conservaton Q Q Q 1 2 = = v = v Q A A Volume Flow n Equals Volume flow Out Q 1 Q 2 3 m Q = volume flow rate, unts of sec m v = velocty, unts of sec A = Area perpendcular to velocty, unts of m 2
5 Example: Channel Flow of Varyng Depth L L v 1 H 1 H 2 v 2 Suppose the flow of velocty v 1 = 1 m/sec from a rver, L = 1 km wde and H 1 =3 m deep, emptes nto the contnental shelf at a depth of H 2 = 20 m, what s the ext velocty v 2 of ths flow? 3 Q 1 = nput volume flow rate = v1a 1 = 1 x(10 m)x(3m) = Q 2 = output volume flow rate v2a 2 = v2x((10 m)x(20m) 3 m m Usng Q 1 = Q2! v 2 = = sec sec m sec 3 m sec
6 Mass and Scalar Conservaton: Box Models Example Medterranean Outflow Salt Flow Conservaton V V S = V O O S VO S O (.79Sv)(38.3) = = S 36.2 m Sv = sec =! V + R + P = V + E Volume Flow Conservaton Input + Rverne + Precp = Output + Evaporaton o Estmate of fresh water nput R + P - E = V - V o = ? 10 m sec
7 Seawater s only slghtly compressble d! = dt 0 ρ Path of a flud parcel of densty ρ d! "! " u! " x u! " = + + y + u! z = 0 dt " t " x " y " z ds dt Homework Queston : Are = 0? = 0? dt dt T = temperature; S = salnty. Explan n words.
8 Generalzng Conservaton of Mass flow: Contnuty Equaton!u A = 0 sum of velocty tmes area over all 6 faces = 0 Contnuty Equaton!! u! v! w " # u = + + = 0! x! y! z
9 Example of Applcaton of Contnuty Equaton Estmate value of vertcal velocty n coastal upwellng 200m w =? u = cm 10 sec! 20km!! u! v! w " u " w # $ u = + + = 0 % + & 0! x! y! z " x " z Dmensonal Analyss! z 200 cm cm m! w " w "! u = 10 =.1 = 86! x sec sec day
10 Momentum (Euler) Equatons Total Force actng on a body = mass tmes ts acceleraton F = ma The forces on a cube of water (PD) Pressure dfference (PD) (Co) Corols Force (W) Weght (Fr) Frcton F du 1 a = " = ( PD + Co + Fr + W ) m dt! Note the subscrpt. "! = V densty of seawater
11 Fr = 0 No Frcton Case PD = "!p Why s there a mnus sgn?! x!! Co =(u? f)? s the "cross" product of vectors, f =2Ùsn(è), è s lattude; f =f =0 (an approxmaton) z x y W = -mg W =W =0 z x y f!! u! f! Corols force s always perpendcular to earth rotaton vector u!!!!! u " f! f " u Exercse Show that = f! u! and
12 Momentum Equaton Component Form (No Frcton) du 1 " p = # ( ) + f v dt! " x dv 1 " p = # ( ) # fu dt! " y dw 1 " p = # ( ) # g dt! " z where d " " " " = + u + v + w dt " t " x " y " z du 1 " p # fv = # ( ) dt! " x dv + fu = # dt 1 " p ( )! " y dw 1 " p = # ( ) # g dt! " z where d " " " " = + u + v + w dt " t " x " y " z
13 Summary of Fundamental Equatons du!! " p I. Momentum + ( f # u) = $ $ g + Fr dt " x! " u II. Contnuty % & u = = 0 " x d! III. Incompressblty = 0 dt Note that g g z x = = g g y =0 Homework: Wrte out equatons (1), (2) and (3) n component form (x,y,z); use the expanson of the total dervatve n tme.
14 The Hydrostatc Condton and Buoyancy Startng pont: vertcal momentum equaton 0 5 dw 1 " P = # ( ) # g dt! " z If the densty,!, s constant " p = #! g $ p = p0 #! gz " z where z = 0 surface, z = -H bottom, p s the pressure at the surface, atmospherc pressure, N p0 % 10 = 1 bar 2 m What s Pressure? Pressure s force (Unts of Newtons)per unt Area.)
15 p = 10 n m C z = 20m D z=4m A B Homework Problem kg! = 1000 m 3 A cylndrcal vessel of heght H = 20 m s flled wth water of densty to a heght of 4m. What s the pressure at: () pont A located on the bottom at the center, () at pont B located at the bottom of the vessel but at the rght sdewall; () at pont C at the surface of the water; (v) at pont D located at the vessel sdewall 5 2 m above the bottom.? Take the atmospherc pressure as p0 = 10 n 2. m
16 kg! = 1000 m 3 Homework Problems Contnued. II. Usng for an approxmaton of seawater densty at what depth would the pressure double from that of atmospherc pressure? A decbar s.1 bar, how much would you have to go beneath water for the pressure to ncrease 1 dbar pressure above atmospherc pressure. Can you see why some oceanographers use decbars nstead of meter to ndcate depth?
Friction and Ocean Turbulence Part I
Frcton and Ocean Trblence Part I L. Goodman General Physcal Oceanography MAR 555 School for Marne Scences and Technology Umass-Dartmoth Frcton and Ocean Trblence Part I 3 Types of Flow Potental Flow No
More informationWeek 11: Chapter 11. The Vector Product. The Vector Product Defined. The Vector Product and Torque. More About the Vector Product
The Vector Product Week 11: Chapter 11 Angular Momentum There are nstances where the product of two vectors s another vector Earler we saw where the product of two vectors was a scalar Ths was called the
More information2.29 Numerical Fluid Mechanics Fall 2011 Lecture 6
REVIEW of Lecture 5 2.29 Numercal Flud Mechancs Fall 2011 Lecture 6 Contnuum Hypothess and conservaton laws Macroscopc Propertes Materal covered n class: Dfferental forms of conservaton laws Materal Dervatve
More informationEN40: Dynamics and Vibrations. Homework 4: Work, Energy and Linear Momentum Due Friday March 1 st
EN40: Dynamcs and bratons Homework 4: Work, Energy and Lnear Momentum Due Frday March 1 st School of Engneerng Brown Unversty 1. The fgure (from ths publcaton) shows the energy per unt area requred to
More information2 Finite difference basics
Numersche Methoden 1, WS 11/12 B.J.P. Kaus 2 Fnte dfference bascs Consder the one- The bascs of the fnte dfference method are best understood wth an example. dmensonal transent heat conducton equaton T
More informationA Tale of Friction Basic Rollercoaster Physics. Fahrenheit Rollercoaster, Hershey, PA max height = 121 ft max speed = 58 mph
A Tale o Frcton Basc Rollercoaster Physcs Fahrenhet Rollercoaster, Hershey, PA max heght = 11 t max speed = 58 mph PLAY PLAY PLAY PLAY Rotatonal Movement Knematcs Smlar to how lnear velocty s dened, angular
More informationWeek3, Chapter 4. Position and Displacement. Motion in Two Dimensions. Instantaneous Velocity. Average Velocity
Week3, Chapter 4 Moton n Two Dmensons Lecture Quz A partcle confned to moton along the x axs moves wth constant acceleraton from x =.0 m to x = 8.0 m durng a 1-s tme nterval. The velocty of the partcle
More informationPart C Dynamics and Statics of Rigid Body. Chapter 5 Rotation of a Rigid Body About a Fixed Axis
Part C Dynamcs and Statcs of Rgd Body Chapter 5 Rotaton of a Rgd Body About a Fxed Axs 5.. Rotatonal Varables 5.. Rotaton wth Constant Angular Acceleraton 5.3. Knetc Energy of Rotaton, Rotatonal Inerta
More informationStudy Guide For Exam Two
Study Gude For Exam Two Physcs 2210 Albretsen Updated: 08/02/2018 All Other Prevous Study Gudes Modules 01-06 Module 07 Work Work done by a constant force F over a dstance s : Work done by varyng force
More informationPhysics 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 informationAngular Momentum and Fixed Axis Rotation. 8.01t Nov 10, 2004
Angular Momentum and Fxed Axs Rotaton 8.01t Nov 10, 2004 Dynamcs: Translatonal and Rotatonal Moton Translatonal Dynamcs Total Force Torque Angular Momentum about Dynamcs of Rotaton F ext Momentum of a
More informationτ rf = Iα I point = mr 2 L35 F 11/14/14 a*er lecture 1
A mass s attached to a long, massless rod. The mass s close to one end of the rod. Is t easer to balance the rod on end wth the mass near the top or near the bottom? Hnt: Small α means sluggsh behavor
More informationPhysics 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 informationPhysics 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 informationModule 1 : The equation of continuity. Lecture 1: Equation of Continuity
1 Module 1 : The equaton of contnuty Lecture 1: Equaton of Contnuty 2 Advanced Heat and Mass Transfer: Modules 1. THE EQUATION OF CONTINUITY : Lectures 1-6 () () () (v) (v) Overall Mass Balance Momentum
More informationImportant Dates: Post Test: Dec during recitations. If you have taken the post test, don t come to recitation!
Important Dates: Post Test: Dec. 8 0 durng rectatons. If you have taken the post test, don t come to rectaton! Post Test Make-Up Sessons n ARC 03: Sat Dec. 6, 0 AM noon, and Sun Dec. 7, 8 PM 0 PM. Post
More informationPHYS 705: Classical Mechanics. Newtonian Mechanics
1 PHYS 705: Classcal Mechancs Newtonan Mechancs Quck Revew of Newtonan Mechancs Basc Descrpton: -An dealzed pont partcle or a system of pont partcles n an nertal reference frame [Rgd bodes (ch. 5 later)]
More informationChapter 11 Angular Momentum
Chapter 11 Angular Momentum Analyss Model: Nonsolated System (Angular Momentum) Angular Momentum of a Rotatng Rgd Object Analyss Model: Isolated System (Angular Momentum) Angular Momentum of a Partcle
More information11. Dynamics in Rotating Frames of Reference
Unversty of Rhode Island DgtalCommons@URI Classcal Dynamcs Physcs Course Materals 2015 11. Dynamcs n Rotatng Frames of Reference Gerhard Müller Unversty of Rhode Island, gmuller@ur.edu Creatve Commons
More informationGravitational Acceleration: A case of constant acceleration (approx. 2 hr.) (6/7/11)
Gravtatonal Acceleraton: A case of constant acceleraton (approx. hr.) (6/7/11) Introducton The gravtatonal force s one of the fundamental forces of nature. Under the nfluence of ths force all objects havng
More informationWeek 8: Chapter 9. Linear Momentum. Newton Law and Momentum. Linear Momentum, cont. Conservation of Linear Momentum. Conservation of Momentum, 2
Lnear omentum Week 8: Chapter 9 Lnear omentum and Collsons The lnear momentum of a partcle, or an object that can be modeled as a partcle, of mass m movng wth a velocty v s defned to be the product of
More informationSpin-rotation coupling of the angularly accelerated rigid body
Spn-rotaton couplng of the angularly accelerated rgd body Loua Hassan Elzen Basher Khartoum, Sudan. Postal code:11123 E-mal: louaelzen@gmal.com November 1, 2017 All Rghts Reserved. Abstract Ths paper s
More informationPHYS 1101 Practice problem set 12, Chapter 32: 21, 22, 24, 57, 61, 83 Chapter 33: 7, 12, 32, 38, 44, 49, 76
PHYS 1101 Practce problem set 1, Chapter 3: 1,, 4, 57, 61, 83 Chapter 33: 7, 1, 3, 38, 44, 49, 76 3.1. Vsualze: Please reer to Fgure Ex3.1. Solve: Because B s n the same drecton as the ntegraton path s
More informationParabola Model with the Application to the Single-Point Mooring System
Journal of Multdscplnary Engneerng Scence and Technology (JMEST) ISSN: 58-93 Vol. Issue 3, March - 7 Parabola Model wth the Applcaton to the Sngle-Pont Moorng System Chunle Sun, Yuheng Rong, Xn Wang, Mengjao
More informationNormally, in one phase reservoir simulation we would deal with one of the following fluid systems:
TPG4160 Reservor Smulaton 2017 page 1 of 9 ONE-DIMENSIONAL, ONE-PHASE RESERVOIR SIMULATION Flud systems The term sngle phase apples to any system wth only one phase present n the reservor In some cases
More informationCHAPTER 10 ROTATIONAL MOTION
CHAPTER 0 ROTATONAL MOTON 0. ANGULAR VELOCTY Consder argd body rotates about a fxed axs through pont O n x-y plane as shown. Any partcle at pont P n ths rgd body rotates n a crcle of radus r about O. The
More informationPhysics 111: Mechanics Lecture 11
Physcs 111: Mechancs Lecture 11 Bn Chen NJIT Physcs Department Textbook Chapter 10: Dynamcs of Rotatonal Moton q 10.1 Torque q 10. Torque and Angular Acceleraton for a Rgd Body q 10.3 Rgd-Body Rotaton
More informationFour Bar Linkages in Two Dimensions. A link has fixed length and is joined to other links and also possibly to a fixed point.
Four bar lnkages 1 Four Bar Lnkages n Two Dmensons lnk has fed length and s oned to other lnks and also possbly to a fed pont. The relatve velocty of end B wth regard to s gven by V B = ω r y v B B = +y
More informationWork 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 informationModule 14: THE INTEGRAL Exploring Calculus
Module 14: THE INTEGRAL Explorng Calculus Part I Approxmatons and the Defnte Integral It was known n the 1600s before the calculus was developed that the area of an rregularly shaped regon could be approxmated
More informationSTATISTICAL MECHANICS
STATISTICAL MECHANICS Thermal Energy Recall that KE can always be separated nto 2 terms: KE system = 1 2 M 2 total v CM KE nternal Rgd-body rotaton and elastc / sound waves Use smplfyng assumptons KE of
More informationExperiment 1 Mass, volume and density
Experment 1 Mass, volume and densty Purpose 1. Famlarze wth basc measurement tools such as verner calper, mcrometer, and laboratory balance. 2. Learn how to use the concepts of sgnfcant fgures, expermental
More information8.1 Arc Length. What is the length of a curve? How can we approximate it? We could do it following the pattern we ve used before
.1 Arc Length hat s the length of a curve? How can we approxmate t? e could do t followng the pattern we ve used before Use a sequence of ncreasngly short segments to approxmate the curve: As the segments
More informationSpring 2002 Lecture #13
44-50 Sprng 00 ecture # Dr. Jaehoon Yu. Rotatonal Energy. Computaton of oments of nerta. Parallel-as Theorem 4. Torque & Angular Acceleraton 5. Work, Power, & Energy of Rotatonal otons Remember the md-term
More informationFirst Law: A body at rest remains at rest, a body in motion continues to move at constant velocity, unless acted upon by an external force.
Secton 1. Dynamcs (Newton s Laws of Moton) Two approaches: 1) Gven all the forces actng on a body, predct the subsequent (changes n) moton. 2) Gven the (changes n) moton of a body, nfer what forces act
More informationAs it can be observed from Fig. a) and b), applying Newton s Law for the tangential force component results into: mg sin mat
PHY4HF Exercse : Numercal ntegraton methods The Pendulum Startng wth small angles of oscllaton, you wll get expermental data on a smple pendulum and wll wrte a Python program to solve the equaton of moton.
More informationBasic concept of reactive flows. Basic concept of reactive flows Combustion Mixing and reaction in high viscous fluid Application of Chaos
Introducton to Toshhsa Ueda School of Scence for Open and Envronmental Systems Keo Unversty, Japan Combuston Mxng and reacton n hgh vscous flud Applcaton of Chaos Keo Unversty 1 Keo Unversty 2 What s reactve
More informationA large scale tsunami run-up simulation and numerical evaluation of fluid force during tsunami by using a particle method
A large scale tsunam run-up smulaton and numercal evaluaton of flud force durng tsunam by usng a partcle method *Mtsuteru Asa 1), Shoch Tanabe 2) and Masaharu Isshk 3) 1), 2) Department of Cvl Engneerng,
More informationPhysics 53. Rotational Motion 3. Sir, I have found you an argument, but I am not obliged to find you an understanding.
Physcs 53 Rotatonal Moton 3 Sr, I have found you an argument, but I am not oblged to fnd you an understandng. Samuel Johnson Angular momentum Wth respect to rotatonal moton of a body, moment of nerta plays
More informationNumerical Heat and Mass Transfer
Master degree n Mechancal Engneerng Numercal Heat and Mass Transfer 06-Fnte-Dfference Method (One-dmensonal, steady state heat conducton) Fausto Arpno f.arpno@uncas.t Introducton Why we use models and
More informationRotational and Translational Comparison. Conservation of Angular Momentum. Angular Momentum for a System of Particles
Conservaton o Angular Momentum 8.0 WD Rotatonal and Translatonal Comparson Quantty Momentum Ang Momentum Force Torque Knetc Energy Work Power Rotaton L cm = I cm ω = dl / cm cm K = (/ ) rot P rot θ W =
More informationMoments of Inertia. and reminds us of the analogous equation for linear momentum p= mv, which is of the form. The kinetic energy of the body is.
Moments of Inerta Suppose a body s movng on a crcular path wth constant speed Let s consder two quanttes: the body s angular momentum L about the center of the crcle, and ts knetc energy T How are these
More informationPlease initial the statement below to show that you have read it
EN40: Dynamcs and Vbratons Mdterm Examnaton Thursday March 5 009 Dvson of Engneerng rown Unversty NME: Isaac Newton General Instructons No collaboraton of any knd s permtted on ths examnaton. You may brng
More informationMATH 5630: Discrete Time-Space Model Hung Phan, UMass Lowell March 1, 2018
MATH 5630: Dscrete Tme-Space Model Hung Phan, UMass Lowell March, 08 Newton s Law of Coolng Consder the coolng of a well strred coffee so that the temperature does not depend on space Newton s law of collng
More informationarxiv: v1 [physics.flu-dyn] 16 Sep 2013
Three-Dmensonal Smoothed Partcle Hydrodynamcs Method for Smulatng Free Surface Flows Rzal Dw Prayogo a,b, Chrstan Fredy Naa a a Faculty of Mathematcs and Natural Scences, Insttut Teknolog Bandung, Jl.
More informationPublication 2006/01. Transport Equations in Incompressible. Lars Davidson
Publcaton 2006/01 Transport Equatons n Incompressble URANS and LES Lars Davdson Dvson of Flud Dynamcs Department of Appled Mechancs Chalmers Unversty of Technology Göteborg, Sweden, May 2006 Transport
More informationG4023 Mid-Term Exam #1 Solutions
Exam1Solutons.nb 1 G03 Md-Term Exam #1 Solutons 1-Oct-0, 1:10 p.m to :5 p.m n 1 Pupn Ths exam s open-book, open-notes. You may also use prnt-outs of the homework solutons and a calculator. 1 (30 ponts,
More informationSo far: simple (planar) geometries
Physcs 06 ecture 5 Torque and Angular Momentum as Vectors SJ 7thEd.: Chap. to 3 Rotatonal quanttes as vectors Cross product Torque epressed as a vector Angular momentum defned Angular momentum as a vector
More informationOne-sided finite-difference approximations suitable for use with Richardson extrapolation
Journal of Computatonal Physcs 219 (2006) 13 20 Short note One-sded fnte-dfference approxmatons sutable for use wth Rchardson extrapolaton Kumar Rahul, S.N. Bhattacharyya * Department of Mechancal Engneerng,
More informationLAGRANGIAN MECHANICS
LAGRANGIAN MECHANICS Generalzed Coordnates State of system of N partcles (Newtonan vew): PE, KE, Momentum, L calculated from m, r, ṙ Subscrpt covers: 1) partcles N 2) dmensons 2, 3, etc. PE U r = U x 1,
More informationIntroduction to Computational Fluid Dynamics
Introducton to Computatonal Flud Dynamcs M. Zanub 1, T. Mahalakshm 2 1 (PG MATHS), Department of Mathematcs, St. Josephs College of Arts and Scence for Women-Hosur, Peryar Unversty 2 Assstance professor,
More informationSCHOOL OF COMPUTING, ENGINEERING AND MATHEMATICS SEMESTER 2 EXAMINATIONS 2011/2012 DYNAMICS ME247 DR. N.D.D. MICHÉ
s SCHOOL OF COMPUTING, ENGINEERING ND MTHEMTICS SEMESTER EXMINTIONS 011/01 DYNMICS ME47 DR. N.D.D. MICHÉ Tme allowed: THREE hours nswer: ny FOUR from SIX questons Each queston carres 5 marks Ths s a CLOSED-BOOK
More informationTransfer Functions. Convenient representation of a linear, dynamic model. A transfer function (TF) relates one input and one output: ( ) system
Transfer Functons Convenent representaton of a lnear, dynamc model. A transfer functon (TF) relates one nput and one output: x t X s y t system Y s The followng termnology s used: x y nput output forcng
More informationDUE: WEDS FEB 21ST 2018
HOMEWORK # 1: FINITE DIFFERENCES IN ONE DIMENSION DUE: WEDS FEB 21ST 2018 1. Theory Beam bendng s a classcal engneerng analyss. The tradtonal soluton technque makes smplfyng assumptons such as a constant
More informationLNG CARGO TRANSFER CALCULATION METHODS AND ROUNDING-OFFS
CARGO TRANSFER CALCULATION METHODS AND ROUNDING-OFFS CONTENTS 1. Method for determnng transferred energy durng cargo transfer. Calculatng the transferred energy.1 Calculatng the gross transferred energy.1.1
More informationPhysics 114 Exam 2 Fall 2014 Solutions. Name:
Physcs 114 Exam Fall 014 Name: For gradng purposes (do not wrte here): Queston 1. 1... 3. 3. Problem Answer each of the followng questons. Ponts for each queston are ndcated n red. Unless otherwse ndcated,
More informationTensor Smooth Length for SPH Modelling of High Speed Impact
Tensor Smooth Length for SPH Modellng of Hgh Speed Impact Roman Cherepanov and Alexander Gerasmov Insttute of Appled mathematcs and mechancs, Tomsk State Unversty 634050, Lenna av. 36, Tomsk, Russa RCherepanov82@gmal.com,Ger@npmm.tsu.ru
More information(Online First)A Lattice Boltzmann Scheme for Diffusion Equation in Spherical Coordinate
Internatonal Journal of Mathematcs and Systems Scence (018) Volume 1 do:10.494/jmss.v1.815 (Onlne Frst)A Lattce Boltzmann Scheme for Dffuson Equaton n Sphercal Coordnate Debabrata Datta 1 *, T K Pal 1
More informationMotion in One Dimension
Moton n One Dmenson Speed ds tan ce traeled Aerage Speed tme of trael Mr. Wolf dres hs car on a long trp to a physcs store. Gen the dstance and tme data for hs trp, plot a graph of hs dstance ersus tme.
More informationConservation of Angular Momentum = "Spin"
Page 1 of 6 Conservaton of Angular Momentum = "Spn" We can assgn a drecton to the angular velocty: drecton of = drecton of axs + rght hand rule (wth rght hand, curl fngers n drecton of rotaton, thumb ponts
More informationNumerical Transient Heat Conduction Experiment
Numercal ransent Heat Conducton Experment OBJECIVE 1. o demonstrate the basc prncples of conducton heat transfer.. o show how the thermal conductvty of a sold can be measured. 3. o demonstrate the use
More information9/19/2013. PHY 113 C General Physics I 11 AM-12:15 PM MWF Olin 101
PHY 3 C General Physcs I AM-:5 PM MF Oln 0 Plan or Lecture 8: Chapter 8 -- Conservaton o energy. Potental and knetc energy or conservatve orces. Energy and non-conservatve orces 3. Power PHY 3 C Fall 03--
More informationCOMPOSITE BEAM WITH WEAK SHEAR CONNECTION SUBJECTED TO THERMAL LOAD
COMPOSITE BEAM WITH WEAK SHEAR CONNECTION SUBJECTED TO THERMAL LOAD Ákos Jósef Lengyel, István Ecsed Assstant Lecturer, Professor of Mechancs, Insttute of Appled Mechancs, Unversty of Mskolc, Mskolc-Egyetemváros,
More informationChapter 11 Torque and Angular Momentum
Chapter Torque and Angular Momentum I. Torque II. Angular momentum - Defnton III. Newton s second law n angular form IV. Angular momentum - System of partcles - Rgd body - Conservaton I. Torque - Vector
More informationWeek 9 Chapter 10 Section 1-5
Week 9 Chapter 10 Secton 1-5 Rotaton Rgd Object A rgd object s one that s nondeformable The relatve locatons of all partcles makng up the object reman constant All real objects are deformable to some extent,
More informationENGN 40 Dynamics and Vibrations Homework # 7 Due: Friday, April 15
NGN 40 ynamcs and Vbratons Homework # 7 ue: Frday, Aprl 15 1. Consder a concal hostng drum used n the mnng ndustry to host a mass up/down. A cable of dameter d has the mass connected at one end and s wound/unwound
More informationChapter 11: Angular Momentum
Chapter 11: ngular Momentum Statc Equlbrum In Chap. 4 we studed the equlbrum of pontobjects (mass m) wth the applcaton of Newton s aws F 0 F x y, 0 Therefore, no lnear (translatonal) acceleraton, a0 For
More informationPHYS 1441 Section 002 Lecture #15
PHYS 1441 Secton 00 Lecture #15 Monday, March 18, 013 Work wth rcton Potental Energy Gravtatonal Potental Energy Elastc Potental Energy Mechancal Energy Conservaton Announcements Mdterm comprehensve exam
More informationThe classical spin-rotation coupling
LOUAI H. ELZEIN 2018 All Rghts Reserved The classcal spn-rotaton couplng Loua Hassan Elzen Basher Khartoum, Sudan. Postal code:11123 louaelzen@gmal.com Abstract Ths paper s prepared to show that a rgd
More information. You need to do this for each force. Let s suppose that there are N forces, with components ( N) ( N) ( N) = i j k
EN3: Introducton to Engneerng and Statcs Dvson of Engneerng Brown Unversty 3. Resultant of systems of forces Machnes and structures are usually subected to lots of forces. When we analyze force systems
More informationLecture 16. Chapter 11. Energy Dissipation Linear Momentum. Physics I. Department of Physics and Applied Physics
Lecture 16 Chapter 11 Physcs I Energy Dsspaton Lnear Momentum Course webste: http://aculty.uml.edu/andry_danylov/teachng/physcsi Department o Physcs and Appled Physcs IN IN THIS CHAPTER, you wll learn
More informationWorkshop: Approximating energies and wave functions Quantum aspects of physical chemistry
Workshop: Approxmatng energes and wave functons Quantum aspects of physcal chemstry http://quantum.bu.edu/pltl/6/6.pdf Last updated Thursday, November 7, 25 7:9:5-5: Copyrght 25 Dan Dll (dan@bu.edu) Department
More informationDynamics 4600:203 Homework 08 Due: March 28, Solution: We identify the displacements of the blocks A and B with the coordinates x and y,
Dynamcs 46:23 Homework 8 Due: March 28, 28 Name: Please denote your answers clearly,.e., box n, star, etc., and wrte neatly. There are no ponts for small, messy, unreadable work... please use lots of paper.
More informationMacroscopic Momentum Balances
Lecture 13 F. Morrson CM3110 2013 10/22/2013 CM3110 Transport I Part I: Flud Mechancs Macroscopc Momentum Balances Professor Fath Morrson Department of Chemcal Engneerng Mchgan Technologcal Unersty 1 Macroscopc
More informationMechanics Cycle 3 Chapter 9++ Chapter 9++
Chapter 9++ More on Knetc Energy and Potental Energy BACK TO THE FUTURE I++ More Predctons wth Energy Conservaton Revst: Knetc energy for rotaton Potental energy M total g y CM for a body n constant gravty
More informationThermodynamics General
Thermodynamcs General Lecture 1 Lecture 1 s devoted to establshng buldng blocks for dscussng thermodynamcs. In addton, the equaton of state wll be establshed. I. Buldng blocks for thermodynamcs A. Dmensons,
More informationMath1110 (Spring 2009) Prelim 3 - Solutions
Math 1110 (Sprng 2009) Solutons to Prelm 3 (04/21/2009) 1 Queston 1. (16 ponts) Short answer. Math1110 (Sprng 2009) Prelm 3 - Solutons x a 1 (a) (4 ponts) Please evaluate lm, where a and b are postve numbers.
More informationFormal solvers of the RT equation
Formal solvers of the RT equaton Formal RT solvers Runge- Kutta (reference solver) Pskunov N.: 979, Master Thess Long characterstcs (Feautrer scheme) Cannon C.J.: 970, ApJ 6, 55 Short characterstcs (Hermtan
More informationAnnouncements. Lecture #2
Announcements Lectures wll be n 4 LeConte begnnng Frday 8/29 Addtonal dscusson TA Denns Chang (Sectons 101, 105) Offce hours: Mo 2-3 PM; Th 5-6 PM Lab sectons begn Tuesday 9/2 Read Experment #1 onlne Download
More informationSection 8.3 Polar Form of Complex Numbers
80 Chapter 8 Secton 8 Polar Form of Complex Numbers From prevous classes, you may have encountered magnary numbers the square roots of negatve numbers and, more generally, complex numbers whch are the
More informationBulk Air Flow in a Duct. Hoods and Local Exhaust Ventilation. Inside a ventilation system. System Nomenclature
Bulk Ar Flow n a Duct Hoods and Local Exhaust Ventlaton Essental pressure and low relatonshps Ar movement always ollows the pressure gradent Flow goes rom hgher (abs) pressure to lower (abs) pressure regons
More informationTurbulent 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 information10/9/2003 PHY Lecture 11 1
Announcements 1. Physc Colloquum today --The Physcs and Analyss of Non-nvasve Optcal Imagng. Today s lecture Bref revew of momentum & collsons Example HW problems Introducton to rotatons Defnton of angular
More informationParametric fractional imputation for missing data analysis. Jae Kwang Kim Survey Working Group Seminar March 29, 2010
Parametrc fractonal mputaton for mssng data analyss Jae Kwang Km Survey Workng Group Semnar March 29, 2010 1 Outlne Introducton Proposed method Fractonal mputaton Approxmaton Varance estmaton Multple mputaton
More information8.022 (E&M) Lecture 4
Topcs: 8.0 (E&M) Lecture 4 More applcatons of vector calculus to electrostatcs: Laplacan: Posson and Laplace equaton url: concept and applcatons to electrostatcs Introducton to conductors Last tme Electrc
More informationHomework 2: Kinematics and Dynamics of Particles Due Friday Feb 7, 2014 Max Score 45 Points + 8 Extra Credit
EN40: Dynamcs and Vbratons School of Engneerng Brown Unversty Homework : Knematcs and Dynamcs of Partcles Due Frday Feb 7, 014 Max Score 45 Ponts + 8 Extra Credt 1. An expermental mcro-robot (see a descrpton
More informationInductance Calculation for Conductors of Arbitrary Shape
CRYO/02/028 Aprl 5, 2002 Inductance Calculaton for Conductors of Arbtrary Shape L. Bottura Dstrbuton: Internal Summary In ths note we descrbe a method for the numercal calculaton of nductances among conductors
More informationLecture 5.8 Flux Vector Splitting
Lecture 5.8 Flux Vector Splttng 1 Flux Vector Splttng The vector E n (5.7.) can be rewrtten as E = AU (5.8.1) (wth A as gven n (5.7.4) or (5.7.6) ) whenever, the equaton of state s of the separable form
More informationThe Finite Element Method
The Fnte Element Method GENERAL INTRODUCTION Read: Chapters 1 and 2 CONTENTS Engneerng and analyss Smulaton of a physcal process Examples mathematcal model development Approxmate solutons and methods of
More information6.3.4 Modified Euler s method of integration
6.3.4 Modfed Euler s method of ntegraton Before dscussng the applcaton of Euler s method for solvng the swng equatons, let us frst revew the basc Euler s method of numercal ntegraton. Let the general from
More informationIonization fronts in HII regions
Ionzaton fronts n HII regons Intal expanson of HII onzaton front s supersonc, creatng a shock front. Statonary frame: front advances nto neutral materal In frame where shock front s statonary, neutral
More informationPhysics 114 Exam 3 Spring Name:
Physcs 114 Exam 3 Sprng 015 Name: For gradng purposes (do not wrte here): Queston 1. 1... 3. 3. Problem 4. Answer each of the followng questons. Ponts for each queston are ndcated n red. Unless otherwse
More information1. Governing Equations
1. Governng Equatons 1a. Governng Equatons for Mean Varables The governng equatons descrbe the varaton n space and tme of the zonal, merdonal and vertcal wnd components, densty, temperature, specfc humdty
More informationPhysics 207 Lecture 13. Lecture 13
Physcs 07 Lecture 3 Goals: Lecture 3 Chapter 0 Understand the relatonshp between moton and energy Defne Potental Energy n a Hooke s Law sprng Develop and explot conservaton of energy prncple n problem
More informationLinear Feature Engineering 11
Lnear Feature Engneerng 11 2 Least-Squares 2.1 Smple least-squares Consder the followng dataset. We have a bunch of nputs x and correspondng outputs y. The partcular values n ths dataset are x y 0.23 0.19
More informationChapter 7. Potential Energy and Conservation of Energy
Chapter 7 Potental Energy and Conservaton o Energy 1 Forms o Energy There are many orms o energy, but they can all be put nto two categores Knetc Knetc energy s energy o moton Potental Potental energy
More information10/24/2013. PHY 113 C General Physics I 11 AM 12:15 PM TR Olin 101. Plan for Lecture 17: Review of Chapters 9-13, 15-16
0/4/03 PHY 3 C General Physcs I AM :5 PM T Oln 0 Plan or Lecture 7: evew o Chapters 9-3, 5-6. Comment on exam and advce or preparaton. evew 3. Example problems 0/4/03 PHY 3 C Fall 03 -- Lecture 7 0/4/03
More informationFinite Wings Steady, incompressible flow
Steady, ncompressble flow Geometrc propertes of a wng - Fnte thckness much smaller than the span and the chord - Defnton of wng geometry: a) Planform (varaton of chord and sweep angle) b) Secton/Arfol
More informationThe Discretization Process
FMIA F Moukalled L Mangan M Darwsh An Advanced Introducton wth OpenFOAM and Matlab Ths textbook explores both the theoretcal foundaton of the Fnte Volume Method (FVM) and ts applcatons n Computatonal Flud
More informationSpring Force and Power
Lecture 13 Chapter 9 Sprng Force and Power Yeah, energy s better than orces. What s net? Course webste: http://aculty.uml.edu/andry_danylov/teachng/physcsi IN THIS CHAPTER, you wll learn how to solve problems
More information