# Introduction to Fluid Mechanics

Save this PDF as:

Size: px
Start display at page:

## Transcription

1 Chapte Solved Examples Example 1.1 Dimensions and Units A body weighs 1 Ibf when exposed to a standad eath gavity g = ft/s. (a) What is its mass in kg? (b) What will the weight of this body be in N if it is exposed to the moon s standad acceleation g moon = 1.6 m/s? (c) How fast will the body acceleate if a net foce of 4 lbf is applied to it on the moon o on the eath? F = weight and a = g eath : F=W=mg=1 lbf = (m slugs) (3.174 ft/s ) o m = 1/3.174 = (31.8 slugs)( kg/slug) = kg Ans. (a) The change fom 31.8 slugs to kg illustates the pope use of the convesion facto kg/slug. The mass of the body emains kg egadless of its location. F = W moon = m.g moon = (453.6 kg)(1.6 m/s ) = 735 N Ans. (b) This poblem does not involve weight o gavity o position and is simply a diect application of Newton s law with an unbalanced foce: F = 4 lbf = m.a = (31.8 slugs)(a ft/s ) o a =4/31.8 = 1.43 ft/s = 3.79 m/s Ans. (c) This acceleation would be the same on the moon o eath o anywhee. Example 1. Dimensions and Units An ealy viscosity unit in the cgs system is the poise (abbeviated P), o g/(cm.s), named afte J. L. M. Poiseuille, a Fench physician. The viscosity of wate (fesh o salt) at K = C is appoximately μ =.1 P. Expess this value in (a) SI and (b) BG units.

2 Chapte 1 μ = [.1 g/(cm. s)] (1 kg/1 g ) (1cm/m) =.1 kg/(m.s) Ans. (a) μ = [.1 kg/(m. s)] (1 slug/14.59 kg ) (.348 m/ft) = slug/(ft.s) Ans. (b) Note: Result (b) could have been found diectly fom (a) by dividing (a) by the viscosity convesion facto listed in Table (1.). Example 1.3 Popeties of a Fluid Suppose that the fluid being sheaed in Figue (1.5) is SAE 3 oil at C. Compute the shea stess in the oil if u = 3 m/s and h = cm. The shea stess is found fom Eq. (1.13) by diffeentiating Eq. (1.14): du u (E1.1) d y h Fom Table (1.5) fo SAE 3 oil, μ =.9 kg/(m. s). Then, fo the given values of u and h, Eq. (E1.1) pedicts.9kg/( m. s) (3m / s) 43kg/( m. s ) 43N / m 43Pa Ans..m Although oil is vey viscous, this is a modest shea stess, about 4 times less than atmospheic pessue. Viscous stesses in gases and thin liquids ae even smalle. Example 1.4 (14 final Exam) Popeties of a Fluid The velocity pofile is a lamina flow though a ound pipe is expessed as, u U1 whee U = aveage velocity, (a) Daw dimensionless shea stess pofile = adius of pipe. against whee

3 Chapte 1 is wall shea stess. (b) Find, when oil flows with absolute viscosity 4 1 N.s/m and velocity of 4 m/s in a pipe of diamete 15 mm. Given u U1 du 4U du 4 U Then and d d And du d 4 U.. (E1.) So, and theplotis shownin Figue (E4.1) Ans. (a) Fom Eq. (E1.), N m Ans. (b) Fig. E1.4: dimensionless shea stess pofile Example 1.5 Popeties of a Fluid against. Deive an expession fo the change in height h in a cicula tube of a liquid with suface tension σ and contact angle θ, as in Figue (E1.5). The vetical component of the ing suface-tension foce at the inteface in the tube must balance the weight of the column of fluid of height h R cos R gh

4 Chapte 1 3 Solving fo h, we have the desied esult cos h Ans. gr Fig. E1.5 Thus the capillay height inceases invesely with tube adius R and is positive if θ < 9 (wetting liquid) and negative (capillay depession) if θ > 9. Suppose that R = 1 mm. Then the capillay ise fo a wate-ai-glass inteface, θ, σ =.73 N/m, and ρ = 1 kg/m 3 is (.73 N / m)(cos ) h.15( N. s ) / kg.15m 1. 5cm 3 (1 kg/ m )(9.81m / s )(.1m) Fo a mecuy-ai-glass inteface, with θ = 13,, σ =.48 N/m, and ρ = 1136, the capillay ise is h = -.46 cm When a small-diamete tube is used to make pessue measuements, these capillay effects must be coected fo.

5 ϕ18cm ϕ15cm Chapte 1 4 Example 1.6 Popeties of a Fluid A cylinde 7.5 cm adius and 6 cm in length otate coaxially inside a fixed cylinde of the same length and 9 cm inne adius as shown in Figue (E1.6). Glycein μ = 8 Poise fills the space between to cylindes. A Toque.4 N.m is applied to the inne cylinde. Afte a constant velocity is attended, calculate the following: (a) velocity gadient at the cylinde walls, (b) the velocity ustling and (c) the powe dissipated by the fluid esistance. 6cm Fig. E1.6 The shea stess is found fom Eq. (1.13) du (E1.3) d y L L Toque F A.... (E1.4) whee L is the cylinde length then fom Eq. (E1.4).4( N. m) du d y ( m)

6 Chapte 1 5 du dy 8( Poise) 1 du d y innewall (7.51 ).1375 N / m..... (E1.5) 3.6 Ans.(a) du d y outewall (91 ) Ans.(a) Fom Eq. (E1.4) and whee dy =-d du du.1375 d y d.1375 du d (E1.6) by integating Eq. (E1.6): u.75 1 du.1375 d.9 Whee u() = at =.9 m Then u 9.48 m / s Ans.(b).9 N Whee u 6 N N Powe Toque. 1HP (N: evolution pe minute) N 37.5pm Ans.(c)

7 Chapte Poblems 1. Deive the SI unit of foce fom base units.. Explain dynamic viscosity and kinematic viscosity. Give thei dimensions. 3. Explain the phenomenon of capillaity. Obtain an expession fo capillay ise of a fluid. 4. Expess the viscosity and the kinematics' viscosity in SI units. 5. Fo low-speed (lamina) steady flow though a cicula pipe, the velocity u vaies with adius and takes the fom p u B whee μ is the fluid viscosity and Δp is the pessue dop fom entance to exit. What ae the dimensions of the constant B? 6. The density of wate at 4 C and 1 atm is 1 kg/m 3. Obtain the specific volume. 7. The specific weight of a cetain liquid is 1 KN/m 3. Detemine its density and specific gavity. 8. A liquid when poued into a gaduated cylinde is found to weigh 8 N when occupying a volume of 5 ml (millilites). Detemine its specific weight, density, and specific gavity. 9. Obtain the pessue in SI (Pa) necessay fo shinking the volume of wate by 1% at nomal tempeatue and pessue. Assume the compessibility of wate β= Pa A block of weight W slides down an inclined plane while lubicated by a thin film of oil, as in Figue (1.P1). The film contact aea is A and its thickness is h. Assuming a linea velocity distibution in the film, deive an expession fo the teminal (zeo-acceleation) velocity V of the block.

8 Chapte Deive an expession fo the capillay height change h fo a fluid of suface tension σ and contact angle θ between two vetical paallel plates a distance W apat, as in Figue (P1.11). What will h be fo wate at C if W =.5 mm? Fig. 1.P1. Fig. 1.P Find suface tension of a soap bubble of 48 mm diamete while pessue inside is 3.1 Pa highe than atmospheic one. 13. A Newtonian fluid having a specific gavity of.9 and a kinematics viscosity of m /s flows past a fixed suface. Due to the no-slip condition, the velocity at the fixed suface is zeo (as shown), and the velocity pofile nea the suface is shown in Figue (1.P13). Detemine the magnitude and diection of the sheaing stess developed on the plate. Expess you answe in tems of U and δ, with U and δ expessed in units of metes pe second and metes, espectively. Fig. 1.P13.

9 Chapte As shown in Figue (1.P14), a cylinde of diamete 1mm and length mm is placed inside a concentic long pipe of diamete 15 mm. An oil film is intoduced in the gap between the pipe and the cylinde. What foce is necessay to move the cylinde at a velocity of l m/s? Assume that the kinematic viscosity of oil is 3 cst and the specific gavity is.9. Fig. 1.P14

### Vector Calculus: Are you ready? Vectors in 2D and 3D Space: Review

Vecto Calculus: Ae you eady? Vectos in D and 3D Space: Review Pupose: Make cetain that you can define, and use in context, vecto tems, concepts and fomulas listed below: Section 7.-7. find the vecto defined

### PHYSICS 111 HOMEWORK SOLUTION #13. May 1, 2013

PHYSICS 111 HOMEWORK SOLUTION #13 May 1, 2013 0.1 In intoductoy physics laboatoies, a typical Cavendish balance fo measuing the gavitational constant G uses lead sphees with masses of 2.10 kg and 21.0

### VISCOSITY OF BIO-DIESEL FUELS

VISCOSITY OF BIO-DIESEL FUELS One of the key assumptions fo ideal gases is that the motion of a given paticle is independent of any othe paticles in the system. With this assumption in place, one can use

### Deflection of Electrons by Electric and Magnetic Fields

Physics 233 Expeiment 42 Deflection of Electons by Electic and Magnetic Fields Refeences Loain, P. and D.R. Coson, Electomagnetism, Pinciples and Applications, 2nd ed., W.H. Feeman, 199. Intoduction An

### Multiple choice questions [70 points]

Multiple choice questions [70 points] Answe all of the following questions. Read each question caefull. Fill the coect bubble on ou scanton sheet. Each question has exactl one coect answe. All questions

### www.sakshieducation.com

Viscosity. The popety of viscosity in gas is due to ) Cohesive foces between the moecues ) Coisions between the moecues ) Not having a definite voume ) Not having a definite size. When tempeatue is inceased

### Phys 2101 Gabriela González. cos. sin. sin

1 Phys 101 Gabiela González a m t t ma ma m m T α φ ω φ sin cos α τ α φ τ sin m m α τ I We know all of that aleady!! 3 The figue shows the massive shield doo at a neuton test facility at Lawence Livemoe

### Chapter 4: Fluid Kinematics

Oveview Fluid kinematics deals with the motion of fluids without consideing the foces and moments which ceate the motion. Items discussed in this Chapte. Mateial deivative and its elationship to Lagangian

### Voltage ( = Electric Potential )

V-1 of 9 Voltage ( = lectic Potential ) An electic chage altes the space aound it. Thoughout the space aound evey chage is a vecto thing called the electic field. Also filling the space aound evey chage

### XI / PHYSICS FLUIDS IN MOTION 11/PA

Viscosity It is the property of a liquid due to which it flows in the form of layers and each layer opposes the motion of its adjacent layer. Cause of viscosity Consider two neighboring liquid layers A

### Fluids and Solids: Fundamentals

Fluids and Solids: Fundamentals We normally recognize three states of matter: solid; liquid and gas. However, liquid and gas are both fluids: in contrast to solids they lack the ability to resist deformation.

### 4a 4ab b 4 2 4 2 5 5 16 40 25. 5.6 10 6 (count number of places from first non-zero digit to

. Simplify: 0 4 ( 8) 0 64 ( 8) 0 ( 8) = (Ode of opeations fom left to ight: Paenthesis, Exponents, Multiplication, Division, Addition Subtaction). Simplify: (a 4) + (a ) (a+) = a 4 + a 0 a = a 7. Evaluate

### CHAPTER 5 GRAVITATIONAL FIELD AND POTENTIAL

CHATER 5 GRAVITATIONAL FIELD AND OTENTIAL 5. Intoduction. This chapte deals with the calculation of gavitational fields and potentials in the vicinity of vaious shapes and sizes of massive bodies. The

### Structure and evolution of circumstellar disks during the early phase of accretion from a parent cloud

Cente fo Tubulence Reseach Annual Reseach Biefs 2001 209 Stuctue and evolution of cicumstella disks duing the ealy phase of accetion fom a paent cloud By Olusola C. Idowu 1. Motivation and Backgound The

### Chapter 2. Electrostatics

Chapte. Electostatics.. The Electostatic Field To calculate the foce exeted by some electic chages,,, 3,... (the souce chages) on anothe chage Q (the test chage) we can use the pinciple of supeposition.

### Properties of Fluids

CHAPTER Properties of Fluids 1 1.1 INTRODUCTION A fluid can be defined as a substance which deforms or yields continuously when shear stress is applied to it, no matter how small it is. Fluids can be subdivided

### The Role of Gravity in Orbital Motion

! The Role of Gavity in Obital Motion Pat of: Inquiy Science with Datmouth Developed by: Chistophe Caoll, Depatment of Physics & Astonomy, Datmouth College Adapted fom: How Gavity Affects Obits (Ohio State

### Basic Principles in Microfluidics

Basic Principles in Microfluidics 1 Newton s Second Law for Fluidics Newton s 2 nd Law (F= ma) : Time rate of change of momentum of a system equal to net force acting on system!f = dp dt Sum of forces

### 2. TRIGONOMETRIC FUNCTIONS OF GENERAL ANGLES

. TRIGONOMETRIC FUNCTIONS OF GENERAL ANGLES In ode to etend the definitions of the si tigonometic functions to geneal angles, we shall make use of the following ideas: In a Catesian coodinate sstem, an

### Lesson 7 Gauss s Law and Electric Fields

Lesson 7 Gauss s Law and Electic Fields Lawence B. Rees 7. You may make a single copy of this document fo pesonal use without witten pemission. 7. Intoduction While it is impotant to gain a solid conceptual

### Homework 9. Problems: 12.31, 12.32, 14.4, 14.21

Homework 9 Problems: 1.31, 1.3, 14.4, 14.1 Problem 1.31 Assume that if the shear stress exceeds about 4 10 N/m steel ruptures. Determine the shearing force necessary (a) to shear a steel bolt 1.00 cm in

### UNIT CIRCLE TRIGONOMETRY

UNIT CIRCLE TRIGONOMETRY The Unit Cicle is the cicle centeed at the oigin with adius unit (hence, the unit cicle. The equation of this cicle is + =. A diagam of the unit cicle is shown below: + = - - -

### Forces & Magnetic Dipoles. r r τ = μ B r

Foces & Magnetic Dipoles x θ F θ F. = AI τ = U = Fist electic moto invented by Faaday, 1821 Wie with cuent flow (in cup of Hg) otates aound a a magnet Faaday s moto Wie with cuent otates aound a Pemanent

D SEADY SAE HEA CONDUCION () Pabal alukda Aociate Pofeo Depatment of Mecanical Engineeing II Deli E-mail: pabal@mec.iitd.ac.in Palukda/Mec-IID emal Contact eitance empeatue ditibution and eat flow line

### Chapter 2 Modelling of Fluid Flow and Heat Transfer in Rotating-Disk Systems

Chapte 2 Modelling of Fluid Flow and Heat Tansfe in Rotating-Disk Systems 2.1 Diffeential and Integal Equations 2.1.1 Diffeential Navie Stokes and Enegy Equations We will conside hee stationay axisymmetic

### CBE 6333, R. Levicky 1 Review of Fluid Mechanics Terminology

CBE 6333, R. Levicky 1 Review of Fluid Mechanics Terminology The Continuum Hypothesis: We will regard macroscopic behavior of fluids as if the fluids are perfectly continuous in structure. In reality,

### 2. Orbital dynamics and tides

2. Obital dynamics and tides 2.1 The two-body poblem This efes to the mutual gavitational inteaction of two bodies. An exact mathematical solution is possible and staightfowad. In the case that one body

### Module 2: Dynamics of Electric and Hybrid vehicles

NPTEL Electical Engineeing Intoduction to Hybid and Electic Vehicles Module : Dynamics of Electic and Hybid vehicles Lectue 3: Motion and amic equations fo vehicles Motion and amic equations fo vehicles

### Analytical Proof of Newton's Force Laws

Analytical Poof of Newton s Foce Laws Page 1 1 Intouction Analytical Poof of Newton's Foce Laws Many stuents intuitively assume that Newton's inetial an gavitational foce laws, F = ma an Mm F = G, ae tue

### Skills Needed for Success in Calculus 1

Skills Needed fo Success in Calculus Thee is much appehension fom students taking Calculus. It seems that fo man people, "Calculus" is snonmous with "difficult." Howeve, an teache of Calculus will tell

### CE 6303 MECHANICS OF FLUIDS L T P C QUESTION BANK PART - A

CE 6303 MECHANICS OF FLUIDS L T P C QUESTION BANK 3 0 0 3 UNIT I FLUID PROPERTIES AND FLUID STATICS PART - A 1. Define fluid and fluid mechanics. 2. Define real and ideal fluids. 3. Define mass density

### Instituto Superior Técnico Av. Rovisco Pais, 1 1049-001 Lisboa E-mail: virginia.infante@ist.utl.pt

FATIGUE LIFE TIME PREDICTIO OF POAF EPSILO TB-30 AIRCRAFT - PART I: IMPLEMETATIO OF DIFERET CYCLE COUTIG METHODS TO PREDICT THE ACCUMULATED DAMAGE B. A. S. Seano 1, V. I. M.. Infante 2, B. S. D. Maado

### Natural Convection. Buoyancy force

Natural Convection In natural convection, the fluid motion occurs by natural means such as buoyancy. Since the fluid velocity associated with natural convection is relatively low, the heat transfer coefficient

### SELF-INDUCTANCE AND INDUCTORS

MISN-0-144 SELF-INDUCTANCE AND INDUCTORS SELF-INDUCTANCE AND INDUCTORS by Pete Signell Michigan State Univesity 1. Intoduction.............................................. 1 A 2. Self-Inductance L.........................................

### PUMPS STEAM TURBINES BUILDING & FIRE WASTEWATER SERVICE PUMP CLINIC 22 VISCOSITY

PUMP CLINIC 22 VISCOSITY The viscosity of a fluid is that property which tends to resist a shearing force. It can be thought of as the internal friction resulting when one layer of fluid is made to move

### 10. Collisions. Before During After

10. Collisions Use conseation of momentum and enegy and the cente of mass to undestand collisions between two objects. Duing a collision, two o moe objects exet a foce on one anothe fo a shot time: -F(t)

### INVESTIGATION OF FLOW INSIDE AN AXIAL-FLOW PUMP OF GV IMP TYPE

1 INVESTIGATION OF FLOW INSIDE AN AXIAL-FLOW PUMP OF GV IMP TYPE ANATOLIY A. YEVTUSHENKO 1, ALEXEY N. KOCHEVSKY 1, NATALYA A. FEDOTOVA 1, ALEXANDER Y. SCHELYAEV 2, VLADIMIR N. KONSHIN 2 1 Depatment of

### Diffusion and Fluid Flow

Diffusion and Fluid Flow What determines the diffusion coefficient? What determines fluid flow? 1. Diffusion: Diffusion refers to the transport of substance against a concentration gradient. ΔS>0 Mass

### CE 204 FLUID MECHANICS

CE 204 FLUID MECHANICS Onur AKAY Assistant Professor Okan University Department of Civil Engineering Akfırat Campus 34959 Tuzla-Istanbul/TURKEY Phone: +90-216-677-1630 ext.1974 Fax: +90-216-677-1486 E-mail:

### 1. Fluids Mechanics and Fluid Properties. 1.1 Objectives of this section. 1.2 Fluids

1. Fluids Mechanics and Fluid Properties What is fluid mechanics? As its name suggests it is the branch of applied mechanics concerned with the statics and dynamics of fluids - both liquids and gases.

### Problem Set # 9 Solutions

Poblem Set # 9 Solutions Chapte 12 #2 a. The invention of the new high-speed chip inceases investment demand, which shifts the cuve out. That is, at evey inteest ate, fims want to invest moe. The incease

### Questions & Answers Chapter 10 Software Reliability Prediction, Allocation and Demonstration Testing

M13914 Questions & Answes Chapte 10 Softwae Reliability Pediction, Allocation and Demonstation Testing 1. Homewok: How to deive the fomula of failue ate estimate. λ = χ α,+ t When the failue times follow

### Unit 1 INTRODUCTION 1.1.Introduction 1.2.Objectives

Structure 1.1.Introduction 1.2.Objectives 1.3.Properties of Fluids 1.4.Viscosity 1.5.Types of Fluids. 1.6.Thermodynamic Properties 1.7.Compressibility 1.8.Surface Tension and Capillarity 1.9.Capillarity

### Introduction to Microfluidics. Date: 2013/04/26. Dr. Yi-Chung Tung. Outline

Introduction to Microfluidics Date: 2013/04/26 Dr. Yi-Chung Tung Outline Introduction to Microfluidics Basic Fluid Mechanics Concepts Equivalent Fluidic Circuit Model Conclusion What is Microfluidics Microfluidics

### Supplementary Material for EpiDiff

Supplementay Mateial fo EpiDiff Supplementay Text S1. Pocessing of aw chomatin modification data In ode to obtain the chomatin modification levels in each of the egions submitted by the use QDCMR module

### YARN PROPERTIES MEASUREMENT: AN OPTICAL APPROACH

nd INTERNATIONAL TEXTILE, CLOTHING & ESIGN CONFERENCE Magic Wold of Textiles Octobe 03 d to 06 th 004, UBROVNIK, CROATIA YARN PROPERTIES MEASUREMENT: AN OPTICAL APPROACH Jana VOBOROVA; Ashish GARG; Bohuslav

### Ilona V. Tregub, ScD., Professor

Investment Potfolio Fomation fo the Pension Fund of Russia Ilona V. egub, ScD., Pofesso Mathematical Modeling of Economic Pocesses Depatment he Financial Univesity unde the Govenment of the Russian Fedeation

### Dimensional Analysis

Dimensional Analysis An Important Example from Fluid Mechanics: Viscous Shear Forces V d t / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / Ƭ = F/A = μ V/d More generally, the viscous

### Avoided emissions kgco 2eq /m 2 Reflecting surfaces 130

ANALYSIS OF GLOBAL WARMING MITIGATION BY WHITE REFLECTING SURFACES Fedeico Rossi, Andea Nicolini Univesity of Peugia, CIRIAF Via G.Duanti 67 0615 Peugia, Italy T: +9-075-585846; F: +9-075-5848470; E: fossi@unipg.it

### CHAPTER 2: LIQUID VISCOSITY MEASUREMENT

CHAPTER 2: LIQUID VISCOSITY MEASUREMENT Objective Calculate viscosity (dynamic or absolute, and kinematic) and determine how this property varies with changes in temperature for a constant-composition

### FLUID FLOW STREAMLINE LAMINAR FLOW TURBULENT FLOW REYNOLDS NUMBER

VISUAL PHYSICS School of Physics University of Sydney Australia FLUID FLOW STREAMLINE LAMINAR FLOW TURBULENT FLOW REYNOLDS NUMBER? What type of fluid flow is observed? The above pictures show how the effect

### C B A T 3 T 2 T 1. 1. What is the magnitude of the force T 1? A) 37.5 N B) 75.0 N C) 113 N D) 157 N E) 192 N

Three boxes are connected by massless strings and are resting on a frictionless table. Each box has a mass of 15 kg, and the tension T 1 in the right string is accelerating the boxes to the right at a

### Chapter 11: Aggregate Demand II, Applying the IS-LM Model Th LM t

Equilibium in the - model The cuve epesents equilibium in the goods maket. Chapte :, Applying the - Model Th t C ( T) I( ) G The cuve epesents money maket equilibium. M L(, ) The intesection detemines

### Gravitational Mechanics of the Mars-Phobos System: Comparing Methods of Orbital Dynamics Modeling for Exploratory Mission Planning

Gavitational Mechanics of the Mas-Phobos System: Compaing Methods of Obital Dynamics Modeling fo Exploatoy Mission Planning Alfedo C. Itualde The Pennsylvania State Univesity, Univesity Pak, PA, 6802 This

### OUTCOME 1 STATIC FLUID SYSTEMS TUTORIAL 1 - HYDROSTATICS

Unit 41: Fluid Mechanics Unit code: T/601/1445 QCF Level: 4 Credit value: 15 OUTCOME 1 STATIC FLUID SYSTEMS TUTORIAL 1 - HYDROSTATICS 1. Be able to determine the behavioural characteristics and parameters

### Controlling the Money Supply: Bond Purchases in the Open Market

Money Supply By the Bank of Canada and Inteest Rate Detemination Open Opeations and Monetay Tansmission Mechanism The Cental Bank conducts monetay policy Bank of Canada is Canada's cental bank supevises

### AN IMPLEMENTATION OF BINARY AND FLOATING POINT CHROMOSOME REPRESENTATION IN GENETIC ALGORITHM

AN IMPLEMENTATION OF BINARY AND FLOATING POINT CHROMOSOME REPRESENTATION IN GENETIC ALGORITHM Main Golub Faculty of Electical Engineeing and Computing, Univesity of Zageb Depatment of Electonics, Micoelectonics,

### Impulse and Linear Momentum 5

Implse and Linea Momentm 5 How does jet poplsion wok? How can yo mease the speed of a bllet? Wold a meteoite collision significantly change Eath s obit? In pevios chaptes we discoveed that the pshing inteaction

### A r. (Can you see that this just gives the formula we had above?)

24-1 (SJP, Phys 1120) lectic flux, and Gauss' law Finding the lectic field due to a bunch of chages is KY! Once you know, you know the foce on any chage you put down - you can pedict (o contol) motion

### Battery Thermal Management System Design Modeling

Battery Thermal Management System Design Modeling Gi-Heon Kim, Ph.D Ahmad Pesaran, Ph.D (ahmad_pesaran@nrel.gov) National Renewable Energy Laboratory, Golden, Colorado, U.S.A. EVS October -8, 8, 006 Yokohama,

### Lecture 5 Hemodynamics. Description of fluid flow. The equation of continuity

1 Lecture 5 Hemodynamics Description of fluid flow Hydrodynamics is the part of physics, which studies the motion of fluids. It is based on the laws of mechanics. Hemodynamics studies the motion of blood

### Design of Wind Energy System on the Building Tower Applications

ISSN(Online): 39-8753 ISSN (Pint) :347-67 (An ISO 397: 7 Cetified Oganization) Vol. 4, Issue, Febuay 5 Design of Wind Enegy System on the Building owe Applications D.Anusha, L V Suesh Kuma, G.V. Nagesh

### INITIAL MARGIN CALCULATION ON DERIVATIVE MARKETS OPTION VALUATION FORMULAS

INITIAL MARGIN CALCULATION ON DERIVATIVE MARKETS OPTION VALUATION FORMULAS Vesion:.0 Date: June 0 Disclaime This document is solely intended as infomation fo cleaing membes and othes who ae inteested in

### Cost/Benefit Analysis of Aquaponic Systems

Cost/Benefit Analysis of Aquaponic Systems Richad Chiang 1 PURPOSE pupose of this pape is to analyse the costs and benefits of aquaponic systems designed fo home use. Howeve, one can easily extapolate

### The Viscosity of Fluids

Experiment #11 The Viscosity of Fluids References: 1. Your first year physics textbook. 2. D. Tabor, Gases, Liquids and Solids: and Other States of Matter (Cambridge Press, 1991). 3. J.R. Van Wazer et

### Mobile Phone Antenna with Reduced Radiation into Inner Ear

Int. J. Communications, Netwok and System Sciences, 2014, 7, 474-484 Published Online Novembe 2014 in SciRes. http://www.scip.og/jounal/ijcns http://dx.doi.og/10.4236/ijcns.2014.711048 Mobile Phone Antenna

### VISUAL PHYSICS School of Physics University of Sydney Australia. Why do cars need different oils in hot and cold countries?

VISUAL PHYSICS School of Physics University of Sydney Australia FLUID FLOW VISCOSITY POISEUILLE'S LAW? Why do cars need different oils in hot and cold countries? Why does the engine runs more freely as

### The ratio of inertial to viscous forces is commonly used to scale fluid flow, and is called the Reynolds number, given as:

12.001 LAB 3C: STOKES FLOW DUE: WEDNESDAY, MARCH 9 Lab Overview and Background The viscosity of a fluid describes its resistance to deformation. Water has a very low viscosity; the force of gravity causes

### Strength Analysis and Optimization Design about the key parts of the Robot

Intenational Jounal of Reseach in Engineeing and Science (IJRES) ISSN (Online): 2320-9364, ISSN (Pint): 2320-9356 www.ijes.og Volume 3 Issue 3 ǁ Mach 2015 ǁ PP.25-29 Stength Analysis and Optimization Design

### CEE 370 Fall 2015. Laboratory #3 Open Channel Flow

CEE 70 Fall 015 Laboratory # Open Channel Flow Objective: The objective of this experiment is to measure the flow of fluid through open channels using a V-notch weir and a hydraulic jump. Introduction:

### PAN STABILITY TESTING OF DC CIRCUITS USING VARIATIONAL METHODS XVIII - SPETO - 1995. pod patronatem. Summary

PCE SEMINIUM Z PODSTW ELEKTOTECHNIKI I TEOII OBWODÓW 8 - TH SEMIN ON FUNDMENTLS OF ELECTOTECHNICS ND CICUIT THEOY ZDENĚK BIOLEK SPŠE OŽNO P.., CZECH EPUBLIC DLIBO BIOLEK MILITY CDEMY, BNO, CZECH EPUBLIC

### Introduction to COMSOL. The Navier-Stokes Equations

Flow Between Parallel Plates Modified from the COMSOL ChE Library module rev 10/13/08 Modified by Robert P. Hesketh, Chemical Engineering, Rowan University Fall 2008 Introduction to COMSOL The following

### Small Motors Gearmotors Motion Controls

BODIE ELECTRIC COMPAY BODIE ELECTRIC COMPAY Small Mots Geamots Motion Contols MOTOR & GEARMOTOR 1. SELECTIO 2. GUIDE. IT S AS EASY AS 3. Ceated by the Bodine Electic Company, this Mot and Geamot Selection

### An Introduction to Fluid Mechanics

0. Contents of the Course Notes For the First Year Lecture Course: An Introduction to Fluid Mechanics School of Civil Engineering, University of Leeds. CIVE1400 FLUID MECHANICS Dr Andrew Sleigh January

### Angular acceleration α

Angular Acceleration Angular acceleration α measures how rapidly the angular velocity is changing: Slide 7-0 Linear and Circular Motion Compared Slide 7- Linear and Circular Kinematics Compared Slide 7-

### est using the formula I = Prt, where I is the interest earned, P is the principal, r is the interest rate, and t is the time in years.

9.2 Inteest Objectives 1. Undestand the simple inteest fomula. 2. Use the compound inteest fomula to find futue value. 3. Solve the compound inteest fomula fo diffeent unknowns, such as the pesent value,

### Spirotechnics! September 7, 2011. Amanda Zeringue, Michael Spannuth and Amanda Zeringue Dierential Geometry Project

Spiotechnics! Septembe 7, 2011 Amanda Zeingue, Michael Spannuth and Amanda Zeingue Dieential Geomety Poject 1 The Beginning The geneal consensus of ou goup began with one thought: Spiogaphs ae awesome.

DYNAMIS AND STRUTURAL LOADING IN WIND TURBINES M. Ragheb 12/30/2008 INTRODUTION The loading egimes to which wind tubines ae subject to ae extemely complex equiing special attention in thei design, opeation

### Viscosity. Desmond Schipper Andrew R. Barron. 1 Introduction

OpenStax-CNX module: m50215 1 Viscosity Desmond Schipper Andrew R. Barron This work is produced by OpenStax-CNX and licensed under the Creative Commons Attribution License 4.0 Abstract This module discusses

### LATIN SQUARE DESIGN (LS) -With the Latin Square design you are able to control variation in two directions.

Facts about the LS Design LATIN SQUARE DESIGN (LS) -With the Latin Squae design you ae able to contol vaiation in two diections. -Teatments ae aanged in ows and columns -Each ow contains evey teatment.

### An Epidemic Model of Mobile Phone Virus

An Epidemic Model of Mobile Phone Vius Hui Zheng, Dong Li, Zhuo Gao 3 Netwok Reseach Cente, Tsinghua Univesity, P. R. China zh@tsinghua.edu.cn School of Compute Science and Technology, Huazhong Univesity

### Journal bearings/sliding bearings

Journal bearings/sliding bearings Operating conditions: Advantages: - Vibration damping, impact damping, noise damping - not sensitive for vibrations, low operating noise level - dust tight (if lubricated

### VISCOSITY OF A LIQUID. To determine the viscosity of a lubricating oil. Time permitting, the temperature variation of viscosity can also be studied.

VISCOSITY OF A LIQUID August 19, 004 OBJECTIVE: EQUIPMENT: To determine the viscosity of a lubricating oil. Time permitting, the temperature variation of viscosity can also be studied. Viscosity apparatus

### OUTCOME 3 TUTORIAL 5 DIMENSIONAL ANALYSIS

Unit 41: Fluid Mechanics Unit code: T/601/1445 QCF Level: 4 Credit value: 15 OUTCOME 3 TUTORIAL 5 DIMENSIONAL ANALYSIS 3 Be able to determine the behavioural characteristics and parameters of real fluid

### Exam 2 is at 7 pm tomorrow Conflict is at 5:15 pm in 151 Loomis

* By request, but I m not vouching for these since I didn t write them Exam 2 is at 7 pm tomorrow Conflict is at 5:15 pm in 151 Loomis There are extra office hours today & tomorrow Lots of practice exams

### Complex Envelope Vectorization for the solution of mid-high frequency acoustic problems. A. Sestieri

Complex Envelope Vectoization fo the solution of mid-high fequency acoustic poblems A. Sestiei Depatment of Mechanical and Aeospace Engineeing Univesity of Rome la Sapienza Pesentation layout - Low fequency

### PHY121 #8 Midterm I 3.06.2013

PHY11 #8 Midterm I 3.06.013 AP Physics- Newton s Laws AP Exam Multiple Choice Questions #1 #4 1. When the frictionless system shown above is accelerated by an applied force of magnitude F, the tension

### Physics 101 Hour Exam 3 December 1, 2014

Physics 101 Hour Exam 3 December 1, 2014 Last Name: First Name ID Discussion Section: Discussion TA Name: Instructions Turn off your cell phone and put it away. Calculators cannot be shared. Please keep

### Chapter 2 Mathematical Model of the Safety Factor and Control Problem Formulation

Chapte 2 Mathematical Model of the Safety Facto and Contol Poblem Fomulation We ae inteested in contolling the safety facto pofile in a tokamak plasma. As the safety facto depends on the atio of the nomalized

### CO 2 41.2 MPa (abs) 20 C

comp_02 A CO 2 cartridge is used to propel a small rocket cart. Compressed CO 2, stored at a pressure of 41.2 MPa (abs) and a temperature of 20 C, is expanded through a smoothly contoured converging nozzle

### Construction of semi-dynamic model of subduction zone with given plate kinematics in 3D sphere

Eath Planets Space, 62, 665 673, 2010 Constuction of semi-dynamic model of subduction zone with given plate kinematics in 3D sphee M. Moishige 1, S. Honda 1, and P. J. Tackley 2 1 Eathquake Reseach Institute,

### Instructions. Application. FORTIFIed with. www.gkhair.com info@gkhair.com PH: +1.305.390.0044 +1 888.JUVEXIN (888.588.

FORTIFIed with Juvexin Application Instuctions www.gkhai.com info@gkhai.com PH: +1.5.390.0044 +1 888.JUVEXIN (888.588.3946) POWERED BY: GKhai, Global Keatin, Hai Taming System, Juvexin, and ph+ ae tademaks

### Fluid Dynamics Viscosity. Dave Foster Department of Chemical Engineering University of Rochester Email: dafoster@che

Fluid Dynamics Viscosity Dave Foster Department of Chemical Engineering University of Rochester Email: dafoster@che che.rochester.eduedu 1 Chemical Engineering What do Chemical Engineers Do? Manufacturing

### Chapter 3 Savings, Present Value and Ricardian Equivalence

Chapte 3 Savings, Pesent Value and Ricadian Equivalence Chapte Oveview In the pevious chapte we studied the decision of households to supply hous to the labo maket. This decision was a static decision,

### Definitions and terminology

I love the Case & Fai textbook but it is out of date with how monetay policy woks today. Please use this handout to supplement the chapte on monetay policy. The textbook assumes that the Fedeal Reseve

### FREESTUDY HEAT TRANSFER TUTORIAL 3 ADVANCED STUDIES

FREESTUDY HEAT TRANSFER TUTORIAL ADVANCED STUDIES This is the third tutorial in the series on heat transfer and covers some of the advanced theory of convection. The tutorials are designed to bring the

### Equity compensation plans New Income Statement impact on guidance Earnings Per Share Questions and answers

Investos/Analysts Confeence: Accounting Wokshop Agenda Equity compensation plans New Income Statement impact on guidance Eanings Pe Shae Questions and answes IAC03 / a / 1 1 Equity compensation plans The

### Heat transfer analysis of canned food sterilization in a still retort

Available online at www.sciencediect.com Jounal of Food Engineeing xxx (28) xxx xxx www.elsevie.com/locate/jfoodeng Heat tansfe analysis of canned food steilization in a still etot A. Kannan *, P.Ch. Gouisanka