MOMENTUM PRINCIPLE. Review: Last time, we derived the Reynolds Transport Theorem: Chapter 6. where B is any extensive property (proportional to mass),
|
|
- Austen Stanley
- 6 years ago
- Views:
Transcription
1 Chapter 6 MOMENTUM PRINCIPLE Review: Last time, we derived the Reynolds Transport Theorem: where B is any extensive property (proportional to mass), and b is the corresponding intensive property (B / m ). Fluid Mechanics, Spring Term 2011 a) b) c) Recall: The system (e.g., B sys ) is a fluid volume that moves along with the fluid particles. The control volume (cv) may move relative to the fluid; for example, it may be fixed in space. The control surface (cs) is a closed surface that contains the control volume. Meaning: Term a) describes the physical change that takes place for a set of fluid particles. Term b) describes the change observed in a given control volume. Term c) describes the difference: For example, if the property B has not changed for the fluid particles, but B has changed inside the control volume, then this must be because new fluid particles have entered the cv which carried a different amount of B with them.
2 Still review We then applied the Reynolds Transport Theorem to the property of mass (M ). Different ways of writing the results: with Today, we use the Momentum Principle: We will do 2 things: 1) Use the law of conservation of momentum (Newtonʼs 2nd Law). 2) Set B = mv, (where B is the extensive property) and substitute this into the Reynolds Transport Theorem. Notice the similarities to last lecture: 1) Use conservation of mass, dm sys / dt = 0 2) Set B = m Newtonʼs 2nd Law: or Definition of (linear) momentum: The momentum conserved is that of the system: Particles move about in a box. No particles leave or enter, hence the box is a system. Conservation of momentum: Particles can exchange momentum with each other, but that does not affect the total momentum of the system. The only way to change the total momentum is to apply a force to the box.
3 Therefore: Notice the similarities and differences between conservation of mass and momentum: (conservation of mass) (conservation of momentum) 1) Both equations are applied to the system. 2) Mass is conserved absolutely (never changes in classical physics); Momentum is conserved unless a force is applied. 3) Mass conservation is a scalar equation; Momentum conservation is a vector equation (3 equations). Reynolds Transport Theorem with B = mv becomes Notice the little v and the big V in the last term. The big V comes from the Reynolds Transport Theorem. It is the fluid velocity relative to the control surface. and using Newtonʼs 2nd Law we get The little v comes from the momentum definition. It is the fluid velocity relative to the reference frame. v and V are the same only if the control volume is at rest relative to the reference frame.
4 V wall Forces acting on a control volume (Fig. 6.1) V fluid V wall V cv The integral over cv is the change in momentum in the control volume. The last term is again a convective correction in going from the Lagrangian to the Eulerian frame: V fluid In the channel flow illustrated, nothing changed between 1 and 2; only the control volume moved. But the momentum in cv increases because new particles with greater momentum have flowed into cv. cv consists of fluid only. Cv includes the section of the pipe. Choice 1: control volume is entirely within the fluid. Choice 2: The control volume includes the entire section of the pipe. where! is a viscous shear stress acting between the fluid and the pipe wall (its direction depends on whether the fluid is moving up or down). where W p is the weight of the pipe.
5 Momentum Accumulation (Fig 6.2) Momentum equation (general): Steady flow through a nozzle. The momentum of each fluid particle passing through the nozzle changes with time. If v is constant across inlet and outlet: Recall (Chapter 5) the mass flow rate For steady flow, the integrated momentum inside the cv does not change with time. There is no accumulation of momentum in the cv. (Momentum equation for inlet and outlet ports) Momentum Diagram: The change in momentum in the cv may be visualized with a momentum diagram. (Notice that weʼre drawing changes in momentum, i.e., accelerations!) Momentum Equation in Cartesian Coordinates (inlet and outlet ports with constant velocities) (inflow) (outflow) Net outflow of momentum: (a fairly obvious, special form of the momentum equation )
6 Systematic Approach to Solving Problems: 1) Problem Setup Select appropriate control volume. Select inertial reference frame. 2) Force analysis and diagram Sketch body forces on force diagram (gravity). Sketch surface forces: pressures, shear stresses, supports and structures 3) Momentum analysis and diagram Evaluate momentum accumulation term. If the flow is steady, this term is zero. Otherwise evaluate volume integral and add to momentum diagram. Sketch momentum flow vectors on momentum diagram. For uniform velocity, each vector is Example 6.1: Rocket on test stand. Exhaust jet has: Diameter d = 1 cm Speed v = 450 m/s Density " = 0.5 kg/m 3 Assume p in jet is atmospheric p. Neglect momentum changes inside rocket motor. What is the force F b acting on support beam? Example 6.1: Solution Only involves vertical momentum. 1) Forces: Example 6.1 (continued) Substitute forces and momentum into the momentum equation: 2) Momentum change: There is no momentum accumulation because the structure is stationary and because we neglect momentum changes in the rocket motor. or
7 Example 6.2: Concrete flowing onto cart on a scale Example 6.2: Solution Stream of concrete: Given: Density = " Area = A Speed = v Cart + concrete: Weight = W Determine tension in cable and weight recorded by scale. Forces and momenta involve x and z directions. Forces in x: Forces in z: Example 6.2 (continued) Example 6.2 (continued) Since flow is steady and cart does not move, there is no accumulation of momentum inside the cv. The momentum equations in x and z give Momentum changes in x and z: (with ) thus providing T and N as the answer. (Notice in this problem the cv is stationary; hence, the velocities v and V are the same).
8 Example 6.4: Water jet deflected by a vane Example 6.4: Solution Given: Speed of incoming jet = v 1 Speed of outgoing jet = v 2 Diameter of jet = D 1) Forces: Note that mass flow rates have to be equal: 2) Momenta: Net momentum change: Example 6.4 (continued) Example 6.7: Water flow through a 180 o reducing bend Again, substitute into momentum equation: Given: Discharge = Q Where is given by Pressure at center of inlet = p 1 Volume of bend = V Weight of bend = W What force is required to hold the bend in place?
9 Example 6.7: Solution Example 6.7 (continued) Additional difficulties: 1) We donʼt know the velocities. 2) We donʼt know the outlet pressure. 1) Get velocities from continuity equation (incompressible!): 2) Get p 2 from Bernoulli equation: Note: z1 & z2 are at center of pipe. Why? Notice that there is no momentum change in the vertical. In the vertical we only have the force balance Forces in x-direction: Momentum in x-direction: Momentum balance in x: Using continuity and Bernoulli equations (previous slide), all variables are known except R x.
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:
More informationCOURSE NUMBER: ME 321 Fluid Mechanics I 3 credit hour. Basic Equations in fluid Dynamics
COURSE NUMBER: ME 321 Fluid Mechanics I 3 credit hour Basic Equations in fluid Dynamics Course teacher Dr. M. Mahbubur Razzaque Professor Department of Mechanical Engineering BUET 1 Description of Fluid
More informationConservation of Momentum using Control Volumes
Conservation of Momentum using Control Volumes Conservation of Linear Momentum Recall the conservation of linear momentum law for a system: In order to convert this for use in a control volume, use RTT
More informationM E 320 Professor John M. Cimbala Lecture 10. The Reynolds Transport Theorem (RTT) (Section 4-6)
M E 320 Professor John M. Cimbala Lecture 10 Today, we will: Discuss the Reynolds Transport Theorem (RTT) Show how the RTT applies to the conservation laws Begin Chapter 5 Conservation Laws D. The Reynolds
More informationChapter 5 Control Volume Approach and Continuity Equation
Chapter 5 Control Volume Approach and Continuity Equation Lagrangian and Eulerian Approach To evaluate the pressure and velocities at arbitrary locations in a flow field. The flow into a sudden contraction,
More informationME3560 Tentative Schedule Spring 2019
ME3560 Tentative Schedule Spring 2019 Week Number Date Lecture Topics Covered Prior to Lecture Read Section Assignment Prep Problems for Prep Probs. Must be Solved by 1 Monday 1/7/2019 1 Introduction to
More informationFluid Dynamics Exercises and questions for the course
Fluid Dynamics Exercises and questions for the course January 15, 2014 A two dimensional flow field characterised by the following velocity components in polar coordinates is called a free vortex: u r
More informationFluid Mechanics. du dy
FLUID MECHANICS Technical English - I 1 th week Fluid Mechanics FLUID STATICS FLUID DYNAMICS Fluid Statics or Hydrostatics is the study of fluids at rest. The main equation required for this is Newton's
More informationME3560 Tentative Schedule Fall 2018
ME3560 Tentative Schedule Fall 2018 Week Number 1 Wednesday 8/29/2018 1 Date Lecture Topics Covered Introduction to course, syllabus and class policies. Math Review. Differentiation. Prior to Lecture Read
More informationvector H. If O is the point about which moments are desired, the angular moment about O is given:
The angular momentum A control volume analysis can be applied to the angular momentum, by letting B equal to angularmomentum vector H. If O is the point about which moments are desired, the angular moment
More informationPage 1. Neatly print your name: Signature: (Note that unsigned exams will be given a score of zero.)
Page 1 Neatly print your name: Signature: (Note that unsigned exams will be given a score of zero.) Circle your lecture section (-1 point if not circled, or circled incorrectly): Prof. Vlachos Prof. Ardekani
More informationTherefore, the control volume in this case can be treated as a solid body, with a net force or thrust of. bm # V
When the mass m of the control volume remains nearly constant, the first term of the Eq. 6 8 simply becomes mass times acceleration since 39 CHAPTER 6 d(mv ) CV m dv CV CV (ma ) CV Therefore, the control
More informationFluid Mechanics II. Newton s second law applied to a control volume
Fluid Mechanics II Stead flow momentum equation Newton s second law applied to a control volume Fluids, either in a static or dnamic motion state, impose forces on immersed bodies and confining boundaries.
More informationConsider a control volume in the form of a straight section of a streamtube ABCD.
6 MOMENTUM EQUATION 6.1 Momentum and Fluid Flow In mechanics, the momentum of a particle or object is defined as the product of its mass m and its velocity v: Momentum = mv The particles of a fluid stream
More informationWhere does Bernoulli's Equation come from?
Where does Bernoulli's Equation come from? Introduction By now, you have seen the following equation many times, using it to solve simple fluid problems. P ρ + v + gz = constant (along a streamline) This
More informationLesson 6 Review of fundamentals: Fluid flow
Lesson 6 Review of fundamentals: Fluid flow The specific objective of this lesson is to conduct a brief review of the fundamentals of fluid flow and present: A general equation for conservation of mass
More informationMASS, MOMENTUM, AND ENERGY EQUATIONS
MASS, MOMENTUM, AND ENERGY EQUATIONS This chapter deals with four equations commonly used in fluid mechanics: the mass, Bernoulli, Momentum and energy equations. The mass equation is an expression of the
More information5 ENERGY EQUATION OF FLUID MOTION
5 ENERGY EQUATION OF FLUID MOTION 5.1 Introduction In order to develop the equations that describe a flow, it is assumed that fluids are subject to certain fundamental laws of physics. The pertinent laws
More informationMAE 3130: Fluid Mechanics Lecture 7: Differential Analysis/Part 1 Spring Dr. Jason Roney Mechanical and Aerospace Engineering
MAE 3130: Fluid Mechanics Lecture 7: Differential Analysis/Part 1 Spring 2003 Dr. Jason Roney Mechanical and Aerospace Engineering Outline Introduction Kinematics Review Conservation of Mass Stream Function
More informationShell/Integral Balances (SIB)
Shell/Integral Balances (SIB) Shell/Integral Balances Shell or integral (macroscopic) balances are often relatively simple to solve, both conceptually and mechanically, as only limited data is necessary.
More informationChapter 2: Basic Governing Equations
-1 Reynolds Transport Theorem (RTT) - Continuity Equation -3 The Linear Momentum Equation -4 The First Law of Thermodynamics -5 General Equation in Conservative Form -6 General Equation in Non-Conservative
More information2 Navier-Stokes Equations
1 Integral analysis 1. Water enters a pipe bend horizontally with a uniform velocity, u 1 = 5 m/s. The pipe is bended at 90 so that the water leaves it vertically downwards. The input diameter d 1 = 0.1
More informationFE Exam Fluids Review October 23, Important Concepts
FE Exam Fluids Review October 3, 013 mportant Concepts Density, specific volume, specific weight, specific gravity (Water 1000 kg/m^3, Air 1. kg/m^3) Meaning & Symbols? Stress, Pressure, Viscosity; Meaning
More informationwhere = rate of change of total energy of the system, = rate of heat added to the system, = rate of work done by the system
The Energy Equation for Control Volumes Recall, the First Law of Thermodynamics: where = rate of change of total energy of the system, = rate of heat added to the system, = rate of work done by the system
More informationDifferential relations for fluid flow
Differential relations for fluid flow In this approach, we apply basic conservation laws to an infinitesimally small control volume. The differential approach provides point by point details of a flow
More information6. The Momentum Equation
6. The Momentum Equation [This material relates predominantly to modules ELP034, ELP035] 6. Definition of the momentum equation Applications of the momentum equation: 6. The force due to the flow around
More informationMass of fluid leaving per unit time
5 ENERGY EQUATION OF FLUID MOTION 5.1 Eulerian Approach & Control Volume In order to develop the equations that describe a flow, it is assumed that fluids are subject to certain fundamental laws of physics.
More informationThermodynamics ENGR360-MEP112 LECTURE 7
Thermodynamics ENGR360-MEP11 LECTURE 7 Thermodynamics ENGR360/MEP11 Objectives: 1. Conservation of mass principle.. Conservation of energy principle applied to control volumes (first law of thermodynamics).
More informationCHAPTER 3 BASIC EQUATIONS IN FLUID MECHANICS NOOR ALIZA AHMAD
CHAPTER 3 BASIC EQUATIONS IN FLUID MECHANICS 1 INTRODUCTION Flow often referred as an ideal fluid. We presume that such a fluid has no viscosity. However, this is an idealized situation that does not exist.
More informationIntroduction to Fluid Machines and Compressible Flow Prof. S. K. Som Department of Mechanical Engineering Indian Institute of Technology, Kharagpur
Introduction to Fluid Machines and Compressible Flow Prof. S. K. Som Department of Mechanical Engineering Indian Institute of Technology, Kharagpur Lecture - 07 Analysis of Force on the Bucket of Pelton
More informationAngular momentum equation
Angular momentum equation For angular momentum equation, B =H O the angular momentum vector about point O which moments are desired. Where β is The Reynolds transport equation can be written as follows:
More informationHeat and Mass Transfer Prof. S.P. Sukhatme Department of Mechanical Engineering Indian Institute of Technology, Bombay
Heat and Mass Transfer Prof. S.P. Sukhatme Department of Mechanical Engineering Indian Institute of Technology, Bombay Lecture No. 18 Forced Convection-1 Welcome. We now begin our study of forced convection
More informationChapter Four fluid flow mass, energy, Bernoulli and momentum
4-1Conservation of Mass Principle Consider a control volume of arbitrary shape, as shown in Fig (4-1). Figure (4-1): the differential control volume and differential control volume (Total mass entering
More informationM E 320 Professor John M. Cimbala Lecture 10
M E 320 Professor John M. Cimbala Lecture 10 Today, we will: Finish our example problem rates of motion and deformation of fluid particles Discuss the Reynolds Transport Theorem (RTT) Show how the RTT
More informationFluid Mechanics Prof. S. K. Som Department of Mechanical Engineering Indian Institute of Technology, Kharagpur
Fluid Mechanics Prof. S. K. Som Department of Mechanical Engineering Indian Institute of Technology, Kharagpur Lecture - 15 Conservation Equations in Fluid Flow Part III Good afternoon. I welcome you all
More informationLecture 4. Differential Analysis of Fluid Flow Navier-Stockes equation
Lecture 4 Differential Analysis of Fluid Flow Navier-Stockes equation Newton second law and conservation of momentum & momentum-of-momentum A jet of fluid deflected by an object puts a force on the object.
More informationObjectives. Conservation of mass principle: Mass Equation The Bernoulli equation Conservation of energy principle: Energy equation
Objectives Conservation of mass principle: Mass Equation The Bernoulli equation Conservation of energy principle: Energy equation Conservation of Mass Conservation of Mass Mass, like energy, is a conserved
More informationFE Fluids Review March 23, 2012 Steve Burian (Civil & Environmental Engineering)
Topic: Fluid Properties 1. If 6 m 3 of oil weighs 47 kn, calculate its specific weight, density, and specific gravity. 2. 10.0 L of an incompressible liquid exert a force of 20 N at the earth s surface.
More informationPart A: 1 pts each, 10 pts total, no partial credit.
Part A: 1 pts each, 10 pts total, no partial credit. 1) (Correct: 1 pt/ Wrong: -3 pts). The sum of static, dynamic, and hydrostatic pressures is constant when flow is steady, irrotational, incompressible,
More information1.060 Engineering Mechanics II Spring Problem Set 4
1.060 Engineering Mechanics II Spring 2006 Due on Monday, March 20th Problem Set 4 Important note: Please start a new sheet of paper for each problem in the problem set. Write the names of the group members
More information4 Mechanics of Fluids (I)
1. The x and y components of velocity for a two-dimensional flow are u = 3.0 ft/s and v = 9.0x ft/s where x is in feet. Determine the equation for the streamlines and graph representative streamlines in
More informationBasic Fluid Mechanics
Basic Fluid Mechanics Chapter 5: Application of Bernoulli Equation 4/16/2018 C5: Application of Bernoulli Equation 1 5.1 Introduction In this chapter we will show that the equation of motion of a particle
More informationImpact of a Jet. Experiment 4. Purpose. Apparatus. Theory. Symmetric Jet
Experiment 4 Impact of a Jet Purpose The purpose of this experiment is to demonstrate and verify the integral momentum equation. The force generated by a jet of water deflected by an impact surface is
More information3.8 The First Law of Thermodynamics and the Energy Equation
CEE 3310 Control Volume Analysis, Sep 30, 2011 65 Review Conservation of angular momentum 1-D form ( r F )ext = [ˆ ] ( r v)d + ( r v) out ṁ out ( r v) in ṁ in t CV 3.8 The First Law of Thermodynamics and
More informationSignature: (Note that unsigned exams will be given a score of zero.)
Neatly print your name: Signature: (Note that unsigned exams will be given a score of zero.) Circle your lecture section (-1 point if not circled, or circled incorrectly): Prof. Dabiri Prof. Wassgren Prof.
More informationShell Balances in Fluid Mechanics
Shell Balances in Fluid Mechanics R. Shankar Subramanian Department of Chemical and Biomolecular Engineering Clarkson University When fluid flow occurs in a single direction everywhere in a system, shell
More informationROAD MAP... D-0: Reynolds Transport Theorem D-1: Conservation of Mass D-2: Conservation of Momentum D-3: Conservation of Energy
ES06 Fluid Mechani UNIT D: Flow Field Analysis ROAD MAP... D-0: Reynolds Transport Theorem D-1: Conservation of Mass D-: Conservation of Momentum D-3: Conservation of Energy ES06 Fluid Mechani Unit D-0:
More information1. Introduction, tensors, kinematics
1. Introduction, tensors, kinematics Content: Introduction to fluids, Cartesian tensors, vector algebra using tensor notation, operators in tensor form, Eulerian and Lagrangian description of scalar and
More informationFLOW IN CONDUITS. Shear stress distribution across a pipe section. Chapter 10
Chapter 10 Shear stress distribution across a pipe section FLOW IN CONDUITS For steady, uniform flow, the momentum balance in s for the fluid cylinder yields Fluid Mechanics, Spring Term 2010 Velocity
More informationConservation of Angular Momentum
10 March 2017 Conservation of ngular Momentum Lecture 23 In the last class, we discussed about the conservation of angular momentum principle. Using RTT, the angular momentum principle was given as DHo
More information4 Finite Control Volume Analysis Introduction Reynolds Transport Theorem Conservation of Mass
iv 2.3.2 Bourdon Gage................................... 92 2.3.3 Pressure Transducer................................ 93 2.3.4 Manometer..................................... 95 2.3.4.1 Piezometer................................
More information!! +! 2!! +!"!! =!! +! 2!! +!"!! +!!"!"!"
Homework 4 Solutions 1. (15 points) Bernoulli s equation can be adapted for use in evaluating unsteady flow conditions, such as those encountered during start- up processes. For example, consider the large
More informationFluid Mechanics for International Engineers HW #4: Conservation of Linear Momentum and Conservation of Energy
2141-365 Fluid Mechanics for International Engineers 1 Problem 1 RTT and Time Rate of Change of Linear Momentum and The Corresponding Eternal Force Notation: Here a material volume (MV) is referred to
More informationChapter 6: Momentum Analysis
6-1 Introduction 6-2Newton s Law and Conservation of Momentum 6-3 Choosing a Control Volume 6-4 Forces Acting on a Control Volume 6-5Linear Momentum Equation 6-6 Angular Momentum 6-7 The Second Law of
More informationChapter (4) Motion of Fluid Particles and Streams
Chapter (4) Motion of Fluid Particles and Streams Read all Theoretical subjects from (slides Dr.K.AlASTAL) Patterns of Flow Reynolds Number (R e ): A dimensionless number used to identify the type of flow.
More informationLecture 2. Lecture 1. Forces on a rotating planet. We will describe the atmosphere and ocean in terms of their:
Lecture 2 Lecture 1 Forces on a rotating planet We will describe the atmosphere and ocean in terms of their: velocity u = (u,v,w) pressure P density ρ temperature T salinity S up For convenience, we will
More information2 Internal Fluid Flow
Internal Fluid Flow.1 Definitions Fluid Dynamics The study of fluids in motion. Static Pressure The pressure at a given point exerted by the static head of the fluid present directly above that point.
More information150A Review Session 2/13/2014 Fluid Statics. Pressure acts in all directions, normal to the surrounding surfaces
Fluid Statics Pressure acts in all directions, normal to the surrounding surfaces or Whenever a pressure difference is the driving force, use gauge pressure o Bernoulli equation o Momentum balance with
More informationUNIT I FLUID PROPERTIES AND STATICS
SIDDHARTH GROUP OF INSTITUTIONS :: PUTTUR Siddharth Nagar, Narayanavanam Road 517583 QUESTION BANK (DESCRIPTIVE) Subject with Code : Fluid Mechanics (16CE106) Year & Sem: II-B.Tech & I-Sem Course & Branch:
More informationTable tennis ball suspended by an air jet. The control volume momentum principle, studied in this chapter, requires a force to change the direction
38 Table tennis ball suspended by an air jet. The control volume momentum principle, studied in this chapter, requires a force to change the direction of a flow. The jet flow deflects around the ball,
More informationIn this section, mathematical description of the motion of fluid elements moving in a flow field is
Jun. 05, 015 Chapter 6. Differential Analysis of Fluid Flow 6.1 Fluid Element Kinematics In this section, mathematical description of the motion of fluid elements moving in a flow field is given. A small
More informationLecture 1: Kinematics, ideal mechanical systems and Bernoulli s equation
Lecture 1: Kinematics, ideal mechanical systems and Bernoulli s equation Should be able to: Understand some terms used in flow visualization and kinematics Understand Lagrangian and Eulerian frames of
More informationMECH 5810 Module 3: Conservation of Linear Momentum
MECH 5810 Module 3: Conservation of Linear Momentum D.J. Willis Department of Mechanical Engineering University of Massachusetts, Lowell MECH 5810 Advanced Fluid Dynamics Fall 2017 Outline 1 Announcements
More informationLecture 2 Flow classifications and continuity
Lecture 2 Flow classifications and continuity Dr Tim Gough: t.gough@bradford.ac.uk General information 1 No tutorial week 3 3 rd October 2013 this Thursday. Attempt tutorial based on examples from today
More information10.52 Mechanics of Fluids Spring 2006 Problem Set 3
10.52 Mechanics of Fluids Spring 2006 Problem Set 3 Problem 1 Mass transfer studies involving the transport of a solute from a gas to a liquid often involve the use of a laminar jet of liquid. The situation
More informationEXPERIMENT No.1 FLOW MEASUREMENT BY ORIFICEMETER
EXPERIMENT No.1 FLOW MEASUREMENT BY ORIFICEMETER 1.1 AIM: To determine the co-efficient of discharge of the orifice meter 1.2 EQUIPMENTS REQUIRED: Orifice meter test rig, Stopwatch 1.3 PREPARATION 1.3.1
More information2. FLUID-FLOW EQUATIONS SPRING 2019
2. FLUID-FLOW EQUATIONS SPRING 2019 2.1 Introduction 2.2 Conservative differential equations 2.3 Non-conservative differential equations 2.4 Non-dimensionalisation Summary Examples 2.1 Introduction Fluid
More informationCLASS Fourth Units (Second part)
CLASS Fourth Units (Second part) Energy analysis of closed systems Copyright The McGraw-Hill Companies, Inc. Permission required for reproduction or display. MOVING BOUNDARY WORK Moving boundary work (P
More informationChapter 15B - Fluids in Motion. A PowerPoint Presentation by Paul E. Tippens, Professor of Physics Southern Polytechnic State University
Chapter 15B - Fluids in Motion A PowerPoint Presentation by Paul E. Tippens, Professor of Physics Southern Polytechnic State University 007 Paul E. Tippens Fluid Motion The lower falls at Yellowstone National
More informationComputational Fluid Dynamics Prof. Dr. Suman Chakraborty Department of Mechanical Engineering Indian Institute of Technology, Kharagpur
Computational Fluid Dynamics Prof. Dr. Suman Chakraborty Department of Mechanical Engineering Indian Institute of Technology, Kharagpur Lecture No. # 02 Conservation of Mass and Momentum: Continuity and
More informationV/ t = 0 p/ t = 0 ρ/ t = 0. V/ s = 0 p/ s = 0 ρ/ s = 0
UNIT III FLOW THROUGH PIPES 1. List the types of fluid flow. Steady and unsteady flow Uniform and non-uniform flow Laminar and Turbulent flow Compressible and incompressible flow Rotational and ir-rotational
More informationChapter 9: Differential Analysis
9-1 Introduction 9-2 Conservation of Mass 9-3 The Stream Function 9-4 Conservation of Linear Momentum 9-5 Navier Stokes Equation 9-6 Differential Analysis Problems Recall 9-1 Introduction (1) Chap 5: Control
More informationExperiment (4): Flow measurement
Experiment (4): Flow measurement Introduction: The flow measuring apparatus is used to familiarize the students with typical methods of flow measurement of an incompressible fluid and, at the same time
More information6. Basic basic equations I ( )
6. Basic basic equations I (4.2-4.4) Steady and uniform flows, streamline, streamtube One-, two-, and three-dimensional flow Laminar and turbulent flow Reynolds number System and control volume Continuity
More informationPh.D. Qualifying Exam in Fluid Mechanics
Student ID Department of Mechanical Engineering Michigan State University East Lansing, Michigan Ph.D. Qualifying Exam in Fluid Mechanics Closed book and Notes, Some basic equations are provided on an
More informationChapter 5: Mass, Bernoulli, and Energy Equations
Chapter 5: Mass, Bernoulli, and Energy Equations Introduction This chapter deals with 3 equations commonly used in fluid mechanics The mass equation is an expression of the conservation of mass principle.
More informationSYSTEMS VS. CONTROL VOLUMES. Control volume CV (open system): Arbitrary geometric space, surrounded by control surfaces (CS)
SYSTEMS VS. CONTROL VOLUMES System (closed system): Predefined mass m, surrounded by a system boundary Control volume CV (open system): Arbitrary geometric space, surrounded by control surfaces (CS) Many
More informationChapter 9: Differential Analysis of Fluid Flow
of Fluid Flow Objectives 1. Understand how the differential equations of mass and momentum conservation are derived. 2. Calculate the stream function and pressure field, and plot streamlines for a known
More informationcos(θ)sin(θ) Alternative Exercise Correct Correct θ = 0 skiladæmi 10 Part A Part B Part C Due: 11:59pm on Wednesday, November 11, 2015
skiladæmi 10 Due: 11:59pm on Wednesday, November 11, 015 You will receive no credit for items you complete after the assignment is due Grading Policy Alternative Exercise 1115 A bar with cross sectional
More informationExam #2: Fluid Kinematics and Conservation Laws April 13, 2016, 7:00 p.m. 8:40 p.m. in CE 118
CVEN 311-501 (Socolofsky) Fluid Dynamics Exam #2: Fluid Kinematics and Conservation Laws April 13, 2016, 7:00 p.m. 8:40 p.m. in CE 118 Name: : UIN: : Instructions: Fill in your name and UIN in the space
More informationChapter 7 The Energy Equation
Chapter 7 The Energy Equation 7.1 Energy, Work, and Power When matter has energy, the matter can be used to do work. A fluid can have several forms of energy. For example a fluid jet has kinetic energy,
More informationQ1 Give answers to all of the following questions (5 marks each):
FLUID MECHANICS First Year Exam Solutions 03 Q Give answers to all of the following questions (5 marks each): (a) A cylinder of m in diameter is made with material of relative density 0.5. It is moored
More informationHydraulics for Urban Storm Drainage
Urban Hydraulics Hydraulics for Urban Storm Drainage Learning objectives: understanding of basic concepts of fluid flow and how to analyze conduit flows, free surface flows. to analyze, hydrostatic pressure
More informationIntroduction to Fluid Machines, and Compressible Flow Prof. S. K. Som Department of Mechanical Engineering Indian Institute of Technology, Kharagpur
Introduction to Fluid Machines, and Compressible Flow Prof. S. K. Som Department of Mechanical Engineering Indian Institute of Technology, Kharagpur Lecture - 09 Introduction to Reaction Type of Hydraulic
More informationBasic Fluid Mechanics
Basic Fluid Mechanics Chapter 3B: Conservation of Mass C3B: Conservation of Mass 1 3.2 Governing Equations There are two basic types of governing equations that we will encounter in this course Differential
More informationFluid Mechanics Prof. T.I. Eldho Department of Civil Engineering Indian Institute of Technology, Bombay. Lecture - 17 Laminar and Turbulent flows
Fluid Mechanics Prof. T.I. Eldho Department of Civil Engineering Indian Institute of Technology, Bombay Lecture - 17 Laminar and Turbulent flows Welcome back to the video course on fluid mechanics. In
More informationFluid Mechanics Prof. S.K. Som Department of Mechanical Engineering Indian Institute of Technology, Kharagpur
Fluid Mechanics Prof. S.K. Som Department of Mechanical Engineering Indian Institute of Technology, Kharagpur Lecture - 42 Flows with a Free Surface Part II Good morning. I welcome you to this session
More informationIntroduction to Heat and Mass Transfer. Week 10
Introduction to Heat and Mass Transfer Week 10 Concentration Boundary Layer No concentration jump condition requires species adjacent to surface to have same concentration as at the surface Owing to concentration
More informationExperiment- To determine the coefficient of impact for vanes. Experiment To determine the coefficient of discharge of an orifice meter.
SUBJECT: FLUID MECHANICS VIVA QUESTIONS (M.E 4 th SEM) Experiment- To determine the coefficient of impact for vanes. Q1. Explain impulse momentum principal. Ans1. Momentum equation is based on Newton s
More informationME 431A/538A/538B Homework 22 October 2018 Advanced Fluid Mechanics
ME 431A/538A/538B Homework 22 October 2018 Advanced Fluid Mechanics For Friday, October 26 th Start reading the handout entitled Notes on finite-volume methods. Review Chapter 7 on Dimensional Analysis
More informationCE 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
More informationAA210A Fundamentals of Compressible Flow. Chapter 5 -The conservation equations
AA210A Fundamentals of Compressible Flow Chapter 5 -The conservation equations 1 5.1 Leibniz rule for differentiation of integrals Differentiation under the integral sign. According to the fundamental
More informationd v 2 v = d v d t i n where "in" and "rot" denote the inertial (absolute) and rotating frames. Equation of motion F =
Governing equations of fluid dynamics under the influence of Earth rotation (Navier-Stokes Equations in rotating frame) Recap: From kinematic consideration, d v i n d t i n = d v rot d t r o t 2 v rot
More informationVARIED FLOW IN OPEN CHANNELS
Chapter 15 Open Channels vs. Closed Conduits VARIED FLOW IN OPEN CHANNELS Fluid Mechanics, Spring Term 2011 In a closed conduit there can be a pressure gradient that drives the flow. An open channel has
More informationFundamentals of Transport Processes Prof. Kumaran Indian Institute of Science, Bangalore Chemical Engineering
Fundamentals of Transport Processes Prof. Kumaran Indian Institute of Science, Bangalore Chemical Engineering Module No # 05 Lecture No # 25 Mass and Energy Conservation Cartesian Co-ordinates Welcome
More informationME 3560 Fluid Mechanics
ME 3560 Fluid Mechanics 1 4.1 The Velocity Field One of the most important parameters that need to be monitored when a fluid is flowing is the velocity. In general the flow parameters are described in
More informationChapter 8: Flow in Pipes
Objectives 1. Have a deeper understanding of laminar and turbulent flow in pipes and the analysis of fully developed flow 2. Calculate the major and minor losses associated with pipe flow in piping networks
More informationChapter 6: Momentum Analysis of Flow Systems
Chapter 6: Momentum Analysis of Flow Systems Introduction Fluid flow problems can be analyzed using one of three basic approaches: differential, experimental, and integral (or control volume). In Chap.
More informationLast name: First name: Student ID: Discussion: You solution procedure should be legible and complete for full credit (use scratch paper as needed).
University of California, Berkeley Mechanical Engineering ME 106, Fluid Mechanics ODK/Midterm 2, Fall 2015 Last name: First name: Student ID: Discussion: Notes: You solution procedure should be legible
More informationCLASS SCHEDULE 2013 FALL
CLASS SCHEDULE 2013 FALL Class # or Lab # 1 Date Aug 26 2 28 Important Concepts (Section # in Text Reading, Lecture note) Examples/Lab Activities Definition fluid; continuum hypothesis; fluid properties
More information