Conservation Laws—Macroscopic Forms

Slides:



Advertisements
Similar presentations
Chapter 6: Momentum Analysis of Flow Systems
Advertisements

Lecture 15: Capillary motion
Continuity Equation. Continuity Equation Continuity Equation Net outflow in x direction.
Conservation laws • Laws of conservation of mass, energy, and momentum. • Conservation laws are first applied to a fixed quantity of matter called a closed.
Fluid Dynamics.
CONSERVATION OF MASS Control Volumes By: Bashir Momodu.
Fluid Kinematics Fluid Dynamics . Fluid Flow Concepts and Reynolds Transport Theorem ä Descriptions of: ä fluid motion ä fluid flows ä temporal and spatial.
1 MECH 221 FLUID MECHANICS (Fall 06/07) Tutorial 6 FLUID KINETMATICS.
Conservation Vector Review Mass Balance General Statement Simplifications The Control Volume A Useable Form Problems.
1 MFGT 242: Flow Analysis Chapter 4: Governing Equations for Fluid Flow Professor Joe Greene CSU, CHICO.
2-1 Problem Solving 1. Physics  2. Approach methods
Numerical Hydraulics Wolfgang Kinzelbach with Marc Wolf and Cornel Beffa Lecture 1: The equations.
Monroe L. Weber-Shirk S chool of Civil and Environmental Engineering Fluid Kinematics Fluid Mechanics July 14, 2015 
Fluid mechanics 3.1 – key points
Monroe L. Weber-Shirk S chool of Civil and Environmental Engineering Fluid Kinematics Fluid Mechanics July 15, 2015 Fluid Mechanics July 15, 2015 
Module 3 Fluid Flow. Lesson 20 CONTINUITY EQUATION DESCRIBE how the density of a fluid varies with temperature. DEFINE the term buoyancy. DESCRIBE the.
Chapter 2 – sections 1, 2, and 3 vocabulary 1.Force – a push or a pull exerted on an object 2.Unbalance force – a nonzero net force, which changes an object’s.
1 Lec 2: Problem solving, conservation of mass. 2 For next time: –Read: § 1-10 to 1-11; 2-1 to 2-4. Outline: –Properties of systems. –Problem solving.
Fluid Mechanics and Applications MECN 3110
Energy Balance Equation
Molecular Transport Equations. Outline 1.Molecular Transport Equations 2.Viscosity of Fluids 3.Fluid Flow.
Introduction to Fluid Mechanics
Aerodynamics Linear Motion (Moving Air ).
Louisiana Tech University Ruston, LA Momentum Balance Steven A. Jones BIEN 501/CMEN 513 Monday, March 19, 2007.
Chapter 7 Energy of a System. Introduction to Energy A variety of problems can be solved with Newton’s Laws and associated principles. Some problems that.
Newton’s Third Law of Motion
Energy momentum tensor of macroscopic bodies Section 35.
ME 254. Chapter I Integral Relations for a Control Volume An engineering science like fluid dynamics rests on foundations comprising both theory and experiment.
CE 394K.2 Hydrology, Lecture 2 Hydrologic Systems Hydrologic systems and hydrologic models How to apply physical laws to fluid systems Intrinsic and extrinsic.
Chapter 03: Macroscopic interface dynamics Xiangyu Hu Technical University of Munich Part A: physical and mathematical modeling of interface.
Chapter 12: Forces and Motion
Mechanical Energy Balance
Elementary Mechanics of Fluids CE 319 F Daene McKinney Control Volumes.
Integral budgets: mass and momentum Lecture 7 Mecânica de Fluidos Ambiental 2015/2016.
NEWTON’S SECOND LAW: LINEAR MOMENTUM
Lecture Objectives: Define 1) Reynolds stresses and
1. Integral vs Differential Approach
Helen Quinn. Varied usage across fields Physics: kinetic and potential energy, E=mc 2 Chemistry: bond energy, enthalpy… Biology: Food (or biomass) is.
98 Newton’s First Law 97 11/12/2014 Starter: What do you know about Newton’s Laws? Application Notes – Put here Connection: Mini Poster Exit: ( Just write.
Course : Civil Engineering Division : C (3 rd Semester). Subject : Fluid Mechanics Subject Code : Guided By :HIREN JARIWALA(H.O.D) :DIXIT CHAUHAN(ASSI.PROF.)
Remark: foils with „black background“ could be skipped, they are aimed to the more advanced courses Rudolf Žitný, Ústav procesní a zpracovatelské techniky.
1 The total inflow rate of momentum into the control volume is thus MOMENTUM CONSERVATION: CAUCHY EQUATION Consider the illustrated control volume, which.
Sophomore Engineering Clinic I September 25, 2014 Blackboard Back of Room Section 12- Miller Section 13- Reed Section 13- Reed 1 Section 9- Tole Section.
Chapter 6: Introduction to Convection
Chapter: 06 MASS AND ENERGY ANALYSIS OF CONTROL VOLUMES.
Chapter 6 MOMENTUM ANALYSIS OF FLOW SYSTEMS
MAE 5350: Gas Turbines Integral Forms of Mass and Momentum Equations
Energy Loss in Valves Function of valve type and valve position
Energy and Energy Transfer
Newton's Third Law of Motion and Momentum
Modeling and experimental study of coupled porous/channel flow
FLUID FLOW TYPICAL ENGINEERING PROBLEMS:
INFINITESIMALLY SMALL DIFFERENTIAL CUBE IN SPACE
Integrated Science Glencoe Chapter 4
Navier - Stokes Equation
Action and Reaction.
Conservation of momentum
Fluid Kinematics Fluid Dynamics.
Development of Conservation Equations for A CV
Modeling Algorithm Draw a picture Schematic
FLUID MECHANICS REVIEW
Control Volume Analysis Using Energy (continued)
Topic 5 NavierStokes Equations
MAE 3241: AERODYNAMICS AND FLIGHT MECHANICS
Chapter 3, Section 3 Notes The Third Law of Motion.
Conservation Laws Momentum and Impulse
Chapter 2 Section 1 Tools and Measurement.
14. Computational Fluid Dynamics
Section 3 Newton’s Third Law p. 360
Basic concepts of heat transfer: Heat Conduction
Presentation transcript:

Conservation Laws—Macroscopic Forms In this section of the course, we will obtain equations suitable for “macroscopic” balances for conservation of mass, momentum, and energy. On occasion, it will be advantageous to apply conservation laws to an entire unit. We may not know the details at points in space within the unit operation. The conservation laws in a macroscopic form can be valuable to analyze problems of this type. The term “macroscopic” suggests that the balance equation can be applied to a large “black box” without necessarily knowing what’s happening at distinct points in the interior. We choose a boundary to demarcate the region over which we will do our “accounting.” This should be an enclosed surface defining our control volume. Matter, forces and energy can flow or be transmitted across the control surface of the control volume. Experience helps us to make a smart choice for the control volume. By evaluating what’s happening at the surface with particular attention to entrances and exits, we can determine information about changes in the amounts of mass, energy or momentum with time. One of the challenges is how to represent the various quantities of interest in convenient mathematical forms suitable for obtaining information after analysis. While we aspire to apply mathematical equations to these systems, keep the physical picture in mind. Understanding the physical meaning of terms allows you to decide which terms are important and which are not. Later in the course, we’ll see that there are microscopic forms of these equations can be applied to points in space. These yield the continuity equation, equation of motion or the Navier-Stokes equations, but don’t worry about them for now. We will learn how these equations can be used to get velocity profiles, volumetric flowrates, stresses and other information.