Differential Analysis. Continuity Equation Momentum Equation.

Slides:

Advertisements

Similar presentations

HEAT TRANSFER Final Review # 1.

Advertisements

Resistance in Fluid Systems

Particle Acceleration Particle t t+dt. Physical Interpretation Total acceleration of a particle Local acceleration Convective acceleration time velocity.

Basic Governing Differential Equations

Monroe L. Weber-Shirk S chool of Civil and Environmental Engineering Basic Governing Differential Equations CEE 331 June 12, 2015.

Basic Governing Differential Equations

Navier-Stokes. Viscosity  A static fluid cannot support a shear.  A moving fluid with viscosity can have shear. Dynamic viscosity  Kinematic viscosity.

Lecture 4 Pressure variation in a static fluid N.S. Equations & simple solutions Intro DL.

Laminar Incompressible Flow over a Rotating Disk Numerical Analysis for Engineering John Virtue December 1999.

An Essential Need of Modern Civilization… P M V Subbarao Professor Mechanical Engineering Department I I T Delhi Viscous Fluid Flows in Ducts.

P M V Subbarao Professor Mechanical Engineering Department I I T Delhi

Reynolds Method to Diagnosize Symptoms of Infected Flows.... P M V Subbarao Professor Mechanical Engineering Department I I T Delhi Reynolds Averaged.

Monroe L. Weber-Shirk S chool of Civil and Environmental Engineering Basic Governing Differential Equations CEE 331 July 14, 2015 CEE 331 July 14, 2015.

LAMINAR PLANE COUETTE AND OPEN CHANNEL FLOW

1Chapter 2. 2 Example 3Chapter 2 4 EXAMPLE 5Chapter 2.

Conservation Laws for Continua

© 2011 Autodesk Freely licensed for use by educational institutions. Reuse and changes require a note indicating that content has been modified from the.

Biological fluid mechanics at the micro‐ and nanoscale Lecture 2: Some examples of fluid flows Anne Tanguy University of Lyon (France)

© Fox, McDonald & Pritchard Introduction to Fluid Mechanics Chapter 5 Introduction to Differential Analysis of Fluid Motion.

Dynamics of Blood Flow Transport System A closed double-pump system: Systemic Circulation Lung Circulation Left side of heart Right side of heart.

© Cambridge University Press 2010 Brian J. Kirby, PhD Sibley School of Mechanical and Aerospace Engineering, Cornell University, Ithaca, NY Powerpoint.

© Cambridge University Press 2010 Brian J. Kirby, PhD Sibley School of Mechanical and Aerospace Engineering, Cornell University, Ithaca, NY Powerpoint.

11/24/2014PHY 711 Fall Lecture 381 PHY 711 Classical Mechanics and Mathematical Methods 10-10:50 AM MWF Olin 103 Plan for Lecture 38 1.Chapter.

CHAPTER 3 EXACT ONE-DIMENSIONAL SOLUTIONS 3.1 Introduction  Temperature solution depends on velocity  Velocity is governed by non-linear Navier-Stokes.

Fluids Physics 202 Lecture 3. Pascal’s principle: any pressure change will flow through the entire fluid equally.

1 Chapter 6 Flow Analysis Using Differential Methods ( Differential Analysis of Fluid Flow)

Flow In Circular Pipes Objective ä To measure the pressure drop in the straight section of smooth, rough, and packed pipes as a function of flow rate.

© Fox, Pritchard, & McDonald Introduction to Fluid Mechanics Chapter 5 Introduction to Differential Analysis of Fluid Motion.

Pharos University ME 253 Fluid Mechanics II

Pharos University ME 253 Fluid Mechanics 2

Poiseuille (pressure-driven) steady duct flows

CP502 Advanced Fluid Mechanics

Outline Time Derivatives & Vector Notation

Differential Analysis of Fluid Flow. Navier-Stokes equations Example: incompressible Navier-Stokes equations.

Differential Equations Linear Equations with Variable Coefficients.

CEE 262A H YDRODYNAMICS Lecture 12 Steady solutions to the Navier-Stokes equation.

CP502 Advanced Fluid Mechanics

Chapter 21 Exact Differential Equation Chapter 2 Exact Differential Equation.

11/13/2015PHY 711 Fall Lecture 321 PHY 711 Classical Mechanics and Mathematical Methods 10-10:50 AM MWF Olin 103 Plan for Lecture 32 Viscous fluids.

Lecture 6 The boundary-layer equations

MFSacedon Study of Fluids. MFSacedon Fluids in Motion Topics: Fluid flows Continuity equation Bernoulli ‘s Energy Equation.

1. Integral vs Differential Approach

Incompressible Flow in Pipes and Channels

Viscosità Equazioni di Navier Stokes. Viscous stresses are surface forces per unit area. (Similar to pressure) (Viscous stresses)

Fluid Mechanics, KU, 2007 Chap. 8: One-Dimensional Flows Incompressible Newtonian fluids considered here EOC + Navier-Stokes eq. (EOM with Newtonian CE)

Fluid Mechanics, KU, 2011 Chap. 8: One-Dimensional Flows Incompressible Newtonian fluids considered here EOC + Navier-Stokes eq. (EOM with Newtonian CE)

Section 9.4 – Solving Differential Equations Symbolically Separation of Variables.

Internal Flow: General Considerations. Entrance Conditions Must distinguish between entrance and fully developed regions. Hydrodynamic Effects: Assume.

Internal Convection: Overview

Chapter 4 Fluid Mechanics Frank White

Energy Loss in Valves Function of valve type and valve position

Heat and Flow Technology I.

Subject Name: FLUID MECHANICS

Section Euler’s Method

CFD – Fluid Dynamics Equations

Navier - Stokes Equation

Elementary Mechanics of Fluids

Conservation of momentum

PHY 711 Classical Mechanics and Mathematical Methods

Internal Flow: General Considerations

Objective: To know the equations of simple straight lines.

12. Navier-Stokes Applications

Science Building #262 Yonsei University

Chapter 11 Fluids.

We assume here Ideal Fluids

Conservation of momentum

Introduction to Fluid Mechanics

PHY 711 Classical Mechanics and Mathematical Methods

Objective: To know the equations of simple straight lines.

Chapter 9 Analysis of a Differential Fluid Element in Laminar Flow

Presentation transcript:

Differential Analysis

Continuity Equation

Momentum Equation

Under what conditions?????

So, From continuity equation

where

Simplest type of Couette flow

Steady, Laminar Flow in Circular Tubes Probably the best known exact solution to the Navier–Stokes equations is for steady, incompressible, laminar flow through a straight circular tube of constant cross section. This type of flow is commonly called Hagen-Poiseuille flow, or simply Poiseuille flow.

Continuity equation

Navier Stokes equation