V. Fundamentals of Fluid Dynamics. Contents 1. State of Stress in Moving Fluid 2. Equations of Motion 3. Bernoulli Equation.

Slides:

Advertisements

Similar presentations

November 18 AP Physics.

Advertisements

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

Fluid in Motion.

1 MECH 221 FLUID MECHANICS (Fall 06/07) Tutorial 7.

Fluid Mechanics –For Civil Engineers is all about SMU Storing– Moving– Using ( Incompressible fluids - water) To design and manage these systems we need.

Surface Waves. Surface Tension  Water surface is not fixed. Behaves elastically Based on surface tension  Surface tension can be measured in a thin.

California State University, Chico

Fluid Dynamics continued Rotational Flow. First, review-Bernoulli When can we use it?

2-1 Problem Solving 1. Physics  2. Approach methods

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

10-1 Physics I Class 10 Potential Energy and Kinetic Energy in Spring Systems.

Simple Performance Prediction Methods Module 2 Momentum Theory.

Chapter 14 Fluids Key contents Description of fluids

MECH 221 FLUID MECHANICS (Fall 06/07) Chapter 3: FLUID IN MOTIONS

Fluid Flow. Pressure Force  Each volume element in a fluid is subject to force due to pressure. Assume a rectangular boxAssume a rectangular box Pressure.

Fluid mechanics 3.1 – key points

Flow and Thermal Considerations

St Venant Equations Reading: Sections 9.1 – 9.2.

EULER’S EQUATION Fluid Mechanics CHAPTER 4 Dr . Ercan Kahya

Conservation Laws for Continua

SO335 – Course Overview Fall 2014 Magic?. Methods course objectives: review By the end of this course, you should be able to: – Describe meteorological.

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

Introduction to Fluid Mechanics

Aerodynamics Linear Motion (Moving Air ).

Unit: IV-Fluid Dynamic

Flow inside turbomachines

FLUID DYNAMICS BERNOULLI’S EQUATION BY GP CAPT NC CHATTOPADHYAY.

Prof. dr. A. Achterberg, Astronomical Dept., IMAPP, Radboud Universiteit.

USSC3002 Oscillations and Waves Lecture 12 Water Waves Wayne M. Lawton Department of Mathematics National University of Singapore 2 Science Drive 2 Singapore.

Chapter 15FLUIDS 15.1 Fluid and the World Around Us 1.A fluid is a substance that cannot support a shearing stress. 2.Both gases and liquids are fluids.

Measurements in Fluid Mechanics 058:180:001 (ME:5180:0001) Time & Location: 2:30P - 3:20P MWF 218 MLH Office Hours: 4:00P – 5:00P MWF 223B-5 HL Instructor:

Unit 6 : Part 1 Fluids.

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

1 MECH 221 FLUID MECHANICS (Fall 06/07) Tutorial 5.

Dr. Jason Roney Mechanical and Aerospace Engineering

Fluid dynamical equations (Navier-Stokes equations)

Fluid Flow Continuity and Bernoulli’s Equation

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

Reference Book is. 2. The flow is steady. In steady (laminar) flow, the velocity of the fluid at each point remains constant. Fluid DYNAMICS Because the.

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

MAE 5360: Hypersonic Airbreathing Engines

CP502 Advanced Fluid Mechanics

Outline Time Derivatives & Vector Notation

© Fox, McDonald & Pritchard Introduction to Fluid Mechanics Chapter 6 Incompressible Inviscid Flow.

VII. Analysis of Potential Flows. Contents 1. Preservation of Irrotationality 2. Description of 2D Potential Flows 3. Fundamental Solutions 4. Superposition.

Ice cube in a glass of water After the piece of ice melts: Water level, h ? Barge with steel beams:

1 CONSTITUTIVE RELATION FOR NEWTONIAN FLUID The Cauchy equation for momentum balance of a continuous, deformable medium combined with the condition of.

CP502 Advanced Fluid Mechanics

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

1. Integral vs Differential Approach

CHAPTER 3 The Bernoulli Equation. Bernoulli Equation (B.E) ? 4- Unknowns : 4- equations : 1- Continuity Equation & 3 - Momentum Equations (E.E for inviscid.

Computer Animation Rick Parent Computer Animation Algorithms and Techniques Computational Fluid Dynamics.

Great Innovations are possible through General Understanding …. P M V Subbarao Professor Mechanical Engineering Department I I T Delhi Thermodynamic View.

Fluids and Elasticity Readings: Chapter 15.

DIFFERENTIAL EQUATIONS FOR FLUID FLOW Vinay Chandwani (Mtech Struct.)

SIGMA INSTITUTE OF ENGINEERING

Continuum Mechanics (MTH487)

The Bernoulli Equation

Introduction to Fluid Mechanics

FLUID FLOW TYPICAL ENGINEERING PROBLEMS:

INFINITESIMALLY SMALL DIFFERENTIAL CUBE IN SPACE

Conservation of Energy/Bernoulli’s Equation

MAE 3241: AERODYNAMICS AND FLIGHT MECHANICS

Applications of Bernoulli Equations

FLUID MECHANICS - Review

We assume here Ideal Fluids

Introduction to Fluid Mechanics

Introduction to Fluid Mechanics

Presentation transcript:

V. Fundamentals of Fluid Dynamics

Contents 1. State of Stress in Moving Fluid 2. Equations of Motion 3. Bernoulli Equation

1. State of Stress in Moving Fluid

State of Stress in Static Fluid

State of Stress in Moving Fluid

Body force and inertia force are of higher order

Mean pressure

Constitutive Equation of Newtonian Fluid

2. Equation of Motion

External force acting on the control volume Net inflow of momentum through the surface of control volume Increase of momentum within the control volume per unit time Conservation of Momentum

Increase of momentum within the control volume

Net inflow of (x) momentum through the surface of control volume

Net inflow of momentum through the surface of control volume

External (x) force acting on the control volume

Conservation of Momentum

Equation of Motion

Navier-Stokes Equation

Navier-Stokes Equations

Governing Equations of Incompressible Fluid Motion

Governing Equations of Static Fluid Automatically satisfied

Governing Equations of Ideal Fluid Flows Euler Equation

3. Bernolli Equation

Bernoulli Equation for Irrotational Flows Basic Assumptions:  Fluid is inviscid  Fluid is incompressible  Force has potential  Flow is irrotational

Bernoulli Equation for Irrotational Flows

For steady flow under gravity

In static fluid under gravity

Bernoulli Equation for Steady Flows Basic Assumptions:  Fluid is inviscid  Fluid is incompressible  Force has potential  Flow is steady

Bernoulli Equation for Steady Flows

For flows under gravity

Velocity head Pressure head Position head Piezometric head

Kinetic Energy Pressure Potential Energy Gravity Potential Energy

1 2

L