CE 204 FLUID MECHANICS

Size: px
Start display at page:

Download "CE 204 FLUID MECHANICS"

Transcription

1 CE 204 FLUID MECHANICS Onur AKAY Assistant Professor Okan University Department of Civil Engineering Akfırat Campus Tuzla-Istanbul/TURKEY Phone: ext.1974 Fax: Onur Akay, Ph.D. CE 204 Fluid Mechanics 1

2 Kinematics of Fluids: The relationship between pressure and flow velocity is important in many engineering applications. - Blood pressure (flow of blood through veins and arteries. - Weather forecasts (pressure readings of atmospheric flow patterns) - Stirring a cup of coffee (pressure variations enhance mixing) - Design of tall structures (pressure forces from the wind) The eye of a hurricane. - Aircraft design (lift and drag) - Flow systems (heating and air conditioning) The space shuttle during liftoff. Onur Akay, Ph.D. CE 204 Fluid Mechanics 2

3 Streamlines and Flow Patterns: - Flow pattern shows the flow direction. -Streamlinesare drawn tangent to local velocity vectors. The flow pattern provided by the streamlines represent an instantaneous visualization of the flow field. MOVIES Onur Akay, Ph.D. CE 204 Fluid Mechanics 3

4 Uniform Flow: The velocity does not change along a fluid path. s: the distance traveled by a fluid particle along a path. t: time Onur Akay, Ph.D. CE 204 Fluid Mechanics 4

5 Nonuniform Flow: The velocity changes along a fluid path. s: the distance traveled by a fluid particle along a path. t: time Onur Akay, Ph.D. CE 204 Fluid Mechanics 5

6 Steady Flow:The velocity at a given pointon a fluid path does not change with time. Unsteady Flow:The velocity at a given pointon a fluid path changes with time. Streamlines give no indication of the steadiness or unsteadiness of the flow!!! Steady or unsteady? Onur Akay, Ph.D. CE 204 Fluid Mechanics 6

7 Laminar Flow:Well-ordered state of flow in which adjacent flow layers move smoothly with respect to each other.. Turbulent Flow: Unsteady flow characterized by intense cross-stream mixing. MOVIE Instantaneous velocity profile Onur Akay, Ph.D. CE 204 Fluid Mechanics 7

8 Pathlines and Streaklines: Onur Akay, Ph.D. CE 204 Fluid Mechanics 8

9 Pathlines and Streaklines: Examples: MOVIE Onur Akay, Ph.D. CE 204 Fluid Mechanics 9

10 One-Dimensional and Multi-Dimensional Flows: The dimensionality is characterized by the number of spatial dimensions needed to describe the velocity field. One-dimensional Two-dimensional Three-dimensional Onur Akay, Ph.D. CE 204 Fluid Mechanics 10

11 Acceleration: Acceleration is the rate of change of the particle s velocity with time. Velocity Acceleration a n : normal component of acceleration (centripetal) a t : tangential component of acceleration Onur Akay, Ph.D. CE 204 Fluid Mechanics 11

12 Acceleration: local convective centripetal Onur Akay, Ph.D. CE 204 Fluid Mechanics 12

13 Acceleration: local convective centripetal In steady flow the local acceleration is zero. In uniform flow the convective acceleration is zero. Onur Akay, Ph.D. CE 204 Fluid Mechanics 13

14 Onur Akay, Ph.D. CE 204 Fluid Mechanics 14

15 Lagrangian and Eulerian Approach: Objective: To determine the pressure and velocities at arbitrary locations in a flow field. Onur Akay, Ph.D. CE 204 Fluid Mechanics 15

16 Euler s Equation: Leonhard Euler Hydrostatic equations were derived by equating the sum of forces on a fluid element equal to zero. Born: 15 April 1707, Basel, Switzerland Died: 18 September 1783, St. Petersburg, Russia Same ideas are applied to a moving fluid, but now we are executing Newton s second law. Onur Akay, Ph.D. CE 204 Fluid Mechanics 16

17 Euler s Equation: Onur Akay, Ph.D. CE 204 Fluid Mechanics 17

18 Euler s Equation: Euler s Equation: For an incompressible flow, γ is constant Onur Akay, Ph.D. CE 204 Fluid Mechanics 18

19 Euler s Equation: In a static body of fluid, Euler s equation reduces to: (Hydrostatic Equation) REMEMBER Onur Akay, Ph.D. CE 204 Fluid Mechanics 19

20 Onur Akay, Ph.D. CE 204 Fluid Mechanics 20

21 Pressure Distribution in Rotating Flows: Euler s Equation Apply Euler s equation outward from the center of rotation. Since the flow is steady, the partial derivative has been replaced by an ordinary derivative: Uniform or nonuniform? Onur Akay, Ph.D. CE 204 Fluid Mechanics 21

22 Onur Akay, Ph.D. CE 204 Fluid Mechanics 22

23 Bernoulli Equation: Daniel Bernoulli Bernoulli equation is developed by applying Euler s equation along a pathline: Born: 8 February 1700, Groningen, Netherlands Died: 8 March 1782, Basel, Switzerland For steady flow: piezometric kinetic pressure Onur Akay, Ph.D. CE 204 Fluid Mechanics 23

24 Bernoulli Equation: Onur Akay, Ph.D. CE 204 Fluid Mechanics 24

25 Onur Akay, Ph.D. CE 204 Fluid Mechanics 25

26 Onur Akay, Ph.D. CE 204 Fluid Mechanics 26

CE 204 FLUID MECHANICS

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 information

The most common methods to identify velocity of flow are pathlines, streaklines and streamlines.

The most common methods to identify velocity of flow are pathlines, streaklines and streamlines. 4 FLUID FLOW 4.1 Introduction Many civil engineering problems in fluid mechanics are concerned with fluids in motion. The distribution of potable water, the collection of domestic sewage and storm water,

More information

Chapter 3 Bernoulli Equation

Chapter 3 Bernoulli Equation 1 Bernoulli Equation 3.1 Flow Patterns: Streamlines, Pathlines, Streaklines 1) A streamline, is a line that is everywhere tangent to the velocity vector at a given instant. Examples of streamlines around

More information

Detailed Outline, M E 320 Fluid Flow, Spring Semester 2015

Detailed Outline, M E 320 Fluid Flow, Spring Semester 2015 Detailed Outline, M E 320 Fluid Flow, Spring Semester 2015 I. Introduction (Chapters 1 and 2) A. What is Fluid Mechanics? 1. What is a fluid? 2. What is mechanics? B. Classification of Fluid Flows 1. Viscous

More information

6. Basic basic equations I ( )

6. 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 information

Fundamentals of Fluid Mechanics

Fundamentals of Fluid Mechanics Sixth Edition Fundamentals of Fluid Mechanics International Student Version BRUCE R. MUNSON DONALD F. YOUNG Department of Aerospace Engineering and Engineering Mechanics THEODORE H. OKIISHI Department

More information

Mechanical Engineering Science for Medical Engineers Level: 4 Credit value: 8 GLH: 62 TQT: 80

Mechanical Engineering Science for Medical Engineers Level: 4 Credit value: 8 GLH: 62 TQT: 80 This unit has 6 learning outcomes. 1. Be able to solve engineering problems that involve variable and constant acceleration motion. 1.1. Apply dimensional analysis to an equation involving units of length,

More information

Fluid Mechanics. du dy

Fluid 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 information

Chapter 4: Fluid Kinematics

Chapter 4: Fluid Kinematics Overview Fluid kinematics deals with the motion of fluids without considering the forces and moments which create the motion. Items discussed in this Chapter. Material derivative and its relationship to

More information

University of Engineering and Technology, Taxila. Department of Civil Engineering

University of Engineering and Technology, Taxila. Department of Civil Engineering University of Engineering and Technology, Taxila Department of Civil Engineering Course Title: CE-201 Fluid Mechanics - I Pre-requisite(s): None Credit Hours: 2 + 1 Contact Hours: 2 + 3 Text Book(s): Reference

More information

LECTURE NOTES - III. Prof. Dr. Atıl BULU

LECTURE NOTES - III. Prof. Dr. Atıl BULU LECTURE NOTES - III «FLUID MECHANICS» Istanbul Technical University College of Civil Engineering Civil Engineering Department Hydraulics Division CHAPTER KINEMATICS OF FLUIDS.. FLUID IN MOTION Fluid motion

More information

Fluid 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 Fluid Mechanics Prof. S. K. Som Department of Mechanical Engineering Indian Institute of Technology, Kharagpur Lecture - 11 Kinematics of Fluid Part - II Good afternoon, I welcome you all to this session

More information

Lecture 2 Flow classifications and continuity

Lecture 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 information

ME3560 Tentative Schedule Spring 2019

ME3560 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 information

Process Fluid Mechanics

Process Fluid Mechanics Process Fluid Mechanics CENG 2220 Instructor: Francesco Ciucci, Room 2577A (Lift 27-29), Tel: 2358 7187, email: francesco.ciucci@ust.hk. Office Hours: Tuesday 17:00-18:00 or by email appointment Teaching

More information

FLUID MECHANICS. Gaza. Chapter CHAPTER 44. Motion of Fluid Particles and Streams. Dr. Khalil Mahmoud ALASTAL

FLUID MECHANICS. Gaza. Chapter CHAPTER 44. Motion of Fluid Particles and Streams. Dr. Khalil Mahmoud ALASTAL FLUID MECHANICS Gaza Chapter CHAPTER 44 Motion of Fluid Particles and Streams Dr. Khalil Mahmoud ALASTAL Objectives of this Chapter: Introduce concepts necessary to analyze fluids in motion. Identify differences

More information

ME3560 Tentative Schedule Fall 2018

ME3560 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 information

NPTEL Quiz Hydraulics

NPTEL Quiz Hydraulics Introduction NPTEL Quiz Hydraulics 1. An ideal fluid is a. One which obeys Newton s law of viscosity b. Frictionless and incompressible c. Very viscous d. Frictionless and compressible 2. The unit of kinematic

More information

MAE 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 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 information

CEE 3310 Control Volume Analysis, Oct. 7, D Steady State Head Form of the Energy Equation P. P 2g + z h f + h p h s.

CEE 3310 Control Volume Analysis, Oct. 7, D Steady State Head Form of the Energy Equation P. P 2g + z h f + h p h s. CEE 3310 Control Volume Analysis, Oct. 7, 2015 81 3.21 Review 1-D Steady State Head Form of the Energy Equation ( ) ( ) 2g + z = 2g + z h f + h p h s out where h f is the friction head loss (which combines

More information

In steady flow the velocity of the fluid particles at any point is constant as time passes.

In steady flow the velocity of the fluid particles at any point is constant as time passes. Chapter 10 Fluids Fluids in Motion In steady flow the velocity of the fluid particles at any point is constant as time passes. Unsteady flow exists whenever the velocity of the fluid particles at a point

More information

ME 3560 Fluid Mechanics

ME 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 information

B.E/B.Tech/M.E/M.Tech : Chemical Engineering Regulation: 2016 PG Specialisation : NA Sub. Code / Sub. Name : CH16304 FLUID MECHANICS Unit : I

B.E/B.Tech/M.E/M.Tech : Chemical Engineering Regulation: 2016 PG Specialisation : NA Sub. Code / Sub. Name : CH16304 FLUID MECHANICS Unit : I Department of Chemical Engineering B.E/B.Tech/M.E/M.Tech : Chemical Engineering Regulation: 2016 PG Specialisation : NA Sub. Code / Sub. Name : CH16304 FLUID MECHANICS Unit : I LP: CH 16304 Rev. No: 00

More information

1. Introduction, tensors, kinematics

1. 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 information

Lagrangian description from the perspective of a parcel moving within the flow. Streamline Eulerian, tangent line to instantaneous velocity field.

Lagrangian description from the perspective of a parcel moving within the flow. Streamline Eulerian, tangent line to instantaneous velocity field. Chapter 2 Hydrostatics 2.1 Review Eulerian description from the perspective of fixed points within a reference frame. Lagrangian description from the perspective of a parcel moving within the flow. Streamline

More information

COURSE 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 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 information

Fluids. Fluids in Motion or Fluid Dynamics

Fluids. Fluids in Motion or Fluid Dynamics Fluids Fluids in Motion or Fluid Dynamics Resources: Serway - Chapter 9: 9.7-9.8 Physics B Lesson 3: Fluid Flow Continuity Physics B Lesson 4: Bernoulli's Equation MIT - 8: Hydrostatics, Archimedes' Principle,

More information

CLASS SCHEDULE 2013 FALL

CLASS 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

ROAD MAP... D-0: Reynolds Transport Theorem D-1: Conservation of Mass D-2: Conservation of Momentum D-3: Conservation of Energy

ROAD 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 information

Fundamentals of Fluid Dynamics: Ideal Flow Theory & Basic Aerodynamics

Fundamentals of Fluid Dynamics: Ideal Flow Theory & Basic Aerodynamics Fundamentals of Fluid Dynamics: Ideal Flow Theory & Basic Aerodynamics Introductory Course on Multiphysics Modelling TOMASZ G. ZIELIŃSKI (after: D.J. ACHESON s Elementary Fluid Dynamics ) bluebox.ippt.pan.pl/

More information

Introduction to Aerodynamics. Dr. Guven Aerospace Engineer (P.hD)

Introduction to Aerodynamics. Dr. Guven Aerospace Engineer (P.hD) Introduction to Aerodynamics Dr. Guven Aerospace Engineer (P.hD) Aerodynamic Forces All aerodynamic forces are generated wither through pressure distribution or a shear stress distribution on a body. The

More information

Physical Science and Engineering. Course Information. Course Number: ME 100

Physical Science and Engineering. Course Information. Course Number: ME 100 Physical Science and Engineering Course Number: ME 100 Course Title: Course Information Basic Principles of Mechanics Academic Semester: Fall Academic Year: 2016-2017 Semester Start Date: 8/21/2016 Semester

More information

Fluid Dynamics: Theory, Computation, and Numerical Simulation Second Edition

Fluid Dynamics: Theory, Computation, and Numerical Simulation Second Edition Fluid Dynamics: Theory, Computation, and Numerical Simulation Second Edition C. Pozrikidis m Springer Contents Preface v 1 Introduction to Kinematics 1 1.1 Fluids and solids 1 1.2 Fluid parcels and flow

More information

CHAPTER 4. Basics of Fluid Dynamics

CHAPTER 4. Basics of Fluid Dynamics CHAPTER 4 Basics of Fluid Dynamics What is a fluid? A fluid is a substance that can flow, has no fixed shape, and offers little resistance to an external stress In a fluid the constituent particles (atoms,

More information

CEE 3310 Control Volume Analysis, Oct. 10, = dt. sys

CEE 3310 Control Volume Analysis, Oct. 10, = dt. sys CEE 3310 Control Volume Analysis, Oct. 10, 2018 77 3.16 Review First Law of Thermodynamics ( ) de = dt Q Ẇ sys Sign convention: Work done by the surroundings on the system < 0, example, a pump! Work done

More information

Higher Education. Mc Grauu FUNDAMENTALS AND APPLICATIONS SECOND EDITION

Higher Education. Mc Grauu FUNDAMENTALS AND APPLICATIONS SECOND EDITION FLUID MECHANICS FUNDAMENTALS AND APPLICATIONS SECOND EDITION Mc Grauu Higher Education Boston Burr Ridge, IL Dubuque, IA Madison, Wl New York San Francisco St. Louis Bangkok Bogota Caracas Kuala Lumpur

More information

AA210A Fundamentals of Compressible Flow. Chapter 1 - Introduction to fluid flow

AA210A Fundamentals of Compressible Flow. Chapter 1 - Introduction to fluid flow AA210A Fundamentals of Compressible Flow Chapter 1 - Introduction to fluid flow 1 1.2 Conservation of mass Mass flux in the x-direction [ ρu ] = M L 3 L T = M L 2 T Momentum per unit volume Mass per unit

More information

Fluids Applications of Fluid Dynamics

Fluids Applications of Fluid Dynamics Fluids Applications of Fluid Dynamics Lana Sheridan De Anza College April 16, 2018 Last time fluid dynamics the continuity equation Bernoulli s equation Overview Torricelli s law applications of Bernoulli

More information

fluid mechanics as a prominent discipline of application for numerical

fluid mechanics as a prominent discipline of application for numerical 1. fluid mechanics as a prominent discipline of application for numerical simulations: experimental fluid mechanics: wind tunnel studies, laser Doppler anemometry, hot wire techniques,... theoretical fluid

More information

Basic equations of motion in fluid mechanics

Basic equations of motion in fluid mechanics 1 Annex 1 Basic equations of motion in fluid mechanics 1.1 Introduction It is assumed that the reader of this book is familiar with the basic laws of fluid mechanics. Nevertheless some of these laws will

More information

MECHANICAL PROPERTIES OF FLUIDS:

MECHANICAL PROPERTIES OF FLUIDS: Important Definitions: MECHANICAL PROPERTIES OF FLUIDS: Fluid: A substance that can flow is called Fluid Both liquids and gases are fluids Pressure: The normal force acting per unit area of a surface is

More information

Chapter 7 The Energy Equation

Chapter 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 information

BERNOULLI EQUATION. The motion of a fluid is usually extremely complex.

BERNOULLI EQUATION. The motion of a fluid is usually extremely complex. BERNOULLI EQUATION The motion of a fluid is usually extremely complex. The study of a fluid at rest, or in relative equilibrium, was simplified by the absence of shear stress, but when a fluid flows over

More information

General Physics I. Lecture 16: Fluid Mechanics. Prof. WAN, Xin ( 万歆 )

General Physics I. Lecture 16: Fluid Mechanics. Prof. WAN, Xin ( 万歆 ) General Physics I Lecture 16: Fluid Mechanics Prof. WAN, Xin ( 万歆 ) xinwan@zju.edu.cn http://zimp.zju.edu.cn/~xinwan/ Motivations Newton s laws for fluid statics? Force pressure Mass density How to treat

More information

UNIT IV BOUNDARY LAYER AND FLOW THROUGH PIPES Definition of boundary layer Thickness and classification Displacement and momentum thickness Development of laminar and turbulent flows in circular pipes

More information

Chapter 9. Solids and Fluids. 1. Introduction. 2. Fluids at Rest. 3. Fluid Motion

Chapter 9. Solids and Fluids. 1. Introduction. 2. Fluids at Rest. 3. Fluid Motion Chapter 9 Solids and Fluids 1. Introduction 2. Fluids at Rest 3. Fluid Motion 1 States of Matter Solid Liquid Gas Plasma 2 Density and Specific Gravity What is Density? How do I calculate it? What are

More information

conservation of linear momentum 1+8Fr = 1+ Sufficiently short that energy loss due to channel friction is negligible h L = 0 Bernoulli s equation.

conservation of linear momentum 1+8Fr = 1+ Sufficiently short that energy loss due to channel friction is negligible h L = 0 Bernoulli s equation. 174 Review Flow through a contraction Critical and choked flows The hydraulic jump conservation of linear momentum y y 1 = 1+ 1+8Fr 1 8.1 Rapidly Varied Flows Weirs 8.1.1 Broad-Crested Weir Consider the

More information

MECHANICAL PROPERTIES OF FLUIDS

MECHANICAL PROPERTIES OF FLUIDS CHAPTER-10 MECHANICAL PROPERTIES OF FLUIDS QUESTIONS 1 marks questions 1. What are fluids? 2. How are fluids different from solids? 3. Define thrust of a liquid. 4. Define liquid pressure. 5. Is pressure

More information

Part A: 1 pts each, 10 pts total, no partial credit.

Part 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 information

Chapter 5 Control Volume Approach and Continuity Equation

Chapter 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 information

Chapter 14. Lecture 1 Fluid Mechanics. Dr. Armen Kocharian

Chapter 14. Lecture 1 Fluid Mechanics. Dr. Armen Kocharian Chapter 14 Lecture 1 Fluid Mechanics Dr. Armen Kocharian States of Matter Solid Has a definite volume and shape Liquid Has a definite volume but not a definite shape Gas unconfined Has neither a definite

More information

Pressure in a fluid P P P P

Pressure in a fluid P P P P Fluids Gases (compressible) and liquids (incompressible) density of gases can change dramatically, while that of liquids much less so Gels, colloids, liquid crystals are all odd-ball states of matter We

More information

Basic Fluid Mechanics

Basic 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 information

Fluid 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 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 information

Chemical and Biomolecular Engineering 150A Transport Processes Spring Semester 2017

Chemical and Biomolecular Engineering 150A Transport Processes Spring Semester 2017 Chemical and Biomolecular Engineering 150A Transport Processes Spring Semester 2017 Objective: Text: To introduce the basic concepts of fluid mechanics and heat transfer necessary for solution of engineering

More information

PHY121 Physics for the Life Sciences I

PHY121 Physics for the Life Sciences I PHY Physics for the Life Sciences I Lecture 0. Fluid flow: kinematics describing the motion. Fluid flow: dynamics causes and effects, Bernoulli s Equation 3. Viscosity and Poiseuille s Law for narrow tubes

More information

AERODYNAMICS STUDY NOTES UNIT I REVIEW OF BASIC FLUID MECHANICS. Continuity, Momentum and Energy Equations. Applications of Bernouli s theorem

AERODYNAMICS STUDY NOTES UNIT I REVIEW OF BASIC FLUID MECHANICS. Continuity, Momentum and Energy Equations. Applications of Bernouli s theorem AERODYNAMICS STUDY NOTES UNIT I REVIEW OF BASIC FLUID MECHANICS. Continuity, Momentum and Energy Equations. Applications of Bernouli s theorem UNIT II TWO DIMENSIONAL FLOWS Complex Potential, Point Source

More information

Rate of Flow Quantity of fluid passing through any section (area) per unit time

Rate of Flow Quantity of fluid passing through any section (area) per unit time Kinematics of Fluid Flow Kinematics is the science which deals with study of motion of liquids without considering the forces causing the motion. Rate of Flow Quantity of fluid passing through any section

More information

FLUID MECHANICS EQUATIONS

FLUID MECHANICS EQUATIONS FLUID MECHANIC EQUATION M. Ragheb 11/2/2017 INTRODUCTION The early part of the 18 th -century saw the burgeoning of the field of theoretical fluid mechanics pioneered by Leonhard Euler and the father and

More information

Contents. I Introduction 1. Preface. xiii

Contents. I Introduction 1. Preface. xiii Contents Preface xiii I Introduction 1 1 Continuous matter 3 1.1 Molecules................................ 4 1.2 The continuum approximation.................... 6 1.3 Newtonian mechanics.........................

More information

Principles of Convection

Principles of Convection Principles of Convection Point Conduction & convection are similar both require the presence of a material medium. But convection requires the presence of fluid motion. Heat transfer through the: Solid

More information

11.1 Mass Density. Fluids are materials that can flow, and they include both gases and liquids. The mass density of a liquid or gas is an

11.1 Mass Density. Fluids are materials that can flow, and they include both gases and liquids. The mass density of a liquid or gas is an Chapter 11 Fluids 11.1 Mass Density Fluids are materials that can flow, and they include both gases and liquids. The mass density of a liquid or gas is an important factor that determines its behavior

More information

Basics of fluid flow. Types of flow. Fluid Ideal/Real Compressible/Incompressible

Basics of fluid flow. Types of flow. Fluid Ideal/Real Compressible/Incompressible Basics of fluid flow Types of flow Fluid Ideal/Real Compressible/Incompressible Flow Steady/Unsteady Uniform/Non-uniform Laminar/Turbulent Pressure/Gravity (free surface) 1 Basics of fluid flow (Chapter

More information

d v 2 v = d v d t i n where "in" and "rot" denote the inertial (absolute) and rotating frames. Equation of motion F =

d 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 information

Chapter 9. Solids and Fluids 9.3 DENSITY AND PRESSURE

Chapter 9. Solids and Fluids 9.3 DENSITY AND PRESSURE 9.3 DENSITY AND PRESSURE Chapter 9 Solids and Fluids The density of an object having uniform composition is defined as its mass M divided by its volume V: M V [9.6] SI unit: kilogram per meter cubed (kg/m

More information

Study fluid dynamics. Understanding Bernoulli s Equation.

Study fluid dynamics. Understanding Bernoulli s Equation. Chapter Objectives Study fluid dynamics. Understanding Bernoulli s Equation. Chapter Outline 1. Fluid Flow. Bernoulli s Equation 3. Viscosity and Turbulence 1. Fluid Flow An ideal fluid is a fluid that

More information

The Pilot Design Studio-Classroom. Joseph Cataldo The Cooper Union for the Advancement of Science and Art

The Pilot Design Studio-Classroom. Joseph Cataldo The Cooper Union for the Advancement of Science and Art The Pilot Design Studio-Classroom Joseph Cataldo The Cooper Union for the Advancement of Science and Art Studio Method Used for Many decades in Architectural and Art Schools Origins The concept of the

More information

AER210 VECTOR CALCULUS and FLUID MECHANICS. Quiz 4 Duration: 70 minutes

AER210 VECTOR CALCULUS and FLUID MECHANICS. Quiz 4 Duration: 70 minutes AER210 VECTOR CALCULUS and FLUID MECHANICS Quiz 4 Duration: 70 minutes 26 November 2012 Closed Book, no aid sheets Non-programmable calculators allowed Instructor: Alis Ekmekci Family Name: Given Name:

More information

Fluids II (Fluids in motion)

Fluids II (Fluids in motion) hys0 Lectures 6-7 Fluids II (Fluids in motion) Key points: Bernoulli s Equation oiseuille s Law Ref: 0-8,9,0,,. age 0-8 Fluids in Motion; Flow Rate and the Equation of Continuity If the flow of a fluid

More information

Physics 123 Unit #1 Review

Physics 123 Unit #1 Review Physics 123 Unit #1 Review I. Definitions & Facts Density Specific gravity (= material / water) Pressure Atmosphere, bar, Pascal Barometer Streamline, laminar flow Turbulence Gauge pressure II. Mathematics

More information

Recap: Static Fluids

Recap: Static Fluids Recap: Static Fluids Archimedes principal states that the buoyant force acting on an object is equal to the weight of fluid displaced. If the average density of object is greater than density of fluid

More information

Flight Vehicle Terminology

Flight Vehicle Terminology Flight Vehicle Terminology 1.0 Axes Systems There are 3 axes systems which can be used in Aeronautics, Aerodynamics & Flight Mechanics: Ground Axes G(x 0, y 0, z 0 ) Body Axes G(x, y, z) Aerodynamic Axes

More information

Syllabus for AE3610, Aerodynamics I

Syllabus for AE3610, Aerodynamics I Syllabus for AE3610, Aerodynamics I Current Catalog Data: AE 3610 Aerodynamics I Credit: 4 hours A study of incompressible aerodynamics of flight vehicles with emphasis on combined application of theory

More information

MULTIPLE-CHOICE PROBLEMS:(Two marks per answer) (Circle the Letter Beside the Most Correct Answer in the Questions Below.)

MULTIPLE-CHOICE PROBLEMS:(Two marks per answer) (Circle the Letter Beside the Most Correct Answer in the Questions Below.) MULTIPLE-CHOICE PROLEMS:(Two marks per answer) (Circle the Letter eside the Most Correct Answer in the Questions elow.) 1. The absolute viscosity µ of a fluid is primarily a function of: a. Density. b.

More information

V/ t = 0 p/ t = 0 ρ/ t = 0. V/ s = 0 p/ s = 0 ρ/ s = 0

V/ 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 information

FROM NEWTON S MECHANICS TO EULER S EQUATIONS

FROM NEWTON S MECHANICS TO EULER S EQUATIONS 1 EE250 FROM NEWTON S MECHANICS TO EULER S EQUATIONS How the equation of fluid dynamics were born 250 years ago Olivier Darrigol and Uriel Frisch CNRS : Rehseis, Paris, France Laboratoire Cassiopée, UNSA,

More information

3.8 The First Law of Thermodynamics and the Energy Equation

3.8 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 information

V (r,t) = i ˆ u( x, y,z,t) + ˆ j v( x, y,z,t) + k ˆ w( x, y, z,t)

V (r,t) = i ˆ u( x, y,z,t) + ˆ j v( x, y,z,t) + k ˆ w( x, y, z,t) IV. DIFFERENTIAL RELATIONS FOR A FLUID PARTICLE This chapter presents the development and application of the basic differential equations of fluid motion. Simplifications in the general equations and common

More information

Fluid 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 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 information

Lecture 30 (Walker: ) Fluid Dynamics April 15, 2009

Lecture 30 (Walker: ) Fluid Dynamics April 15, 2009 Physics 111 Lecture 30 (Walker: 15.6-7) Fluid Dynamics April 15, 2009 Midterm #2 - Monday April 20 Chap. 7,Chap. 8 (not 8.5) Chap. 9 (not 9.6, 9.8) Chap. 10, Chap. 11 (not 11.8-9) Chap. 13 (not 13.6-8)

More information

PHYSICAL MECHANISM OF CONVECTION

PHYSICAL MECHANISM OF CONVECTION Tue 8:54:24 AM Slide Nr. 0 of 33 Slides PHYSICAL MECHANISM OF CONVECTION Heat transfer through a fluid is by convection in the presence of bulk fluid motion and by conduction in the absence of it. Chapter

More information

An-Najah National University Civil Engineering Department. Fluid Mechanics. Chapter 1. General Introduction

An-Najah National University Civil Engineering Department. Fluid Mechanics. Chapter 1. General Introduction 1 An-Najah National University Civil Engineering Department Fluid Mechanics Chapter 1 General Introduction 2 What is Fluid Mechanics? Mechanics deals with the behavior of both stationary and moving bodies

More information

CE MECHANICS OF FLUIDS

CE MECHANICS OF FLUIDS CE60 - MECHANICS OF FLUIDS (FOR III SEMESTER) UNIT II FLUID STATICS & KINEMATICS PREPARED BY R.SURYA, M.E Assistant Professor DEPARTMENT OF CIVIL ENGINEERING DEPARTMENT OF CIVIL ENGINEERING SRI VIDYA COLLEGE

More information

Given the water behaves as shown above, which direction will the cylinder rotate?

Given the water behaves as shown above, which direction will the cylinder rotate? water stream fixed but free to rotate Given the water behaves as shown above, which direction will the cylinder rotate? ) Clockwise 2) Counter-clockwise 3) Not enough information F y U 0 U F x V=0 V=0

More information

It is important to develop a meaningful and systematic way to perform an experiment.

It is important to develop a meaningful and systematic way to perform an experiment. Chapter 7: Dimensional Analysis, Modeling and Similitude. The solution to many engineering problems is achieved through the use of a combination of analysis and experimental data. One of the goals of an

More information

DEVIL PHYSICS THE BADDEST CLASS ON CAMPUS IB PHYSICS

DEVIL PHYSICS THE BADDEST CLASS ON CAMPUS IB PHYSICS DEVIL PHYSICS THE BADDEST CLASS ON CAMPUS IB PHYSICS OPTION B-3: LUIDS Essential Idea: luids cannot be modelled as point particles. Their distinguishable response to compression from solids creates a set

More information

2.The lines that are tangent to the velocity vectors throughout the flow field are called steady flow lines. True or False A. True B.

2.The lines that are tangent to the velocity vectors throughout the flow field are called steady flow lines. True or False A. True B. CHAPTER 03 1. Write Newton's second law of motion. YOUR ANSWER: F = ma 2.The lines that are tangent to the velocity vectors throughout the flow field are called steady flow lines. True or False 3.Streamwise

More information

CHAPTER 4 KINEMATICS OF FLOW

CHAPTER 4 KINEMATICS OF FLOW CHAPTER 4 KINEMATICS OF FLOW 4.1 Introduction: In hydrostatics one deals with liquids at rest in which there is no relative motion between fluid particles and therefore no shear stresses exist. Since no

More information

m V DEFINITION OF MASS DENSITY The mass density of a substance is the mass of a substance divided by its volume: SI Unit of Mass Density: kg/m 3

m V DEFINITION OF MASS DENSITY The mass density of a substance is the mass of a substance divided by its volume: SI Unit of Mass Density: kg/m 3 Chapter Fluids . Mass Density DEFINITION OF MASS DENSITY The mass density of a substance is the mass of a substance divided by its volume: m V SI Unit of Mass Density: kg/m 3 . Mass Density . Mass Density

More information

Aerodynamics. Basic Aerodynamics. Continuity equation (mass conserved) Some thermodynamics. Energy equation (energy conserved)

Aerodynamics. Basic Aerodynamics. Continuity equation (mass conserved) Some thermodynamics. Energy equation (energy conserved) Flow with no friction (inviscid) Aerodynamics Basic Aerodynamics Continuity equation (mass conserved) Flow with friction (viscous) Momentum equation (F = ma) 1. Euler s equation 2. Bernoulli s equation

More information

HYDRAULICS 1 (HYDRODYNAMICS) SPRING 2005

HYDRAULICS 1 (HYDRODYNAMICS) SPRING 2005 HYDRAULICS (HYDRODYNAMICS) SPRING 005 Part. Fluid-Flow Principles. Introduction. Definitions. Notation and fluid properties.3 Hydrostatics.4 Fluid dynamics.5 Control volumes.6 Visualising fluid flow.7

More information

Chapter 5 Circular Motion; Gravitation

Chapter 5 Circular Motion; Gravitation Chapter 5 Circular Motion; Gravitation Units of Chapter 5 Kinematics of Uniform Circular Motion Dynamics of Uniform Circular Motion Highway Curves, Banked and Unbanked Newton s Law of Universal Gravitation

More information

Turbomachinery. Hasan Ozcan Assistant Professor. Mechanical Engineering Department Faculty of Engineering Karabuk University

Turbomachinery. Hasan Ozcan Assistant Professor. Mechanical Engineering Department Faculty of Engineering Karabuk University Turbomachinery Hasan Ozcan Assistant Professor Mechanical Engineering Department Faculty of Engineering Karabuk University Introduction Hasan Ozcan, Ph.D, (Assistant Professor) B.Sc :Erciyes University,

More information

Lecture 3: 1. Lecture 3.

Lecture 3: 1. Lecture 3. Lecture 3: 1 Lecture 3. Lecture 3: 2 Plan for today Summary of the key points of the last lecture. Review of vector and tensor products : the dot product (or inner product ) and the cross product (or vector

More information

Fluid dynamics - Equation of. continuity and Bernoulli s principle.

Fluid dynamics - Equation of. continuity and Bernoulli s principle. Fluid statics Fluid dynamics - Equation of What is a fluid? Density Pressure Fluid pressure and depth Pascal s principle Buoyancy Archimedes principle continuity and Bernoulli s principle. Lecture 4 Dr

More information

Detailed Outline, M E 521: Foundations of Fluid Mechanics I

Detailed Outline, M E 521: Foundations of Fluid Mechanics I Detailed Outline, M E 521: Foundations of Fluid Mechanics I I. Introduction and Review A. Notation 1. Vectors 2. Second-order tensors 3. Volume vs. velocity 4. Del operator B. Chapter 1: Review of Basic

More information

for what specific application did Henri Pitot develop the Pitot tube? what was the name of NACA s (now NASA) first research laboratory?

for what specific application did Henri Pitot develop the Pitot tube? what was the name of NACA s (now NASA) first research laboratory? 1. 5% short answers for what specific application did Henri Pitot develop the Pitot tube? what was the name of NACA s (now NASA) first research laboratory? in what country (per Anderson) was the first

More information

Aerodynamics. Lecture 1: Introduction - Equations of Motion G. Dimitriadis

Aerodynamics. Lecture 1: Introduction - Equations of Motion G. Dimitriadis Aerodynamics Lecture 1: Introduction - Equations of Motion G. Dimitriadis Definition Aerodynamics is the science that analyses the flow of air around solid bodies The basis of aerodynamics is fluid dynamics

More information

UNIT I FLUID PROPERTIES AND STATICS

UNIT 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 information

MAE 224 Notes #4a Elements of Thermodynamics and Fluid Mechanics

MAE 224 Notes #4a Elements of Thermodynamics and Fluid Mechanics MAE 224 Notes #4a Elements of Thermodynamics and Fluid Mechanics S. H. Lam February 22, 1999 1 Reading and Homework Assignments The problems are due on Wednesday, March 3rd, 1999, 5PM. Please submit your

More information