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

Size: px
Start display at page:

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

Transcription

1 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, and the wave actions on offshore structures are common examples. The viscosity of water is small and therefore in most hydraulic problems associated with civil engineering it is reasonable to ignore the effect of shear forces. 4.2 Velocity of Flow The definition of velocity in a fluid is much more complicated than in the case of a rigid solid. Basically this follows from the fact that the individual particles of a solid are bound together whereas the particles of a fluid can move independently of each other. The most common methods to identify velocity of flow are pathlines, streaklines and streamlines. Pathline - trace the position of a particle at successive intervals of time starting from a given point. Streakline -trace of all particles that have previously passed through a common point. Streamline -an imaginary curve that is tangential to the velocity vectors of a connected series of fluid particles. In unsteady flow, streamlines, pathlines and streaklines are all different, but in steady flow, streamlines, pathlines and streaklines are identical. The streamline is thus a line representing the direction of flow of the series of particles at a given instant. Because the streamline is always tangential to the flow, it follows that there is no flow across a streamline. P.4-1

2 4.3 Types of Flow There are several types of flow that occur in practice: uniform and non-uniform flow, steady and unsteady flow, laminar and turbulent flow. Some of them can be explained by means of streamlines Uniform and Non-uniform Flow In uniform flow the velocity (including its magnitude and direction) does not change from one point to another along any of the streamlines in the flow field. Uniform flow Non-uniform flow This means that both the area and velocity of the flow must be the same at every cross-section, and the streamlines must be straight and parallel. If the streamlines are not straight, there will be a change in the direction of the flow. If the streamlines are not parallel, there will be change in the magnitude of the flow. In non-uniform flow the velocity changes from point to point along streamlines. Mathematically, uniform and non-uniform flow can be defined as: dv = 0 ds (uniform flow) dv 0 ds (non-uniform flow) where V = velocity of flow s = position measuring along a streamline P.4-2

3 4.3.2 Steady and Unsteady Flow Steady flow means the velocity at any point in the flow field does not change with respect to time. If the velocity at a point changes over time, then the flow is unsteady. Mathematically, steady flow and unsteady flow can be presented as follows: dv = 0 dt (steady flow) dv 0 dt (unsteady flow) where V = velocity of flow t = time of study Discharge at a constant rate through a pipe is a common example at steady flow. If the pipe is of a constant diameter, the flow is uniform and steady. In fact, most of the civil engineering hydraulic problems are concerned with steady flow. An example of non-uniform and unsteady flow occurring together is the case of the flow from a nozzle when for some reason there is a change in the discharge rate. There are, therefore, four possible types of flow. Steady uniform flow. Conditions do not change with position or time. The velocity and cross-sectional area of the stream of fluid are the same at each cross-section; e.g. flow of a liquid through a pipe of uniform bore running completely full at constant velocity. Steady non-uniform flow. Conditions change from point to point but not with time. The velocity and cross-sectional area of the stream may vary from crosssection to cross-section, but, for each cross-section, they will not vary with time; e.g. flow of a liquid at a constant rate through a tapering pipe running completely full. Unsteady uniform flow. At a given instant of time the velocity at every point is the same, but this velocity will change with time; e.g. accelerating flow of a P.4-3

4 liquid through a pipe of uniform bore running full, such as would occur when a pump is started up. Unsteady non-uniform flow. The cross-sectional area and velocity vary from point to point and also change with time; e.g. a wave travelling along a channel Real and Ideal Flow When a real fluid flows past a boundary, the fluid immediately in contact with the boundary will have the same velocity as the boundary. The velocity of successive layers of fluid will increase as moving away from the boundary. Boundary layer V = 0.99Vf Ideal Fluid Free velocity =Vf V = 0.99Vf Boundary layer Real Fluid The part of the flow adjoining the boundary in which this change of velocity occurs is known as the boundary layer. In this region, shear stresses are developed between layers of fluid moving with different velocities as a result of viscosity. The thickness of the boundary layer is defined as the distance from the boundary at which the velocity becomes equal to 99% of the free stream velocity. Outside this boundary layer, the effect of the shear stresses due to the boundary can be ignored and the fluid can be treated as if it were an ideal fluid. If the fluid velocity is high and its viscosity low, the boundary layer is comparatively thin, and the assumption that a real fluid can be treated as an ideal fluid greatly simplifies the analysis of the flow and still leads to useful results One, Two and Three Dimensional Flow P.4-4

5 When there is no obstruction or channelling, fluid flow can be thought of as three-dimensional flow. In situations where the velocity of flow in one co-ordinate direction has no changes, the flow can be described as two-dimensional. The flow between two parallel plates is an example. If the velocity of flow is constant across each section but changes in only one direction, it can be described as one-dimensional. The average flow in a duct can be considered as one-dimensional. 4.4 Flow Rate and Mean Velocity The quantity of fluid flowing per unit time across any section is called the flow rate or the discharge. It may be expressed in terms of volume flow rate, m 3 /s; weight flow rate, kn/s or mass flow rate, kg/s. In dealing with incompressible fluids, volume flow rate is commonly used, whereas weight flow rate or mass flow rate is more convenient with compressible fluids. In a real fluid, the velocity adjacent to a solid boundary will be zero. For a pipe, the velocity profile would be as shown in fig (a) below for laminar flow and fig (b) for turbulent flow. u r r dr R u (a) Laminar flow (b) Turbulent flow Flow rate is the volume rate of flow passing a given section of the flow stream. It is also called discharged. Mathematically, flow rate can be defined as follows: Q = A V. da where Q = flow rate, m 3 /s P.4-5

6 If v is constant, Q = V.A V = velocity of flow, m/s da = area normal to the direction of velocity, m 2 In many practical problems, such as the flow of water through a pipe, the diameter of the pipe, and the discharge are given, and the velocity of the flow is the determined from, Q V = A The velocity so obtained is called the average velocity or mean velocity. By definition, it is simply the discharge divided by the cross-sectional area. P.4-6

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

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

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

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

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

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

Figure 3: Problem 7. (a) 0.9 m (b) 1.8 m (c) 2.7 m (d) 3.6 m

Figure 3: Problem 7. (a) 0.9 m (b) 1.8 m (c) 2.7 m (d) 3.6 m 1. For the manometer shown in figure 1, if the absolute pressure at point A is 1.013 10 5 Pa, the absolute pressure at point B is (ρ water =10 3 kg/m 3, ρ Hg =13.56 10 3 kg/m 3, ρ oil = 800kg/m 3 ): (a)

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

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

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

!! +! 2!! +!"!! =!! +! 2!! +!"!! +!!"!"!"

!! +! 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 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

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

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 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

CHAPTER 3 BASIC EQUATIONS IN FLUID MECHANICS NOOR ALIZA AHMAD

CHAPTER 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 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

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

vector H. If O is the point about which moments are desired, the angular moment about O is given:

vector 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 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

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

In which of the following scenarios is applying the following form of Bernoulli s equation: steady, inviscid, uniform stream of water. Ma = 0.

In which of the following scenarios is applying the following form of Bernoulli s equation: steady, inviscid, uniform stream of water. Ma = 0. bernoulli_11 In which of the following scenarios is applying the following form of Bernoulli s equation: p V z constant! g + g + = from point 1 to point valid? a. 1 stagnant column of water steady, inviscid,

More information

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

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

Visualization of flow pattern over or around immersed objects in open channel flow.

Visualization of flow pattern over or around immersed objects in open channel flow. EXPERIMENT SEVEN: FLOW VISUALIZATION AND ANALYSIS I OBJECTIVE OF THE EXPERIMENT: Visualization of flow pattern over or around immersed objects in open channel flow. II THEORY AND EQUATION: Open channel:

More information

2 Internal Fluid Flow

2 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 information

Lecture 3 The energy equation

Lecture 3 The energy equation Lecture 3 The energy equation Dr Tim Gough: t.gough@bradford.ac.uk General information Lab groups now assigned Timetable up to week 6 published Is there anyone not yet on the list? Week 3 Week 4 Week 5

More information

Benha University College of Engineering at Benha Questions For Corrective Final Examination Subject: Fluid Mechanics M 201 May 24/ 2016

Benha University College of Engineering at Benha Questions For Corrective Final Examination Subject: Fluid Mechanics M 201 May 24/ 2016 Benha University College of Engineering at Benha Questions For Corrective Final Examination Subject: Fluid Mechanics M 01 May 4/ 016 Second year Mech. Time :180 min. Examiner:Dr.Mohamed Elsharnoby Attempt

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

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

Mass of fluid leaving per unit time

Mass 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 information

EXPERIMENT No.1 FLOW MEASUREMENT BY ORIFICEMETER

EXPERIMENT 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 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

Week 8. Steady Flow Engineering Devices. GENESYS Laboratory

Week 8. Steady Flow Engineering Devices. GENESYS Laboratory Week 8. Steady Flow Engineering Devices Objectives 1. Solve energy balance problems for common steady-flow devices such as nozzles, compressors, turbines, throttling valves, mixers, heaters, and heat exchangers

More information

Basic Fluid Mechanics

Basic Fluid Mechanics Basic Fluid Mechanics Chapter 6A: Internal Incompressible Viscous Flow 4/16/2018 C6A: Internal Incompressible Viscous Flow 1 6.1 Introduction For the present chapter we will limit our study to incompressible

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

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

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

5 ENERGY EQUATION OF FLUID MOTION

5 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 information

FE Fluids Review March 23, 2012 Steve Burian (Civil & Environmental Engineering)

FE 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 information

HYDRAULICS STAFF SELECTION COMMISSION CIVIL ENGINEERING STUDY MATERIAL HYDRAULICS

HYDRAULICS STAFF SELECTION COMMISSION CIVIL ENGINEERING STUDY MATERIAL HYDRAULICS 1 STAFF SELECTION COMMISSION CIVIL ENGINEERING STUDY MATERIAL Syllabus Hydraulics ( Fluid Mechanics ) Fluid properties, hydrostatics, measurements of flow, Bernoulli's theorem and its application, flow

More information

ch-01.qxd 8/4/04 2:33 PM Page 1 Part 1 Basic Principles of Open Channel Flows

ch-01.qxd 8/4/04 2:33 PM Page 1 Part 1 Basic Principles of Open Channel Flows ch-01.qxd 8/4/04 2:33 PM Page 1 Part 1 Basic Principles of Open Channel Flows ch-01.qxd 8/4/04 2:33 PM Page 3 Introduction 1 Summary The introduction chapter reviews briefly the basic fluid properties

More information

Shell Balances in Fluid Mechanics

Shell 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 information

Chapter 1: Basic Concepts

Chapter 1: Basic Concepts What is a fluid? A fluid is a substance in the gaseous or liquid form Distinction between solid and fluid? Solid: can resist an applied shear by deforming. Stress is proportional to strain Fluid: deforms

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

For example an empty bucket weighs 2.0kg. After 7 seconds of collecting water the bucket weighs 8.0kg, then:

For example an empty bucket weighs 2.0kg. After 7 seconds of collecting water the bucket weighs 8.0kg, then: Hydraulic Coefficient & Flow Measurements ELEMENTARY HYDRAULICS National Certificate in Technology (Civil Engineering) Chapter 3 1. Mass flow rate If we want to measure the rate at which water is flowing

More information

INSTITUTE OF AERONAUTICAL ENGINEERING Dundigal, Hyderabad AERONAUTICAL ENGINEERING QUESTION BANK : AERONAUTICAL ENGINEERING.

INSTITUTE OF AERONAUTICAL ENGINEERING Dundigal, Hyderabad AERONAUTICAL ENGINEERING QUESTION BANK : AERONAUTICAL ENGINEERING. Course Name Course Code Class Branch INSTITUTE OF AERONAUTICAL ENGINEERING Dundigal, Hyderabad - 00 0 AERONAUTICAL ENGINEERING : Mechanics of Fluids : A00 : II-I- B. Tech Year : 0 0 Course Coordinator

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

Fluid Mechanics Qualifying Examination Sample Exam 2

Fluid Mechanics Qualifying Examination Sample Exam 2 Fluid Mechanics Qualifying Examination Sample Exam 2 Allotted Time: 3 Hours The exam is closed book and closed notes. Students are allowed one (double-sided) formula sheet. There are five questions on

More information

Lesson 6 Review of fundamentals: Fluid flow

Lesson 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 information

Objectives. 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 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 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

Experiment- To determine the coefficient of impact for vanes. Experiment To determine the coefficient of discharge of an orifice meter.

Experiment- 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 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

REE Internal Fluid Flow Sheet 2 - Solution Fundamentals of Fluid Mechanics

REE Internal Fluid Flow Sheet 2 - Solution Fundamentals of Fluid Mechanics REE 307 - Internal Fluid Flow Sheet 2 - Solution Fundamentals of Fluid Mechanics 1. Is the following flows physically possible, that is, satisfy the continuity equation? Substitute the expressions for

More information

1 FLUIDS AND THEIR PROPERTIES

1 FLUIDS AND THEIR PROPERTIES FLUID MECHANICS CONTENTS CHAPTER DESCRIPTION PAGE NO 1 FLUIDS AND THEIR PROPERTIES PART A NOTES 1.1 Introduction 1.2 Fluids 1.3 Newton s Law of Viscosity 1.4 The Continuum Concept of a Fluid 1.5 Types

More information

Fluid Dynamics Midterm Exam #2 November 10, 2008, 7:00-8:40 pm in CE 110

Fluid Dynamics Midterm Exam #2 November 10, 2008, 7:00-8:40 pm in CE 110 CVEN 311-501 Fluid Dynamics Midterm Exam #2 November 10, 2008, 7:00-8:40 pm in CE 110 Name: UIN: Instructions: Fill in your name and UIN in the space above. There should be 11 pages including this one.

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

Exam #2: Fluid Kinematics and Conservation Laws April 13, 2016, 7:00 p.m. 8:40 p.m. in CE 118

Exam #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 information

Therefore, the control volume in this case can be treated as a solid body, with a net force or thrust of. bm # V

Therefore, 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 information

Chapter 4 DYNAMICS OF FLUID FLOW

Chapter 4 DYNAMICS OF FLUID FLOW Faculty Of Engineering at Shobra nd Year Civil - 016 Chapter 4 DYNAMICS OF FLUID FLOW 4-1 Types of Energy 4- Euler s Equation 4-3 Bernoulli s Equation 4-4 Total Energy Line (TEL) and Hydraulic Grade Line

More information

Convection. forced convection when the flow is caused by external means, such as by a fan, a pump, or atmospheric winds.

Convection. forced convection when the flow is caused by external means, such as by a fan, a pump, or atmospheric winds. Convection The convection heat transfer mode is comprised of two mechanisms. In addition to energy transfer due to random molecular motion (diffusion), energy is also transferred by the bulk, or macroscopic,

More information

Chapter Four fluid flow mass, energy, Bernoulli and momentum

Chapter 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 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

Chapter 2: Basic Governing Equations

Chapter 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 information

PIPE FLOWS: LECTURE /04/2017. Yesterday, for the example problem Δp = f(v, ρ, μ, L, D) We came up with the non dimensional relation

PIPE FLOWS: LECTURE /04/2017. Yesterday, for the example problem Δp = f(v, ρ, μ, L, D) We came up with the non dimensional relation /04/07 ECTURE 4 PIPE FOWS: Yesterday, for the example problem Δp = f(v, ρ, μ,, ) We came up with the non dimensional relation f (, ) 3 V or, p f(, ) You can plot π versus π with π 3 as a parameter. Or,

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

FLUID MECHANICS. Chapter 3 Elementary Fluid Dynamics - The Bernoulli Equation

FLUID MECHANICS. Chapter 3 Elementary Fluid Dynamics - The Bernoulli Equation FLUID MECHANICS Chapter 3 Elementary Fluid Dynamics - The Bernoulli Equation CHAP 3. ELEMENTARY FLUID DYNAMICS - THE BERNOULLI EQUATION CONTENTS 3. Newton s Second Law 3. F = ma along a Streamline 3.3

More information

ENGINEERING FLUID MECHANICS. CHAPTER 1 Properties of Fluids

ENGINEERING FLUID MECHANICS. CHAPTER 1 Properties of Fluids CHAPTER 1 Properties of Fluids ENGINEERING FLUID MECHANICS 1.1 Introduction 1.2 Development of Fluid Mechanics 1.3 Units of Measurement (SI units) 1.4 Mass, Density, Specific Weight, Specific Volume, Specific

More information

APPLIED FLUID DYNAMICS HANDBOOK

APPLIED FLUID DYNAMICS HANDBOOK APPLIED FLUID DYNAMICS HANDBOOK ROBERT D. BLEVINS H imhnisdia ttodisdiule Darmstadt Fachbereich Mechanik 'rw.-nr.. [VNR1 VAN NOSTRAND REINHOLD COMPANY ' ' New York Contents Preface / v 1. Definitions /

More information

Fluid Mechanics. Spring 2009

Fluid Mechanics. Spring 2009 Instructor: Dr. Yang-Cheng Shih Department of Energy and Refrigerating Air-Conditioning Engineering National Taipei University of Technology Spring 2009 Chapter 1 Introduction 1-1 General Remarks 1-2 Scope

More information

AE/ME 339. K. M. Isaac Professor of Aerospace Engineering. 12/21/01 topic7_ns_equations 1

AE/ME 339. K. M. Isaac Professor of Aerospace Engineering. 12/21/01 topic7_ns_equations 1 AE/ME 339 Professor of Aerospace Engineering 12/21/01 topic7_ns_equations 1 Continuity equation Governing equation summary Non-conservation form D Dt. V 0.(2.29) Conservation form ( V ) 0...(2.33) t 12/21/01

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

Introduction to Chemical Engineering Thermodynamics. Chapter 7. KFUPM Housam Binous CHE 303

Introduction to Chemical Engineering Thermodynamics. Chapter 7. KFUPM Housam Binous CHE 303 Introduction to Chemical Engineering Thermodynamics Chapter 7 1 Thermodynamics of flow is based on mass, energy and entropy balances Fluid mechanics encompasses the above balances and conservation of momentum

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

Engineering Fluid Mechanics

Engineering Fluid Mechanics Engineering Fluid Mechanics Eighth Edition Clayton T. Crowe WASHINGTON STATE UNIVERSITY, PULLMAN Donald F. Elger UNIVERSITY OF IDAHO, MOSCOW John A. Roberson WASHINGTON STATE UNIVERSITY, PULLMAN WILEY

More information

10.52 Mechanics of Fluids Spring 2006 Problem Set 3

10.52 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 information

Chapter 6: Momentum Analysis

Chapter 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 information

Introduction to Marine Hydrodynamics

Introduction to Marine Hydrodynamics 1896 1920 1987 2006 Introduction to Marine Hydrodynamics (NA235) Department of Naval Architecture and Ocean Engineering School of Naval Architecture, Ocean & Civil Engineering First Assignment The first

More information

External Flow and Boundary Layer Concepts

External Flow and Boundary Layer Concepts 1 2 Lecture (8) on Fayoum University External Flow and Boundary Layer Concepts By Dr. Emad M. Saad Mechanical Engineering Dept. Faculty of Engineering Fayoum University Faculty of Engineering Mechanical

More information

In this section, mathematical description of the motion of fluid elements moving in a flow field is

In 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 information

piston control surface

piston control surface Lecture Thermodynamics 4 Enthalpy Consider a quasistatic hydrostatic constant pressure (isobaric) process weights piston, p gas Q control surface fi, p gas U -U 1 = Q +W = Q - Ú pdv = Q - p + p fi (U +

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

Chapter 4 Continuity Equation and Reynolds Transport Theorem

Chapter 4 Continuity Equation and Reynolds Transport Theorem Chapter 4 Continuity Equation and Reynolds Transport Theorem 4.1 Control Volume 4. The Continuity Equation for One-Dimensional Steady Flow 4.3 The Continuity Equation for Two-Dimensional Steady Flow 4.4

More information

FLUID MECHANICS PROF. DR. METİN GÜNER COMPILER

FLUID MECHANICS PROF. DR. METİN GÜNER COMPILER FLUID MECHANICS PROF. DR. METİN GÜNER COMPILER ANKARA UNIVERSITY FACULTY OF AGRICULTURE DEPARTMENT OF AGRICULTURAL MACHINERY AND TECHNOLOGIES ENGINEERING 1 5. FLOW IN PIPES 5.1.3. Pressure and Shear Stress

More information

Introduction to Fluid Dynamics

Introduction to Fluid Dynamics Introduction to Fluid Dynamics Roger K. Smith Skript - auf englisch! Umsonst im Internet http://www.meteo.physik.uni-muenchen.de Wählen: Lehre Manuskripte Download User Name: meteo Password: download Aim

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 c) Orificemeter a) Viscous force, Turbulence force, Compressible force a) Turbulence force c) Integration d) The flow is rotational

Fluid Mechanics c) Orificemeter a) Viscous force, Turbulence force, Compressible force a) Turbulence force c) Integration d) The flow is rotational Fluid Mechanics 1. Which is the cheapest device for measuring flow / discharge rate. a) Venturimeter b) Pitot tube c) Orificemeter d) None of the mentioned 2. Which forces are neglected to obtain Euler

More information

BACHELOR OF TECHNOLOGY IN MECHANICAL ENGINEERING (COMPUTER INTEGRATED MANUFACTURING)

BACHELOR OF TECHNOLOGY IN MECHANICAL ENGINEERING (COMPUTER INTEGRATED MANUFACTURING) No. of Printed Pages : 6 BME-028 BACHELOR OF TECHNOLOGY IN MECHANICAL ENGINEERING (COMPUTER INTEGRATED MANUFACTURING) Term-End Examination December, 2011 00792 BME-028 : FLUID MECHANICS Time : 3 hours

More information

UNIT II CONVECTION HEAT TRANSFER

UNIT II CONVECTION HEAT TRANSFER UNIT II CONVECTION HEAT TRANSFER Convection is the mode of heat transfer between a surface and a fluid moving over it. The energy transfer in convection is predominately due to the bulk motion of the fluid

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

1 One-dimensional analysis

1 One-dimensional analysis One-dimensional analysis. Introduction The simplest models for gas liquid flow systems are ones for which the velocity is uniform over a cross-section and unidirectional. This includes flows in a long

More information

Microfluidic Devices. Microfluidic Device Market. Microfluidic Principles Part 1. Introduction to BioMEMS & Medical Microdevices.

Microfluidic Devices. Microfluidic Device Market. Microfluidic Principles Part 1. Introduction to BioMEMS & Medical Microdevices. Introduction to BioMEMS & Medical Microdevices Microfluidic Principles Part 1 Companion lecture to the textbook: Fundamentals of BioMEMS and Medical Microdevices, by Prof., http://saliterman.umn.edu/,

More information

Review of Fluid Mechanics

Review of Fluid Mechanics Chapter 3 Review of Fluid Mechanics 3.1 Units and Basic Definitions Newton s Second law forms the basis of all units of measurement. For a particle of mass m subjected to a resultant force F the law may

More information

6.1 Momentum Equation for Frictionless Flow: Euler s Equation The equations of motion for frictionless flow, called Euler s

6.1 Momentum Equation for Frictionless Flow: Euler s Equation The equations of motion for frictionless flow, called Euler s Chapter 6 INCOMPRESSIBLE INVISCID FLOW All real fluids possess viscosity. However in many flow cases it is reasonable to neglect the effects of viscosity. It is useful to investigate the dynamics of an

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

CHAPTER 2 INVISCID FLOW

CHAPTER 2 INVISCID FLOW CHAPTER 2 INVISCID FLOW Changes due to motion through a field; Newton s second law (f = ma) applied to a fluid: Euler s equation; Euler s equation integrated along a streamline: Bernoulli s equation; Bernoulli

More information

CHAPTER 7 NUMERICAL MODELLING OF A SPIRAL HEAT EXCHANGER USING CFD TECHNIQUE

CHAPTER 7 NUMERICAL MODELLING OF A SPIRAL HEAT EXCHANGER USING CFD TECHNIQUE CHAPTER 7 NUMERICAL MODELLING OF A SPIRAL HEAT EXCHANGER USING CFD TECHNIQUE In this chapter, the governing equations for the proposed numerical model with discretisation methods are presented. Spiral

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