# Liquids and solids are essentially incompressible substances and the variation of their density with pressure is usually negligible.

Size: px
Start display at page:

Download "Liquids and solids are essentially incompressible substances and the variation of their density with pressure is usually negligible."

Transcription

1 Properties of Fluids Intensive properties are those that are independent of the mass of a system i.e. temperature, pressure and density. Extensive properties are those whose values depend on the size of the system. Generally uppercase letters are used to denote extensive properties and lowercase letters are used for intensive properties. Extensive properties per unit mass are called specific properties. The number of properties required to fix the state of a system is given by the state postulate: the state of a simple compressible system is completely specified by two independent, intensive properties. A continuum is a continuous, homogeneous matter with no holes. The continuum idealization allows us to treat properties as point functions and to assume the properties vary continually in space with no jump discontinuities. This idealization is valid as long as the size of the system we deal with is large relative to the space between the molecules. Density and specific gravity Density is defined as mass per unit volume: The reciprocal of density is the specific volume which is defined as volume per unit mass. The density of a substance depends on temperature and pressure. The density of most gases is proportional to pressure and inversely proportional to temperature. Liquids and solids are essentially incompressible substances and the variation of their density with pressure is usually negligible. Specific gravity or relative density is defined as the ratio of the density of a substance to the density of some standard substance at a specified temperature. That is The specific gravity of a substance is a dimensionless quantity. However in SI units the numerical value of the specific gravity of a substance is exactly equal to its density. Substances with specific gravities less than 1 are lighter than water, and thus will float on water. The weight of a unit volume of a substance is called specific weight and is expressed as: (N/m 3 ) where G is gravitational acceleration. Recall that densities of liquids are essentially constant and thus they can often be approximated as being incompressible substances during most processes. Density of Ideal Gases Any equation that relates the pressure, temperature and density (or specific volume) of a substance is called an equation of state. The simplest is the ideal-gas equation of state: Where P is absolute pressure, v is specific volume, T is thermodynamic temperature, constant. is density and R is gas The gas constant R is different for each gas and is determined from Where R U is the universal gas constant which equals 8.314kJ/kmol K and M is the molar (molecular) mass. P a g e 1

2 In SI the thermodynamic temperature scale is the Kelvin Scale (K) and the English system uses the Rankine scale (R) Any gas that obeys the ideal-gas equation of state (or ideal-gas relation) is called an ideal gas. For an ideal gas of Volume V, mass m and number of moles N =m/m the ideal gas equation of state can also be written as: For a fixed mass m, the properties of an ideal gas at two different states are related to each other by: An ideal gas is a hypothetical substance that obeys the ideal gas relation; however it has been experimentally observed that it closely approximates the P-v-T behaviour of real gases at low densities. At low pressures and high temperatures the density of a gas decreases and the gas behaves much like an ideal gas. Some familiar gases such as air, nitrogen, oxygen, hydrogen, helium, argon, neon and krypton and even heavier gases such as carbon dioxide can be treated as ideal gases with neglible error. Dense gases such as water vapour and refrigerant vapour however should not be treated as ideal gases since they usually exist at a state near saturation. Vapor Pressure and Cavitation Temperature and pressure are dependent properties for pure substances during phase change processes, and there is one-to-one correspondence between temperatures and pressures. At a given pressure the temperature at which a pure substance changes phase is called the saturation temperature T sat. Similiarly the pressure at which a pure substance changes phase is called the saturation pressure P sat. The Vapor pressure P v of a pure substance is defined as the pressure exerted by its vapour in phase equilibrium with its liquid at a given temperature. Vapor pressure is a property of the pure substance and turns out to be identical the to the saturation pressure of the liquid (P V =P sat ). Partial pressure is defined as the pressure of a gas or vapour in a mixture with other gases. The partial pressure of a vapour must be less than or equal to the vapour pressure if there is no liquid present. However, when both vapour and liquid are present and the system is in phase equilibrium the partial pressure of the vapour must equal the vapour pressure and the system is said to be saturated. For phase-change processes between the liquid and vapour phases of a pure substance, the saturation pressure and the vapour pressure are equivalent since the vapour is pure. Note that the pressure would be the same whether it is measured in the vapour or liquid phase, provided that it is measured at a location close to the liquid-vapor interface to avoid hydrostatic effects). Vapor pressure increases with temperature. The reason for our interest in vapour pressure is the possibility of the liquid pressure in liquid-flow systems dropping below the vapour pressure at some locations, and the resulting unplanned vaporization. For example, water at 10 C will flash into vapour and form bubbles at locations (such as the tip of impellers or suction sides of pumps) where the pressure drops below 1.23kPa. The vapour bubbles (Cavitation bubbles since they create cavities in the liquid) collapse as they are swept away from the low-pressure regions, generating highly destructive, extremely high pressure waves. This phenomenon is called cavitation and it is an important consideration in the design of hydraulic turbines and pumps. Cavitation must be avoided or at least minimized in flow systems since it reduces performance, generates annoying vibrations and noise and causes damage to equipment. It can be characterised by a tumbling sound. P a g e 2

3 Energy and specific heats Total Energy E The summation of all other forms of energy within a given system Internal Energy U The sum of all microscopic forms of energy of a system Kinetic Energy Ke The energy that a system possesses as a result of its motion relative to some reference frame, when all parts of the system move with the same velocity Ke = V 2 /2 Potential Energy Pe The energy that a system possesses as a result of its elevation in a gravitational field can be expressed as pe = gz (g = Gravity, z = elevation above an arbitrary axis) Thermal Energy The sensible and latent forms of internal energy (heat) simililarly known as thermal energy The international unit of energy is the Joule or kilojoule. In the analysis of systems that involve fluid flow we frequently encounter the combination of properties u and Pv. For convenience, this combination is called Enthalpy, h. where ( ). Which is the energy per unit mass needed to move the fluid and maintain flow. In the energy analysis of flowing fluids, it is convenient to treat the flow energy as part of the energy of the fluid and to represent the microscropic energy of a fluid stream by enthalpy. Enthalpy is a quantity per unit mass, and thus it is a specific property. In the absence of magnetic, electric and surface tension a system is called a simple compressible system. The total energy of a simple compressible system consists of three parts: Internal, kinetic and potential energies. Then the total energy of a flowing fluid on a unit-mass basis becomes. V is velocity, z is elevation. (kj/kg) where h = is the enthalpy. By using enthalpy instead of the internal energy to represent the energy of a flowing fluid, one does not need to be concerned about the flow work. The energy associated with pushing the fluid is automatically taken care of by enthalpy. The differential and finite changes in the internal energy and enthalpy of an ideal gas can be expressed in terms of the specific heats as and Where C v and C p are the constant-volume and constant pressure specific heats of the ideal gas. Using specific heat values at the average temperature, the finite changes in internal energy and enthalpy can be expressed approximately as and For liquids and are identical therefore and the change in the internal energy of liquids can be expressed as. Enthalpy change can be written as Therefore for constant pressure processes and for constant-temperature processes of liquids. P a g e 3

4 Coefficient of compressibility To determine the amount of volume change you need to define properties that relate volume changes to the changes in pressure and temperature. Two such properties are the bulk modulus of elasticity κ and the coefficient of volume expansion β. It is known that fluids act like solids with respect to pressure. Therefore the coefficient of compressibility κ (also called the bulk modulus of compressibility or bulk modulus of elasticity) for fluids is: In terms of finite changes it can be expressed as ( ) ( ) ( ) ( )are dimensionless, must have the dimension of pressure. Also, the coefficient of compressibility represents the change in pressure corresponding to a fractional change in volume or density of the fluid while the temperature remains constant. Then it follows that the coefficient of compressibility of a truly incompressible substance (v = constant) is infinity. A large coefficient of compressibility ( ) indicates that a large change in pressure is needed to cause a small fractional change in volume, and thus a fluid with a large is essentially incompressible. Note that volume and pressure are inversely proportional. Also differentiating pressure gives that Is, the fractional changes in the specific volume and the density of a fluid are equal in magnitude but opposite sign. For an ideal gas, and ( ) And thus: gives: substituting this into the definition of the coefficient of compressibility and rearranging Therefore the percent increase of density of an ideal gas during isothermal compression is equal to the percent increase in pressure. Due to this, a small fractional change in the volume of a gas can cause a large change in pressure at very high pressures. The inverse of the coefficient of compressibility is called the isothermal compressibility α and is expressed as The isothermal compressibility of a fluid represents the fractional change in volume or density corresponding to a unit change in pressure. P a g e 4

5 Coefficient of Volume Expansion The density of a fluid, in general, depends more strongly on temperature than it does on pressure. To quantify this relationship you need to use the coefficient of volume expansion: It can also be expressed approximately in terms of finite changes as: A large value of for a fluid means a large change in density with temperature, and the product represents the fraction of volume change of a fluid that corresponds to a temperature change of at constant pressure. It can be shown easily that the volume expansion coefficient of an ideal gas (P= ) at a temperature T is equivalent to the inverse of the temperature ( ) In the study of natural convection currents, the condition of the main fluid body that surrounds the finite hot or cold regions is indicated by the subscript infinity to serve as a reminder that this is the value at a distance where the presence of the hot or cold region is not felt. In such cases, the volume expansion coefficient can be expressed approximately as ( ) ( ) ( ) Where is the density and is the temperature of the quiescent fluid away from the confined hot or cold fluid pocket. The combined effects of pressure and temperature changes on the volume change of a fluid can be determined by taking the specific volume to be a function of T and P. Differentiating v=v(t,p) and using the definitions of the compression and expansion coefficients α and β gives: Then the fractional change in volume (or density) due to changes in pressure and temperature can be expressed approximately as Viscosity Just as two solids moving in contact with each other develop friction the same applies for liquids, however it is called viscosity. This property represents the internal resistance of a fluid to motion or the fluidity. The force a flowing fluid exerts on a body in the flow direction is called the drag force, and the magnitude of this force depends, in part, on viscosity. The shear stress as a result of viscosity can be shown as Where F = the force applied, A = the contact area between the plate (object) and the fluid. Note that the fluid layer deforms continuously under the influence of shear stress. In steady laminar flow the fluid velocity between the plates varies linearly between 0 and V and thus the velocity profile and the P a g e 5

6 velocity gradient are: is the distance between two plates. where y is the vertical distance from the lower plate and l During a differential time interval dt, the sides of fluid particules along a vertical line MN rotate through a differential angle dβ while the upper plate moves a differential distance da = V dt. The angular displacement or deformation (or shear strain) can be expressed as: Rearrangig the rate of deformation under the influence of shear stress τ becomes : We can conclude that the rate of deformation of a fluid element is equivalent to the velocity gradient du/dy. Further it can be verified experimentally that for most fluids the rate of deformation (and thus the velocity gradient) is directly proportional to the shear stress τ. Fluids where the rate of deformation is proportional to the shear stress are called Newtonian fluids. In onedimensional shear flow of Newtonian fluids, shear stress can be expressed by the linear relationship The constant of proportionality μ is called the coefficient of viscosity or the dynamic (or Absolute) viscosity of the fluid (kg/m.s). Note that viscosity is independent of the rate of deformation. The shear force acting on a Newtonian fluid layer is Then the force F required to move the upper plate at a constant velocity of V while the lower plate remains stationary is: Fluids for which the apparent viscosity increases with the rate of deformation are referred to as dilatant or shear thickening fluids and those that exhibit the opposite behaviour (the fluid becoming less viscous as it is sheared harder) are referred to as pseudoplastic or shear thinning fluids. In fluid mechanics and heat transfer the ratio of dynamic viscosity to density appears frequently. For convenience the ratio is given the name kinematic viscosity v and is expressed as v=u/p (1 stoke = 1cm 2 /s). In general the viscosity of a fluid depends on both temperature and pressure, although much less so on pressure. For gases this is also the case for dynamic viscosity, but not for kinematic viscosity since the density of a gas is proportional to its pressure. P a g e 6

7 The viscosity of a fluid is a measure of its resistance to deformation. The viscosity of liquids decreases with temperature, whereas the viscosity of gases increases with temperature. The viscosity of a fluid is directly related to the pumping power needed to transport a fluid in a pipe or to move a body through a fluid. The viscosity of gases is expressed as a function of temperature as: where T is absolute temperature, and a and b are experimentally determined constants. (measuring the viscosities at two different temperatures is sufficient to determine these constants). Viscosity increases at high pressures due to the increase in density. The viscosity of liquids can be expressed as a function of temperature as: T again is absolute temperature and a,b,c are experimentally determined. Two concentric cylinders can be used as a viscometer, a device that measures viscosity. The following equation can be used to measure the viscosity of a fluid by measuring torque at a specified angular velocity: Where L is the length of the cylinder and N is the number of revolutions per unit time, ω is the angular velocity. Angular distance travelled during one rotation is 2π rad and thus the relation between and angular velocity in rad/min and the rpm is ω=2πn. Surface Tension and Capillary Effect In some instances liquid droplets behave like small spherical balloons filled with the liquid, and the surface of the liquid acts like a stretched membrane under tension. The magnitude of this force per unit length is called the surface tension (or surface energy) σ s (N/m). It represents the stretching work that needs to be done to increase the surface area of the liquid by a unit amount. Surface tension on a wire can be expressed as: The surface tension of a liquid generally decreases with temperature and becomes zero at the critical point (and thus there is no distinct liquid-vapor interface at temperatures above the critical point). The effect of pressure on surface tension is usually negligible. The surface tension can also be changed considerably by impurities. We speak of surface tension for liquids only at liquid-liquid or liquid-gas interfaces. Therefore it is important to specify the adjacent liquid or gas when specifying surface tension. Surface tension also determines the size of the liquid droplets that form. Noting that surface tension acts along the circumference and the pressure acts on the area, horizontal force balances for the droplet and the bubble give. P a g e 7

8 Where P i and P o are the pressures inside and outside the droplet or bubble, respectively. Note that the excess pressure in a droplet or bubble is inversely proportional to the radius and is given by Capillary Effect The capillary effect is the rise and fall of a liquid in a small-diameter tube inserted into the liquid(like water rising to the top of trees). Such narrow tubes or confined flow channels are called capillaries. The curved free surface of a liquid in a capillary tube is called the meniscus. The strength of the capillary effect is quantified by the contact (or wetting) angle φ defined as the angle that the tangent to the liquid surface makes with the solid surface at the point of contact. A liquid is said to wet the surface when φ < 90 and now to wet the surface when φ > 90. The capillary effect can be explained microscopically and comes down to the strength of the cohesive forces (like forces) and adhesive forces (unlike forces). In a glass of water the water is more attracted to the glass than it is to other water molecules, therefore it rises in a glass. The magnitude of the capillary rise in a circular tube can be expressed as: Only applicable for constant-diameter tubes and should not be used for tubes of variable cross section. Where h = capillary rise, σ s is surface tension, ρ is density, g is gravity and φ is contact angle. In the case of a capillary drop (mercury in a glass) the expression will provide a negative value, therefore a drop. Capillary rise is inversely proportional to the radius of the tube. Therefore the thinner the tube is, the greater the rise (or fall) of the liquid in the tub. The capillary effect is usually negligible in tubes with diameter greater than 1cm. Capillary rise is also inversely proportional to the density of the liquid. Summary from page 55 of textbook: P a g e 8

### A drop forms when liquid is forced out of a small tube. The shape of the drop is determined by a balance of pressure, gravity, and surface tension

A drop forms when liquid is forced out of a small tube. The shape of the drop is determined by a balance of pressure, gravity, and surface tension forces. 2 Objectives 3 i i 2 1 INTRODUCTION Property:

### Lecturer, Department t of Mechanical Engineering, SVMIT, Bharuch

Fluid Mechanics By Ashish J. Modi Lecturer, Department t of Mechanical Engineering, i SVMIT, Bharuch Review of fundamentals Properties of Fluids Introduction Any characteristic of a system is called a

### Welcome to MECH 280. Ian A. Frigaard. Department of Mechanical Engineering, University of British Columbia. Mech 280: Frigaard

Welcome to MECH 280 Ian A. Frigaard Department of Mechanical Engineering, University of British Columbia Lectures 1 & 2: Learning goals/concepts: What is a fluid Apply continuum hypothesis Stress and viscosity

### 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

### BFC FLUID MECHANICS BFC NOOR ALIZA AHMAD

BFC 10403 FLUID MECHANICS CHAPTER 1.0: Principles of Fluid 1.1 Introduction to Fluid Mechanics 1.2 Thermodynamic Properties of a Fluid: Density, specific weight, specific gravity, viscocity (kelikatan)berat

### Fluid Mechanics Introduction

Fluid Mechanics Introduction Fluid mechanics study the fluid under all conditions of rest and motion. Its approach is analytical, mathematical, and empirical (experimental and observation). Fluid can be

### 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

### - Apply closed system energy balances, observe sign convention for work and heat transfer.

CHAPTER : ENERGY AND THE FIRST LAW OF THERMODYNAMICS Objectives: - In this chapter we discuss energy and develop equations for applying the principle of conservation of energy. Learning Outcomes: - Demonstrate

### CHAPTER 1 Fluids and their Properties

FLUID MECHANICS Gaza CHAPTER 1 Fluids and their Properties Dr. Khalil Mahmoud ALASTAL Objectives of this Chapter: Define the nature of a fluid. Show where fluid mechanics concepts are common with those

### AMME2261: Fluid Mechanics 1 Course Notes

Module 1 Introduction and Fluid Properties Introduction Matter can be one of two states: solid or fluid. A fluid is a substance that deforms continuously under the application of a shear stress, no matter

### University of Hail Faculty of Engineering DEPARTMENT OF MECHANICAL ENGINEERING. ME Fluid Mechanics Lecture notes. Chapter 1

University of Hail Faculty of Engineering DEPARTMENT OF MECHANICAL ENGINEERING ME 311 - Fluid Mechanics Lecture notes Chapter 1 Introduction and fluid properties Prepared by : Dr. N. Ait Messaoudene Based

### COURSE NUMBER: ME 321 Fluid Mechanics I. Fluid: Concept and Properties

COURSE NUMBER: ME 321 Fluid Mechanics I Fluid: Concept and Properties Course teacher Dr. M. Mahbubur Razzaque Professor Department of Mechanical Engineering BUET 1 What is Fluid Mechanics? Fluid mechanics

### Petroleum Engineering Department Fluid Mechanics Second Stage Assist Prof. Dr. Ahmed K. Alshara

Continents Petroleum Engineering Department Fluid Mechanics Second Stage Assist Prof. Dr. Ahmed K. Alshara Chapter 1. Fluid Mechanics -Properties of fluids -Density, specific gravity, specific volume and

### 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

### Chapter 1 Fluid Characteristics

Chapter 1 Fluid Characteristics 1.1 Introduction 1.1.1 Phases Solid increasing increasing spacing and intermolecular liquid latitude of cohesive Fluid gas (vapor) molecular force plasma motion 1.1.2 Fluidity

### Petroleum Engineering Dept. Fluid Mechanics Second Stage Dr. Ahmed K. Alshara

Continents Chapter 1. Fluid Mechanics -Properties of fluids -Density, specific gravity, specific volume and Viscosity -Newtonian and non Newtonian fluids -Surface tension Compressibility -Pressure -Cavitations

### 1. The Properties of Fluids

1. The Properties of Fluids [This material relates predominantly to modules ELP034, ELP035] 1.1 Fluids 1.1 Fluids 1.2 Newton s Law of Viscosity 1.3 Fluids Vs Solids 1.4 Liquids Vs Gases 1.5 Causes of viscosity

### P = 1 3 (σ xx + σ yy + σ zz ) = F A. It is created by the bombardment of the surface by molecules of fluid.

CEE 3310 Thermodynamic Properties, Aug. 27, 2010 11 1.4 Review A fluid is a substance that can not support a shear stress. Liquids differ from gasses in that liquids that do not completely fill a container

### CHARACTERISTIC OF FLUIDS. A fluid is defined as a substance that deforms continuously when acted on by a shearing stress at any magnitude.

CHARACTERISTIC OF FLUIDS A fluid is defined as a substance that deforms continuously when acted on by a shearing stress at any magnitude. In a fluid at rest, normal stress is called pressure. 1 Dimensions,

### INTRODUCTION DEFINITION OF FLUID. U p F FLUID IS A SUBSTANCE THAT CAN NOT SUPPORT SHEAR FORCES OF ANY MAGNITUDE WITHOUT CONTINUOUS DEFORMATION

INTRODUCTION DEFINITION OF FLUID plate solid F at t = 0 t > 0 = F/A plate U p F fluid t 0 t 1 t 2 t 3 FLUID IS A SUBSTANCE THAT CAN NOT SUPPORT SHEAR FORCES OF ANY MAGNITUDE WITHOUT CONTINUOUS DEFORMATION

### 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

### Fluid Mechanics Theory I

Fluid Mechanics Theory I Last Class: 1. Introduction 2. MicroTAS or Lab on a Chip 3. Microfluidics Length Scale 4. Fundamentals 5. Different Aspects of Microfluidcs Today s Contents: 1. Introduction to

### Non-Newtonian fluids is the fluids in which shear stress is not directly proportional to deformation rate, such as toothpaste,

CHAPTER1: Basic Definitions, Zeroth, First, and Second Laws of Thermodynamics 1.1. Definitions What does thermodynamic mean? It is a Greeks word which means a motion of the heat. Water is a liquid substance

### Thermodynamics I. Properties of Pure Substances

Thermodynamics I Properties of Pure Substances Dr.-Eng. Zayed Al-Hamamre 1 Content Pure substance Phases of a pure substance Phase-change processes of pure substances o Compressed liquid, Saturated liquid,

### Chapter 1: Basic Concepts of Thermodynamics. Thermodynamics and Energy. Dimensions and Units

Chapter 1: Basic Concepts of Thermodynamics Every science has its own unique vocabulary associated with it. recise definition of basic concepts forms a sound foundation for development of a science and

### first law of ThermodyNamics

first law of ThermodyNamics First law of thermodynamics - Principle of conservation of energy - Energy can be neither created nor destroyed Basic statement When any closed system is taken through a cycle,

### Middle East Technical University Department of Mechanical Engineering ME 305 Fluid Mechanics I Fall 2018 Section 4 (Dr.

Reading Assignments Middle East Technical University Department of Mechanical Engineering ME 305 Fluid Mechanics I Fall 2018 Section 4 (Dr. Sert) Study Set 1 You can find the answers of some of the following

### Thermodynamic System. A thermodynamic system is a volume in space containing a quantity of matter that is being studied for thermodynamic analysis.

Thermodynamic System A thermodynamic system is a volume in space containing a quantity of matter that is being studied for thermodynamic analysis. The system is bounded by an arbitrary surface called the

### Basic Thermodynamics Module 1

Basic Thermodynamics Module 1 Lecture 9: Thermodynamic Properties of Fluids Thermodynamic Properties of fluids Most useful properties: Properties like pressure, volume and temperature which can be measured

### 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

### First Law of Thermodynamics Closed Systems

First Law of Thermodynamics Closed Systems Content The First Law of Thermodynamics Energy Balance Energy Change of a System Mechanisms of Energy Transfer First Law of Thermodynamics in Closed Systems Moving

### 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

### We may have a general idea that a solid is hard and a fluid is soft. This is not satisfactory from

Chapter 1. Introduction 1.1 Some Characteristics of Fluids We may have a general idea that a solid is hard and a fluid is soft. This is not satisfactory from scientific or engineering point of view. In

### 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.

### 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.........................

### Lecture 3. Properties of Fluids 11/01/2017. There are thermodynamic properties of fluids like:

11/01/2017 Lecture 3 Properties of Fluids There are thermodynamic properties of fluids like: Pressure, p (N/m 2 ) or [ML -1 T -2 ], Density, ρ (kg/m 3 ) or [ML -3 ], Specific weight, γ = ρg (N/m 3 ) or

### 1. Introduction, fluid properties (1.1, 2.8, 4.1, and handouts)

1. Introduction, fluid properties (1.1, 2.8, 4.1, and handouts) Introduction, general information Course overview Fluids as a continuum Density Compressibility Viscosity Exercises: A1 Fluid mechanics Fluid

### DIVIDED SYLLABUS ( ) - CLASS XI PHYSICS (CODE 042) COURSE STRUCTURE APRIL

DIVIDED SYLLABUS (2015-16 ) - CLASS XI PHYSICS (CODE 042) COURSE STRUCTURE APRIL Unit I: Physical World and Measurement Physics Need for measurement: Units of measurement; systems of units; SI units, fundamental

### Fluid Mechanics-61341

An-Najah National University College of Engineering Fluid Mechanics-61341 Chapter [1] Fundamentals 1 The Book (Elementary Fluid Mechanics by Street, Watters and Vennard) Each chapter includes: Concepts

### Class XI Physics Syllabus One Paper Three Hours Max Marks: 70

Class XI Physics Syllabus 2013 One Paper Three Hours Max Marks: 70 Class XI Weightage Unit I Physical World & Measurement 03 Unit II Kinematics 10 Unit III Laws of Motion 10 Unit IV Work, Energy & Power

### 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

### Fluid Mechanics Abdusselam Altunkaynak

Fluid Mechanics Abdusselam Altunkaynak 1. Unit systems 1.1 Introduction Natural events are independent on units. The unit to be used in a certain variable is related to the advantage that we get from it.

### Thermodynamics ENGR360-MEP112 LECTURE 3

Thermodynamics ENGR360-MEP11 LECTURE 3 ENERGY, ENERGY TRANSFER, AND ENERGY ANALYSIS Objectives: 1. Introduce the concept of energy and define its various forms.. Discuss the nature of internal energy.

### s and FE X. A. Flow measurement B. properties C. statics D. impulse, and momentum equations E. Pipe and other internal flow 7% of FE Morning Session I

Fundamentals of Engineering (FE) Exam General Section Steven Burian Civil & Environmental Engineering October 26, 2010 s and FE X. A. Flow measurement B. properties C. statics D. impulse, and momentum

### Fluid Properties and Units

Fluid Properties and Units CVEN 311 Continuum Continuum All materials, solid or fluid, are composed of molecules discretely spread and in continuous motion. However, in dealing with fluid-flow flow relations

### Nicholas J. Giordano. Chapter 10 Fluids

Nicholas J. Giordano www.cengage.com/physics/giordano Chapter 10 Fluids Fluids A fluid may be either a liquid or a gas Some characteristics of a fluid Flows from one place to another Shape varies according

### Chapter 10. Solids and Fluids

Chapter 10 Solids and Fluids Surface Tension Net force on molecule A is zero Pulled equally in all directions Net force on B is not zero No molecules above to act on it Pulled toward the center of the

### Summary PHY101 ( 2 ) T / Hanadi Al Harbi

الكمية Physical Quantity القانون Low التعريف Definition الوحدة SI Unit Linear Momentum P = mθ be equal to the mass of an object times its velocity. Kg. m/s vector quantity Stress F \ A the external force

### PHYSICS. Course Structure. Unit Topics Marks. Physical World and Measurement. 1 Physical World. 2 Units and Measurements.

PHYSICS Course Structure Unit Topics Marks I Physical World and Measurement 1 Physical World 2 Units and Measurements II Kinematics 3 Motion in a Straight Line 23 4 Motion in a Plane III Laws of Motion

### ME 262 BASIC FLUID MECHANICS Assistant Professor Neslihan Semerci Lecture 4. (Buoyancy and Viscosity of water)

ME 262 BASIC FLUID MECHANICS Assistant Professor Neslihan Semerci Lecture 4 (Buoyancy and Viscosity of water) 16. BUOYANCY Whenever an object is floating in a fluid or when it is completely submerged in

### TOPICS. Density. Pressure. Variation of Pressure with Depth. Pressure Measurements. Buoyant Forces-Archimedes Principle

Lecture 6 Fluids TOPICS Density Pressure Variation of Pressure with Depth Pressure Measurements Buoyant Forces-Archimedes Principle Surface Tension ( External source ) Viscosity ( External source ) Equation

### Please remember all the unit that you use in your calculation. There are no marks for correct answer without unit.

CHAPTER 1 : PROPERTIES OF FLUIDS What is fluid? A fluid is defined as a substance that deforms continuously when acted on by a shearing stress at any magnitude. In a fluid at rest, normal stress is called

### T H E R M O D Y N A M I C S M T

T H E R M O D Y N A M I C S M T THERMODYNAMICS AND RATE PROCESSES CONTENTS CHAPTER DESCRIPTION PAGE NO 1 Thermodynamics NOTES 1.1. Definitions 1 1.2. Laws of Thermodynamics 3 1.2.1. Zeroth Law of Thermodynamics

### T H E R M O D Y N A M I C S M E

T H E R M O D Y N A M I C S M E THERMODYNAMICS CONTENTS 1 BASIC CONCEPTS IN THERMODYNAMICS 2 TEMPERATURE 3 WORK AND HEAT TRANSFER Thermodynamic system, surroundings, universe, system boundary Types of

### CE MECHANICS OF FLUIDS UNIT I

CE 6303- MECHANICS OF FLUIDS UNIT I 1. Define specific volume of a fluid and write its unit [N/D-14][M/J-11] Volume per unit mass of a fluid is called specific volume. Unit: m3 / kg. 2. Name the devices

### Chapter 3 PROPERTIES OF PURE SUBSTANCES. Thermodynamics: An Engineering Approach, 6 th Edition Yunus A. Cengel, Michael A. Boles McGraw-Hill, 2008

Chapter 3 PROPERTIES OF PURE SUBSTANCES Thermodynamics: An Engineering Approach, 6 th Edition Yunus A. Cengel, Michael A. Boles McGraw-Hill, 2008 Objectives Introduce the concept of a pure substance. Discuss

### Part II Fundamentals of Fluid Mechanics By Munson, Young, and Okiishi

Part II Fundamentals of Fluid Mechanics By Munson, Young, and Okiishi WHAT we will learn I. Characterization of Fluids - What is the fluid? (Physical properties of Fluid) II. Behavior of fluids - Fluid

### 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

### CPO Science Foundations of Physics. Unit 8, Chapter 27

CPO Science Foundations of Physics Unit 8, Chapter 27 Unit 8: Matter and Energy Chapter 27 The Physical Properties of Matter 27.1 Properties of Solids 27.2 Properties of Liquids and Fluids 27.3 Properties

### Class Notes Fall 2014

57:020 Fluid Mechanics Class Notes Fall 2014 Prepared by: Professor Fred Stern Typed by: Stephanie Schrader (Fall 1999) Corrected by: Jun Shao (Fall 2003, Fall 2005) Corrected by: Jun Shao, Tao Xing (Fall

### What s important: viscosity Poiseuille's law Stokes' law Demo: dissipation in flow through a tube

PHYS 101 Lecture 29x - Viscosity 29x - 1 Lecture 29x Viscosity (extended version) What s important: viscosity Poiseuille's law Stokes' law Demo: dissipation in flow through a tube Viscosity We introduced

### 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,

### 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

### D.A.V. PUBLIC SCHOOL, UPPAL S SOUTHEND, SECTOR 49, GURUGRAM CLASS XI (PHYSICS) Academic plan for

D.A.V. PUBLIC SCHOOL, UPPAL S SOUTHEND, SECTOR 49, GURUGRAM CLASS XI (PHYSICS) Academic plan for 2017-2018 UNIT NAME OF UNIT WEIGHTAGE 1. 2. 3. Physical World and Measurement Kinemetics Laws of Motion

### 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

### Future coaching Institute Tirupur

1 Higher secondary first year Physics volume I Laws and definitions Force: Force is the external agency applied on a body to change its state of rest and motion. Fundamental quantities Fundamental quantities

### Summary of Dimensionless Numbers of Fluid Mechanics and Heat Transfer

1. Nusselt number Summary of Dimensionless Numbers of Fluid Mechanics and Heat Transfer Average Nusselt number: convective heat transfer Nu L = conductive heat transfer = hl where L is the characteristic

### 2. For a S.H.O. determine, (a) the total energy (E), the kinetic and potential energies. of half amplitude:

The amplitude of vibration and hence, the energy transferred into the vibrating system is found to depend on the difference between f and, its maximum when the frequency of the external force is equal

### 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

### Engineering Thermodynamics. Chapter 1. Introductory Concepts and Definition

1.1 Introduction Chapter 1 Introductory Concepts and Definition Thermodynamics may be defined as follows : Thermodynamics is an axiomatic science which deals with the relations among heat, work and properties

### 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

### INTRODUCTION AND BASIC CONCEPTS. Chapter 1. Mehmet Kanoglu. Thermodynamics: An Engineering Approach, 6 th Edition. Yunus A. Cengel, Michael A.

Thermodynamics: An Engineering Approach, 6 th Edition Yunus A. Cengel, Michael A. Boles McGraw-Hill, 2008 Chapter 1 INTRODUCTION AND BASIC CONCEPTS Mehmet Kanoglu Copyright The McGraw-Hill Companies, Inc.

### Fluids and their Properties

Chapter (1) Fluids and their Properties Dr. KHALIL MAHMOUD ALASTAL Eng.Mohammed AbuRahma Eng.Reem Sbaih 2017 Newton s Law of Viscosity: - / Non-Newtonian Fluids: - Mass Density: - / Specific weight: -

### ME3250 Fluid Dynamics I

ME3250 Fluid Dynamics I Section I, Fall 2012 Instructor: Prof. Zhuyin Ren Department of Mechanical Engineering University of Connecticut Course Information Website: http://www.engr.uconn.edu/~rzr11001/me3250_f12/

### CENG 501 Examination Problem: Estimation of Viscosity with a Falling - Cylinder Viscometer

CENG 501 Examination Problem: Estimation of Viscosity with a Falling - Cylinder Viscometer You are assigned to design a fallingcylinder viscometer to measure the viscosity of Newtonian liquids. A schematic

### Chapter -5(Section-1) Friction in Solids and Liquids

Chapter -5(Section-1) Friction in Solids and Liquids Que 1: Define friction. What are its causes? Ans : Friction:- When two bodies are in contact with each other and if one body is made to move then the

### Steven Burian Civil & Environmental Engineering September 25, 2013

Fundamentals of Engineering (FE) Exam Mechanics Steven Burian Civil & Environmental Engineering September 25, 2013 s and FE Morning ( Mechanics) A. Flow measurement 7% of FE Morning B. properties Session

### 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

### Chapter 1 Introduction and Basic Concepts

Chapter 1 Introduction and Basic Concepts 1-1 Thermodynamics and Energy Application Areas of Thermodynamics 1-2 Importance of Dimensions and Units Some SI and English Units Dimensional Homogeneity Unity

### CHAPTER (2) FLUID PROPERTIES SUMMARY DR. MUNZER EBAID MECH.ENG.DEPT.

CHAPTER () SUMMARY DR. MUNZER EBAID MECH.ENG.DEPT. 08/1/010 DR.MUNZER EBAID 1 System Is defined as a given quantity of matter. Extensive Property Can be identified when it is Dependent on the total mass

### PROPERTIES OF PURE SUBSTANCES. Chapter 3. Mehmet Kanoglu. Thermodynamics: An Engineering Approach, 6 th Edition. Yunus A. Cengel, Michael A.

Thermodynamics: An Engineering Approach, 6 th Edition Yunus A. Cengel, Michael A. Boles McGraw-Hill, 2008 Chapter 3 PROPERTIES OF PURE SUBSTANCES Mehmet Kanoglu Copyright The McGraw-Hill Companies, Inc.

### Differential relations for fluid flow

Differential relations for fluid flow In this approach, we apply basic conservation laws to an infinitesimally small control volume. The differential approach provides point by point details of a flow

### Chapter 9: Solids and Fluids

Chapter 9: Solids and Fluids State of matters: Solid, Liquid, Gas and Plasma. Solids Has definite volume and shape Can be crystalline or amorphous Molecules are held in specific locations by electrical

### 1.3 Molecular Level Presentation

1.3.1 Introduction A molecule is the smallest chemical unit of a substance that is capable of stable, independent existence. Not all substances are composed of molecules. Some substances are composed of

### 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

### 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

### CHARACTERISTIC OF FLUIDS. A fluid is defined as a substance that deforms continuously when acted on by a shearing stress at any magnitude.

CHARACTERISTIC OF FLUIDS A fluid is defined as a substance that deforms continuously when acted on by a shearing stress at any magnitude. In a fluid at rest, normal stress is called pressure. 1 Dimensions,

### Boundary Conditions in Fluid Mechanics

Boundary Conditions in Fluid Mechanics R. Shankar Subramanian Department of Chemical and Biomolecular Engineering Clarkson University The governing equations for the velocity and pressure fields are partial

### 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

### Thermodynamics INTRODUCTION AND BASIC CONCEPTS. Copyright The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

Thermodynamics INTRODUCTION AND BASIC CONCEPTS Copyright The McGraw-Hill Companies, Inc. Permission required for reproduction or display. THERMODYNAMICS AND ENERGY Thermodynamics: The science of energy.

### Chapter 1 INTRODUCTION AND BASIC CONCEPTS

Thermodynamics: An Engineering Approach Seventh Edition in SI Units Yunus A. Cengel, Michael A. Boles McGraw-Hill, 2011 Chapter 1 INTRODUCTION AND BASIC CONCEPTS Mehmet Kanoglu University of Gaziantep

### ACE Engineering College

ACE Engineering College Ankushapur (V), Ghatkesar (M), R.R.Dist 501 301. * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * MECHANICS OF FLUIDS & HYDRAULIC

### CHAPTER 10. States of Matter

CHAPTER 10 States of Matter Kinetic Molecular Theory Kinetikos - Moving Based on the idea that particles of matter are always in motion The motion has consequences Explains the behavior of Gases, Liquids,

### CHAPTER 10. Kinetic Molecular Theory. Five Assumptions of the KMT. Atmospheric Pressure

Kinetic Molecular Theory CHAPTER 10 States of Matter Kinetikos - Moving Based on the idea that particles of matter are always in motion The motion has consequences Explains the behavior of Gases, Liquids,

### Although different gasses may differ widely in their chemical properties, they share many physical properties

IV. Gases (text Chapter 9) A. Overview of Chapter 9 B. Properties of gases 1. Ideal gas law 2. Dalton s law of partial pressures, etc. C. Kinetic Theory 1. Particulate model of gases. 2. Temperature and

### ME 2322 Thermodynamics I PRE-LECTURE Lesson 10 Complete the items below Name:

Lesson 10 1. (5 pt) If P > P sat (T), the phase is a subcooled liquid. 2. (5 pt) if P < P sat (T), the phase is superheated vapor. 3. (5 pt) if T > T sat (P), the phase is superheated vapor. 4. (5 pt)

### Fundamentals of Fluid Dynamics: Elementary Viscous Flow

Fundamentals of Fluid Dynamics: Elementary Viscous Flow Introductory Course on Multiphysics Modelling TOMASZ G. ZIELIŃSKI bluebox.ippt.pan.pl/ tzielins/ Institute of Fundamental Technological Research

### 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