Stream Tube. When density do not depend explicitly on time then from continuity equation, we have V 2 V 1. δa 2. δa 1 PH6L24 1


 Myles Glenn
 3 years ago
 Views:
Transcription
1 Stream Tube A region of the moving fluid bounded on the all sides by streamlines is called a tube of flow or stream tube. As streamline does not intersect each other, no fluid enters or leaves across the sides. V V 1 δa 1 δa When density do not depend explicitly on time then from continuity equation, we have ( vρ) = 0 PH6L4 1
2 = V s ( vρ) 0 ( vρ ). ds= 0 Where V is the volume of the streamtube between faces δa 1 and δa From divergence theorem v ρ and vρ are the mean values of ρvover δa and δa 1 vρ δa= vρ δa For a homogeneous, incompressible, Nonviscous fluids v δa= v δa 1 1 Thus, whenever stream tube is constricted, i.e., wherever streamlines gets crowded, the speed of flow of liquid is larger PH6L4
3 For the entire collection of the stream tubes occupying the whole cross section of the passage through which the fluid flows ρvds A is constant along the passage In the case of constant density vds is constant or v A= v A 1 1 A PH6L4 3
4 Bernoulli s Principle and Physical Significance of different terms In the steady flow of homogeneous, incompressible nonviscous fluid, P 1 v gz Constant where gravitional potential ρ + + = Ω =gz Along a very narrow stream tube In the case of the gases last term is negligible w.r.t. first two terms as the Density is very low for the gases Third term is gravitational potential energy of the unit mass Second term is kinetic energy of the unit mass First term also has units of energy per unit mass What energy this term represents? PH6L4 4
5 δl 1 δl P 1 P A B 1 1 A B Consider the volume of fluid element between A1 and A which is moved after some time to volume between B1 and B δlδa = δl δa = δv 1 1 Work done during the motion by the pressure forces is given by δlpδa δlpδa = ( P P) δv Work done during the motion by the pressure forces in moving the volume element from A1B1 to AB per unit mass is given by P ( P1 P) δv P1 P dp = = ρδv ρ ρ PH6L4 5 P1
6 P 0 P1 dp dp P = = ρ ρ ρ P Therefore, P/ρ term represents the work that will be done on the unit mass of the fluid by the pressure forces, as the element flows from a point where pressure is P to a point where pressure is zero. At two different point in the stream tube P 1 P 1 + v + gz = + v + gz ρ ρ P P ρ gz ( 1 z) = v v1 In the steady flow of an incompressible, homogeneous, nonviscous fluid, moving from position 1 to, the increase in kinetic energy per unit mass is equal to the work done on unit mass of the fluid by pressure and gravity forces. PH6L4 6
7 The three terms is therefore called as pressure energy, kinetic energy and gravitational energy P v,, z are known as pressure head, velocity head ρg g and gravity head and each having the dimention of length PH6L4 7
8 Application 1: Velocity of efflux from a reservoir P 1 Flow from a sharp edged orifice in a tank P Vena Contracta Following assumptions are made in order to simplify the problem steady state flow of Incompressible, homogeneous, nonviscous fluid (frictional effects can be neglected) Cross sectional area of the reservoir is very large compared to that of orifice. Hence the velocity of the fluid at the surface is negligibly small. Practically hydrostatic equilibrium condition exist for points at the surface. PH6L4 8
9 From the Bernoulli s principle, we can write P P atm v1 = 0 1 atm 1 P 1 P 1 + v + z = + v + z ρg g ρg g z = 0 when centre of the orifice is chosen as the horizontal plane for the gravitaional head P P = ρg( h z ) from the hydrostatic condition Putting these all values v = gh PH6L4 9
10 Identical relation for velocity of efflux is obtained for a discharge from one reservoir to another reservoir where h now stand for difference between the gravitational head across the orifice The rate of discharge Q, i.e., the volume of the fluid flowing out of the reservoir per unit time is given by Q Av A gh actual = αα c v = αd Q= Av = A gh Actual Velocity where αv = ; αc = Cofficient of contraction Ideal Velocity and αα = α is called coefficient of discharge c v d PH6L4 10
11 Application : Flow meters From the Bernoulli s principle for the streamline OA 1 1 P0 + ρv0 + ρgz0 = PA + ρva + ρgza For steady state, and OA taken as horizontal and velocity at A is zero from the definition of stagnation point 1 1 PA = P0 + ρv0 or PA P0 = ρv0 Thus pressure at the stagnation point exceed the pressure at any other point on the streamline OA exceeds by 1 ρv Dynamic pressure PH6L4 11
12 Vortex Line In the steady flow of homogeneous, incompressible, nonviscous fluid the Eulers equation is given by v 1 1 v ( v) = p v +Ω t ρ Instead of taking a dot product with velocity vector as we have taken earlier, we take dot product with vorticity vector χ χ φ ρ P 1. v Ω = = Therefore, the potential φ is constant along the vortex line PH6L4 1
13 P v + ρ + Ω = C May be satisfied by more than one stream line and more than one vortex line Circular flow with straight streamline?? Nonzero curl or circulation does not necessary mean that the streamlines are circular or curved Ex. v v = v ( y) ˆ x e x dvx ( y) = eˆ dy z 0 Flow is rotational even though the stream lines are parallel straight lines PH6L4 13
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 informationMass 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 information5 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 informationFLUID 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 informationCEE 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 1D 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 informationChapter 4 DYNAMICS OF FLUID FLOW
Faculty Of Engineering at Shobra nd Year Civil  016 Chapter 4 DYNAMICS OF FLUID FLOW 41 Types of Energy 4 Euler s Equation 43 Bernoulli s Equation 44 Total Energy Line (TEL) and Hydraulic Grade Line
More informationThe Bernoulli Equation
The Bernoulli Equation The most used and the most abused equation in fluid mechanics. Newton s Second Law: F = ma In general, most real flows are 3D, unsteady (x, y, z, t; r,θ, z, t; etc) Let consider
More informationCEE 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 information3.25 Pressure form of Bernoulli Equation
CEE 3310 Control Volume Analysis, Oct 3, 2012 83 3.24 Review The Energy Equation Q Ẇshaft = d dt CV ) (û + v2 2 + gz ρ d + (û + v2 CS 2 + gz + ) ρ( v n) da ρ where Q is the heat energy transfer rate, Ẇ
More informationEGN 3353C Fluid Mechanics
Lecture 8 Bernoulli s Equation: Limitations and Applications Last time, we derived the steady form of Bernoulli s Equation along a streamline p + ρv + ρgz = P t static hydrostatic total pressure q = dynamic
More informationIn 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 informationChapter 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 informationIf a stream of uniform velocity flows into a blunt body, the stream lines take a pattern similar to this: Streamlines around a blunt body
Venturimeter & Orificemeter ELEMENTARY HYDRAULICS National Certificate in Technology (Civil Engineering) Chapter 5 Applications of the Bernoulli Equation The Bernoulli equation can be applied to a great
More information3.8 The First Law of Thermodynamics and the Energy Equation
CEE 3310 Control Volume Analysis, Sep 30, 2011 65 Review Conservation of angular momentum 1D 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 informationPart 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 informationRate 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 informationLesson 37 Transmission Of Air In Air Conditioning Ducts
Lesson 37 Transmission Of Air In Air Conditioning Ducts Version 1 ME, IIT Kharagpur 1 The specific objectives of this chapter are to: 1. Describe an Air Handling Unit (AHU) and its functions (Section 37.1).
More informationLecture23. Flowmeter Design.
Lecture23 Flowmeter Design. Contents of lecture Design of flowmeter Principles of flow measurement; i) Venturi and ii) Orifice meter and nozzle Relationship between flow rate and pressure drop Relation
More informationChapter 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
More informationFluids. Fluids in Motion or Fluid Dynamics
Fluids Fluids in Motion or Fluid Dynamics Resources: Serway  Chapter 9: 9.79.8 Physics B Lesson 3: Fluid Flow Continuity Physics B Lesson 4: Bernoulli's Equation MIT  8: Hydrostatics, Archimedes' Principle,
More informationObjectives. 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 informationLesson 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 informationChapter 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
More informationPressure in stationary and moving fluid Lab Lab On On Chip: Lecture 2
Pressure in stationary and moving fluid LabOnChip: Lecture Lecture plan what is pressure e and how it s distributed in static fluid water pressure in engineering problems buoyancy y and archimedes law;
More informationCHAPTER 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 information10.52 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 informationFluid 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 informationUseful concepts associated with the Bernoulli equation. Dynamic
Useful concets associated with the Bernoulli equation  Static, Stagnation, and Dynamic Pressures Bernoulli eq. along a streamline + ρ v + γ z = constant (Unit of Pressure Static (Thermodynamic Dynamic
More informationm 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 11 Fluids 11.1 Mass Density DEFINITION OF MASS DENSITY The mass density of a substance is the mass of a substance divided by its volume: ρ m V SI Unit of Mass Density: kg/m 3 11.1 Mass Density
More informationBasic 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 informationFor 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 informationV (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 informationPressure in stationary and moving fluid. LabOnChip: Lecture 2
Pressure in stationary and moving fluid LabOnChip: Lecture Fluid Statics No shearing stress.no relative movement between adjacent fluid particles, i.e. static or moving as a single block Pressure at
More informationExperiment No.4: Flow through Venturi meter. Background and Theory
Experiment No.4: Flow through Venturi meter Background and Theory Introduction Flow meters are used in the industry to measure the volumetric flow rate of fluids. Differential pressure type flow meters
More informationFLUID 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 4. ELEMENTARY FLUID DYNAMICS THE BERNOULLI EQUATION
More informationPhysics 3 Summer 1990 Lab 7  Hydrodynamics
Physics 3 Summer 1990 Lab 7  Hydrodynamics Theory Consider an ideal liquid, one which is incompressible and which has no internal friction, flowing through pipe of varying cross section as shown in figure
More informationThe Design of Gating System 3. Theoretical considerations in gating design
MME 345 Lecture 16 The Design of Gating System 3. Theoretical considerations in gating design Ref: [1] ASM Metal Handbook, Vol. 15: Casting, ASM International [] Taylor, Flemings, and Wulff. Foundry engineering,
More informationChapter 5: Mass, Bernoulli, and Energy Equations
Chapter 5: Mass, Bernoulli, and Energy Equations Introduction This chapter deals with 3 equations commonly used in fluid mechanics The mass equation is an expression of the conservation of mass principle.
More informationOffshore Hydromechanics
Offshore Hydromechanics Module 1 : Hydrostatics Constant Flows Surface Waves OE4620 Offshore Hydromechanics Ir. W.E. de Vries Offshore Engineering Today First hour: Schedule for remainder of hydromechanics
More informationChapter Four fluid flow mass, energy, Bernoulli and momentum
41Conservation of Mass Principle Consider a control volume of arbitrary shape, as shown in Fig (41). Figure (41): the differential control volume and differential control volume (Total mass entering
More information5.1 Fluid momentum equation Hydrostatics Archimedes theorem The vorticity equation... 42
Chapter 5 Euler s equation Contents 5.1 Fluid momentum equation........................ 39 5. Hydrostatics................................ 40 5.3 Archimedes theorem........................... 41 5.4 The
More informationChapter 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 informationExperiment (4): Flow measurement
Experiment (4): Flow measurement Introduction: The flow measuring apparatus is used to familiarize the students with typical methods of flow measurement of an incompressible fluid and, at the same time
More informationChapter 11  Fluids in Motion. Sections 79
Chapter  Fluids in Motion Sections 79 Fluid Motion The lower falls at Yellowstone National Park: the water at the top of the falls passes through a narrow slot, causing the velocity to increase at that
More informationFluid Dynamics Problems M.Sc MathematicsSecond Semester Dr. Dinesh KhattarK.M.College
Fluid Dynamics Problems M.Sc MathematicsSecond Semester Dr. Dinesh KhattarK.M.College 1. (Example, p.74, Chorlton) At the point in an incompressible fluid having spherical polar coordinates,,, the velocity
More informationLecture 30 (Walker: ) Fluid Dynamics April 15, 2009
Physics 111 Lecture 30 (Walker: 15.67) 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 11.89) Chap. 13 (not 13.68)
More information!! +! 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 informationLecture 27 (Walker: ) Fluid Dynamics Nov. 9, 2009
Physics 111 Lecture 27 (Walker: 15.57) Fluid Dynamics Nov. 9, 2009 Midterm #2  Monday Nov. 16 Chap. 7,Chap. 8 (not 8.5) Chap. 9 (not 9.6, 9.8) Chap. 10, Chap. 11 (not 11.89) Chap. 13 (not 13.68) Chap.
More information6.1 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 informationNew Website: Mr. Peterson s Address:
Brad Peterson, P.E. New Website: http://njut2009fall.weebly.com Mr. Peterson s Email Address: bradpeterson@engineer.com Lesson 1, Properties of Fluids, 2009 Sept 04, Rev Sept 18 Lesson 2, Fluid Statics,
More informationFLOW MEASUREMENT IN PIPES EXPERIMENT
University of Leicester Engineering Department FLOW MEASUREMENT IN PIPES EXPERIMENT Page 1 FORMAL LABORATORY REPORT Name of the experiment: FLOW MEASUREMENT IN PIPES Author: Apollin nana chaazou Partner
More informationLECTURE 4 FLUID FLOW & SURFACE TENSION. Lecture Instructor: Kazumi Tolich
LECTURE 4 FLUID FLOW & SURFACE TENSION Lecture Instructor: Kazumi Tolich Lecture 4 2 Reading chapter 15.6 to 15.9 Continuity equation Bernoulli s equation n Torricelli s law Viscosity Surface tension Equation
More informationQ1 Give answers to all of the following questions (5 marks each):
FLUID MECHANICS First Year Exam Solutions 03 Q Give answers to all of the following questions (5 marks each): (a) A cylinder of m in diameter is made with material of relative density 0.5. It is moored
More informationFluid Statics. Pressure. Pressure
Pressure Fluid Statics Variation of Pressure with Position in a Fluid Measurement of Pressure Hydrostatic Thrusts on Submerged Surfaces Plane Surfaces Curved Surfaces ddendum First and Second Moment of
More informationPressure 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 oddball states of matter We
More informationStudy 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 informationBERNOULLI EQUATION. The motion of a fluid is usually extremely complex.
Chapter 5 Fluid in Motion The Bernoulli Equation 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
More informationequation 4.1 INTRODUCTION
4 The momentum equation 4.1 INTRODUCTION It is often important to determine the force produced on a solid body by fluid flowing steadily over or through it. For example, there is the force exerted on a
More informationSYSTEMS VS. CONTROL VOLUMES. Control volume CV (open system): Arbitrary geometric space, surrounded by control surfaces (CS)
SYSTEMS VS. CONTROL VOLUMES System (closed system): Predefined mass m, surrounded by a system boundary Control volume CV (open system): Arbitrary geometric space, surrounded by control surfaces (CS) Many
More informationWhere does Bernoulli's Equation come from?
Where does Bernoulli's Equation come from? Introduction By now, you have seen the following equation many times, using it to solve simple fluid problems. P ρ + v + gz = constant (along a streamline) This
More information2.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 informationFluids, Continuity, and Bernouli
Fluids, Continuity, and Bernouli Announcements: Exam Tomorrow at 7:30pm in same rooms as before. Web page: http://www.colorado.edu/physics/phys1110/phys1110_sp12/ Clicker question 1 A satellite, mass m,
More informationChapter (6) Energy Equation and Its Applications
Chapter (6) Energy Equation and Its Applications Bernoulli Equation Bernoulli equation is one of the most useful equations in fluid mechanics and hydraulics. And it s a statement of the principle of conservation
More informationUnit C1: List of Subjects
Unit C: List of Subjects The elocity Field The Acceleration Field The Material or Substantial Derivative Steady Flow and Streamlines Fluid Particle in a Flow Field F=ma along a Streamline Bernoulli s
More informationExperiment 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 informationf= flow rate (m 3 /s) A = crosssectional area of the pipe (m 2 ) v= flow speed (m/s)
Fluid Mechanics Flow Rate and Continuity Equation If you have a pipe that is flowing a liquid you will have a flow rate. The flow rate is the volume of fluid that passes any particular point per unit of
More informationFor more info
Characteristic of Ideal fluid: (a) It is incompressible (b) It is nonviscous (c) Flow of ideal fluid is irrational (d) It is capable of exhibiting steady flow Stream line flow: Flow of a liquid fluid
More informationvector 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 informationOffshore Hydromechanics Module 1
Offshore Hydromechanics Module 1 Dr. ir. Pepijn de Jong 4. Potential Flows part 2 Introduction Topics of Module 1 Problems of interest Chapter 1 Hydrostatics Chapter 2 Floating stability Chapter 2 Constant
More informationV/ 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 nonuniform flow Laminar and Turbulent flow Compressible and incompressible flow Rotational and irrotational
More informationChapter 15B  Fluids in Motion. A PowerPoint Presentation by Paul E. Tippens, Professor of Physics Southern Polytechnic State University
Chapter 15B  Fluids in Motion A PowerPoint Presentation by Paul E. Tippens, Professor of Physics Southern Polytechnic State University 007 Paul E. Tippens Fluid Motion The lower falls at Yellowstone National
More informationFluid Dynamics. Type of Flows Continuity Equation Bernoulli Equation Steady Flow Energy Equation Applications of Bernoulli Equation
Tye of Flows Continity Eqation Bernolli Eqation Steady Flow Energy Eqation Alications of Bernolli Eqation Flid Dynamics Streamlines Lines having the direction of the flid velocity Flids cannot cross a
More informationMECHANICAL 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 informationChapter 11. Fluids. continued
Chapter 11 Fluids continued 11.2 Pressure Pressure is the amount of force acting on an area: Example 2 The Force on a Swimmer P = F A SI unit: N/m 2 (1 Pa = 1 N/m 2 ) Suppose the pressure acting on the
More informationLecture 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 information2.25 Advanced Fluid Mechanics
MIT Department of Mechanical Engineering.5 Advanced Fluid Mechanics Problem 4.05 This problem is from Advanced Fluid Mechanics Problems by A.H. Shapiro and A.A. Sonin Consider the frictionless, steady
More informationChapter 6 Equations of Continuity and Motion
Chapter 6 Equations of Continuity and Motion Derivation of 3D Eq. conservation of mass Continuity Eq. conservation of momentum Eq. of motion NavierStrokes Eq. 6.1 Continuity Equation Consider differential
More informationMECHANICAL PROPERTIES OF FLUIDS
CHAPTER10 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 informationChapter 15: Fluid Mechanics Dynamics Using Pascal s Law = F 1 = F 2 2 = F 2 A 2
Lecture 24: Archimedes Principle and Bernoulli s Law 1 Chapter 15: Fluid Mechanics Dynamics Using Pascal s Law Example 15.1 The hydraulic lift A hydraulic lift consists of a small diameter piston of radius
More informationMASS, MOMENTUM, AND ENERGY EQUATIONS
MASS, MOMENTUM, AND ENERGY EQUATIONS This chapter deals with four equations commonly used in fluid mechanics: the mass, Bernoulli, Momentum and energy equations. The mass equation is an expression of the
More information11.1 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 informationAerodynamics. 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 information2.25 Advanced Fluid Mechanics
MIT Department of Mechanical Engineering 2.25 Advanced Fluid Mechanics Problem 10.3 This problem is from Advanced Fluid Mechanics Problems by A.H. Shapiro and A.A. Sonin Consider the three different, steady,
More informationBACHELOR OF TECHNOLOGY IN MECHANICAL ENGINEERING (COMPUTER INTEGRATED MANUFACTURING)
No. of Printed Pages : 6 BME028 BACHELOR OF TECHNOLOGY IN MECHANICAL ENGINEERING (COMPUTER INTEGRATED MANUFACTURING) TermEnd Examination December, 2011 00792 BME028 : FLUID MECHANICS Time : 3 hours
More informationVENTURIMETER EXPERIMENT
ENTURIMETER EXERIMENT. OBJECTİE The main objectives of this experiment is to obtain the coefficient of discharge from experimental data by utilizing venturi meter and, also the relationship between Reynolds
More informationPhysics 201 Chapter 13 Lecture 1
Physics 201 Chapter 13 Lecture 1 Fluid Statics Pascal s Principle Archimedes Principle (Buoyancy) Fluid Dynamics Continuity Equation Bernoulli Equation 11/30/2009 Physics 201, UWMadison 1 Fluids Density
More informationNPTEL Course Developer for Fluid Mechanics DYMAMICS OF FLUID FLOW
Module 04; Lecture DYMAMICS OF FLUID FLOW Energy Equation (Conservation of Energy) In words, the conservation of energy can be stated as, Time rate of increase in stored energy of the system = Net time
More informationExam #2: Fluid Kinematics and Conservation Laws April 13, 2016, 7:00 p.m. 8:40 p.m. in CE 118
CVEN 311501 (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 informationAER210 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 Nonprogrammable calculators allowed Instructor: Alis Ekmekci Family Name: Given Name:
More informationFundamentals 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 informationME 305 Fluid Mechanics I. Part 8 Viscous Flow in Pipes and Ducts. Flow in Pipes and Ducts. Flow in Pipes and Ducts (cont d)
ME 305 Fluid Mechanics I Flow in Pipes and Ducts Flow in closed conduits (circular pipes and noncircular ducts) are very common. Part 8 Viscous Flow in Pipes and Ducts These presentations are prepared
More informationLecture 8 Equilibrium and Elasticity
Lecture 8 Equilibrium and Elasticity July 19 EQUILIBRIUM AND ELASTICITY CHAPTER 12 Give a sharp blow one end of a stick on the table. Find center of percussion. Baseball bat center of percussion Equilibrium
More information3.5 Vorticity Equation
.0  Marine Hydrodynamics, Spring 005 Lecture 9.0  Marine Hydrodynamics Lecture 9 Lecture 9 is structured as follows: In paragraph 3.5 we return to the full NavierStokes equations (unsteady, viscous
More informationCH.1 Overview of Fluid Mechanics/22 MARKS. 1.1 Fluid Fundamentals.
Content : 1.1 Fluid Fundamentals. 08 Marks Classification of Fluid, Properties of fluids like Specific Weight, Specific gravity, Surface tension, Capillarity, Viscosity. Specification of hydraulic oil
More informationChapter 4: Non uniform flow in open channels
Chapter 4: Non uniform flow in open channels Learning outcomes By the end of this lesson, students should be able to: Relate the concept of specific energy and momentum equations in the effect of change
More informationMAE 101A. Homework 7  Solutions 3/12/2018
MAE 101A Homework 7  Solutions 3/12/2018 Munson 6.31: The stream function for a twodimensional, nonviscous, incompressible flow field is given by the expression ψ = 2(x y) where the stream function has
More information주요명칭 수직날개. Vertical Wing. Flap. Rudder. Elevator 수평날개
High Lift Devices 주요명칭 동체 Flap 수직날개 Vertical Wing Rudder Elevator 수평날개 방향전환 () Rolling Yawing Pitching 방향전환 () Rolling Yawing Pitching Potential Flow of Helicopter PNU ME CFD LAB. =0 o =60 o =90 o =0 o
More informationFluid 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 informationDETERMINATION OF DISCHARGE AND HEAD LOSS USING A FLOWMEASURING APPARATUS
DETERMINATION OF DISCHARGE AND HEAD LOSS USING A FLOWMEASURING APPARATUS 1. INTRODUCTION Through use of the FlowMeasuring Apparatus, this experiment is designed to accustom students to typical methods
More informationcos(θ)sin(θ) Alternative Exercise Correct Correct θ = 0 skiladæmi 10 Part A Part B Part C Due: 11:59pm on Wednesday, November 11, 2015
skiladæmi 10 Due: 11:59pm on Wednesday, November 11, 015 You will receive no credit for items you complete after the assignment is due Grading Policy Alternative Exercise 1115 A bar with cross sectional
More information