FLUID MECHANICS. Chapter 3 Elementary Fluid Dynamics  The Bernoulli Equation


 Sheryl Jennings
 1 years ago
 Views:
Transcription
1 FLUID MECHANICS Chapter 3 Elementary Fluid Dynamics  The Bernoulli Equation
2 CHAP 3. ELEMENTARY FLUID DYNAMICS  THE BERNOULLI EQUATION CONTENTS 3. Newton s Second Law 3. F = ma along a Streamline 3.3 F = ma Normal to a Streamline 3.4 Physical Interpretation 3.5 Static, Stagnation, Dynamic, and Total Pressure 3.6 Examples of Use of the Bernoulli Equation 3.7 The Energy Line and the Hydraulic Grade Line 3.8 Restrictions on Use of the Bernoulli Equation
3 3. Newton s Second Law Newton s Second Law F d ( m v) dt Fma Streamline The lines that are tangent to the velocity vector throughout the flow field a dv dt V (3.) as V, a V n s R where, R : Local radius of curvature of the streamline (a) Flow in the x z plane. (b) Flow in terms of streamline and normal coordinates.
4 3. Newton s Second Law Isolation of a small fluid particle in a flow field. (Photo courtesy of Diana Sailplanes.) For force, Important force: gravity, pressure Negligible force: viscous force, surface tension effects
5 3. F = ma along a Streamline Sum of s components of forces acting on the particle (3.) Gravity force (Weight) F V V s mas mv V V s s Ws V W W sin V sin s Pressure force p p s s s F ( p p ) n y ( p p ) n y ps s s ps n y p s n y s p V s Freebody diagram of a fluid particle for which the important forces are those due to pressure and gravity.
6 3. F = ma along a Streamline Net force in the streamline dir. p (3.3) Fs Ws Fps sin V s (3.4) Along the streamline, sin dz / ds dz dp d( V ) V d( V ) V ds ds ds s ds (3.5) dp d( V ) dz 0 (along a streamline) integrated to dp (3.6) V gz C (along a streamline) For steady, inviscid, incompressible flow p sin V V a s s const. s (3.7) p V z const. along the streamline Bernoulli Equation
7 Example 3. GIVEN Inviscid, incompressible, steady flow along the horizontal streamline A B Radius of the sphere: a 3 Fluid velocity along this streamline: 0 a V V x3 FIND Determine the pressure variation along the streamline from point A to point B on the sphere x and V V A A x a and V 0 B B 0 SOL) () () (Ans) p V V s s V V a 3Va V V V s x x x 3V x3 x p 3 a V0 ( a x ) x x4 p V a x 3 a a ( a/ x) 6
8 3.3 F = ma Normal to a Streamline Sum of normal components of forces acting on the particle (3.8) mv R Fn Gravity force (Weight) V V R W W cos V cos n Pressure force F ( p p ) s y ( p p ) s y p s y pn n n n p p s n y V n n Net force in the streamline dir. p (3.9) Fn Wn Fpn cos V n dz p V (3.0a) dn n R p V (3.0b) n R Freebody diagram of a fluid particle for which the important forces are those due to pressure and gravity.
9 3.3 F = ma Normal to a Streamline Across the streamline p dp If s const., n dn integrate across the streamline dp V (3.) dn gz const. (across the streamline) R For steady, inviscid, incompressible flow const. (3.) p V dnz const. (across the streamline) R Final form of Newton s law (Bernoulli Equation)
10 Example 3.3 GIVEN Shown in Figure E3.3 are two flow fields with circular streamlines Velocity distributions are V ( r) ( V0/ r0) r for case (a) where V0:velocity at r r0 V ( r) ( V r ) / r for case (b) FIND Determine the pressure distributions, p = p(r), for each, given that p = p 0 at r = r 0. SOL) 00 p V r r p (a) ( / ) r ( Vr p 00) (b) r r3 V 0 r0 r Integrate these equations with repect to r (Ans) p p ( V / )[( r / r ) ] for case (a) (Ans) p p ( V / )[ ( r / r) ] for case (b) (a) Rigid body rotation (b) Free vortex (Bathtube vortex)
11 3.4 Physical Interpretation Basic assumption (3.3) (3.4) p V z ) steady ) inviscid 3) incompressible const. along the streamline p V dnz const. across the streamline R Workenergy principle The work done on a particle by all forces acting on the particle is equal to the change of the kinetic energy of the particle. Bernoulli Equation p V z Pressure Head g Kinetic Elevation Energy Head (Velocity Head) const. on a streamline Work done by pressure & gravitational force
12 z 3.5 Static, Stagnation, Dynamic, and Total Pressure From the Bernoulli equation, p V z const. Static pressure Dynamic pressure ; Hydrostatic pressure ; ; Actual thermodynamic pressure ; Move along with the fluid Static relative to the moving fluid ; p h p p 3 3 h 3 43 V Measurement of static and stagnation pressures. Total pressure = Static pressure + Dynamic pressure + Hydrostatic pressure = const. Stagnation point ; V 0 For z z, p p V If elevation effect are neglected, the stagnation pressure( p V /) is the largest pressure along the streamline. All of the kinetic energy converse into a pressure rise.
13 3.6 Examples of Use of the Bernoulli Equation Free jets Bernoulli equation between () and () (3.7) p V z p V z p p, p p p a 4 V 0, V V z h, z 0 h V (3.8) V h gh a Vertical flow from a tank. Bernoulli equation between () and (5) Bernoulli equation between (3) and (4) p V z p V z p V z p V z p p p, V 0, z h H, z 0 p p, V 0, z l, z 0 5 a 5 ( h H) V V g( h H) a p l v ( hl) 3
14 3.6 Examples of Use of the Bernoulli Equation For horizontal nozzle, V V V 3 In general, d h we can use Average velocity Vena contracta effect If the exit is NOT a smooth, wellcontoured nozzle, dj dh d j : areas of the jet where, d : area of the hole h Contraction coefficient Cc Aj Ah where, Aj : areas of the jet at the vena contracta A : area of the hole h Horizontal flow from a tank. Vena contracta effect for a sharpedged orifice.
15 3.6 Examples of Use of the Bernoulli Equation Confined flows Nozzles Pipes of variable diameter Conservation of mass AV A V If density const., Continuity equation (3.9) A V A V or Q Q (a) Flow through a syringe. (b) Steady flow into and out of a volume.
16 Example 3.7 GIVEN A stream of refreshing beverage of diameter d = 0.0 m flows steadily from the cooler of diameter D = 0.0 m as shown in Figs. E3.7 FIND Determine the flowrate, Q, from the bottle into the cooler if the depth of beverage in the cooler is to remain constant at h = 0.0 m SOL) () p V z p V z p p 0 z h, z 0 () V gh V Q Q, where Q AV A V D d V V 4 4 (3) V d V D V gh (9.8)(0.0).98 m/s 4 4 ( d/ D) (0.0/ 0.0) Q AV A V (0.0) (.98) 4 (Ans) Q m /s
17 Example 3.9 GIVEN Water flows through a pipe reducer as is shown in Fig. E3.9. The static pressures at () and () are measured by the inverted Utube manometer containing oil of specific gravity, SG, less than one. FIND Determine the manometer reading, h. SOL) p V z p V z Q AV A V () p p ( z z ) V [ ( A / A ) ] p p ( z z ) ( SG) h ( SG) h V [ ( A / A ) ] V [ ( A / A ) ] h ( SG) Q AV (Ans) ( Q / A ) [ ( A / A h ) ] g( SG)
18 3.6 Examples of Use of the Bernoulli Equation Flowrate measurement To measure fluid velocities and flowrates using Bernoulli equation. Orifice meter Nozzle meter Venturi meter If flow is horizontal ( z z ) p V p V If the velocity profiles are uniform at () and (), Continuity equation is Q A V A V Therefore, (3.0) Q A ( p p ) A A [ ( ) ] Typical devices for measuring flowrate in pipes
19 3.6 Examples of Use of the Bernoulli Equation. Open channel Sluice gates Bernoulli equation p V z p V z If the gate is the same width ( A bz and A bz ) Continuity equation If Q AV bvz AV bvz (3.) Q z b g( z z ) ( z z) z z, Q z b gz Vena contracta effect Contraction coefficient Cc z a Weir Q C Hb gh C b gh 3/ Sluice gate geometry. (Photograph courtesy of Plasti Fab, Inc.) Rectangular, sharpcrested weir geometry.
20 3.7 The Energy Line and the Hydraulic Grade Line For steady, inviscid, incompressible flow, the Bernoulli equation (3.) p V g p z p V z constant on a streamline H g z ; Energy Line (EL) ; Hydraulic Grade Line (HGL) Representation of the energy line and the hydraulic grade line.
21 3.8 Restrictions on Use of the Bernoulli Equation Compressibility effects For a simple case of compressible flow with the temperature of a perfect gas, p RT, where T const. For steady, inviscid, isothermal flow, dp RT V gz constant p V RT p V (3.3) z ln z g g p g p p p where, p p ln( ) for small RT V z z V g g g For steady, isentropic flow, k p/ C where, k : specific heat ratio / k / k C p dp V gz constant / k p / k / k k ( k )/ k ( k )/ k C p dp C [ p p ] p k (3.4) k p k k p V k p V gz gz k k p
22 3.8 Restrictions on Use of the Bernoulli Equation For stagnation point flow, ) Compressible flow If z z, V 0, Ma V / c, c krt (3.5) k/( k) p p k Ma (compressible) p ) Incompressible flow Bernoulli equation V p p p p V V ( p RT) p p RT (3.6) Ma p p k p (incompressible)
23 3.8 Restrictions on Use of the Bernoulli Equation Unsteady effects Bernoulli equation including the unsteady effect ( V/ t 0) V ds dp d ( V ) dz 0 (along a streamline) t For incompressible flow, s V (3.7) p V z ds p s V z t (along a streamline) Other effects Rotational effects Viscous effects Pump or turbine
24 Example 3.6 GIVEN An incompressible, inviscid liquid is placed in a vertical, constant diameter Utube as indicated in Fig. E3.6. When released from the nonequilibrium position shown, the liquid column will oscillate at a specific frequency. FIND Determine this frequency. SOL) p p 0 z z, z z where, z z( t) V V V V ds dv ds l dv where, l: length of liquid column t dt dt s s s s ( z) l dv z dt d z g z 0 V dz, g dt l dt solution : g (Ans) l z( t) C sin( g / lt) C cos( g / lt) Period of this oscillation: t l / g 0
The 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 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 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 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 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 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 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 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 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 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 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 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 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 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 information3.25 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 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 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 informationStream 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
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
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 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 informationFundamentals 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 informationNPTEL 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 informationME3560 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 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 informationME3560 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 informationHOMEWORK ASSIGNMENT ON BERNOULLI S EQUATION
AMEE 0 Introduction to Fluid Mechanics Instructor: Marios M. Fyrillas Email: m.fyrillas@frederick.ac.cy HOMEWORK ASSIGNMENT ON BERNOULLI S EQUATION. Conventional sprayguns operate by achieving a low pressure
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 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 informationFE 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 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 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 information2 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 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 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 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 informationTOPICS. Density. Pressure. Variation of Pressure with Depth. Pressure Measurements. Buoyant ForcesArchimedes Principle
Lecture 6 Fluids TOPICS Density Pressure Variation of Pressure with Depth Pressure Measurements Buoyant ForcesArchimedes Principle Surface Tension ( External source ) Viscosity ( External source ) Equation
More informationEXPERIMENT No.1 FLOW MEASUREMENT BY ORIFICEMETER
EXPERIMENT No.1 FLOW MEASUREMENT BY ORIFICEMETER 1.1 AIM: To determine the coefficient of discharge of the orifice meter 1.2 EQUIPMENTS REQUIRED: Orifice meter test rig, Stopwatch 1.3 PREPARATION 1.3.1
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 informationENGINEERING 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 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 informationDetailed 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 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 (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 informationApproximate physical properties of selected fluids All properties are given at pressure kn/m 2 and temperature 15 C.
Appendix FLUID MECHANICS Approximate physical properties of selected fluids All properties are given at pressure 101. kn/m and temperature 15 C. Liquids Density (kg/m ) Dynamic viscosity (N s/m ) Surface
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 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 informationMeasurements using Bernoulli s equation
An Internet Book on Fluid Dynamics Measurements using Bernoulli s equation Many fluid measurement devices and techniques are based on Bernoulli s equation and we list them here with analysis and discussion.
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 informationCLASS 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 informationBERNOULLI 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 informationChapter 7 The Energy Equation
Chapter 7 The Energy Equation 7.1 Energy, Work, and Power When matter has energy, the matter can be used to do work. A fluid can have several forms of energy. For example a fluid jet has kinetic energy,
More informationUNIT I FLUID PROPERTIES AND STATICS
SIDDHARTH GROUP OF INSTITUTIONS :: PUTTUR Siddharth Nagar, Narayanavanam Road 517583 QUESTION BANK (DESCRIPTIVE) Subject with Code : Fluid Mechanics (16CE106) Year & Sem: IIB.Tech & ISem Course & Branch:
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 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 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 informationCHEN 3200 Fluid Mechanics Spring Homework 3 solutions
Homework 3 solutions 1. An artery with an inner diameter of 15 mm contains blood flowing at a rate of 5000 ml/min. Further along the artery, arterial plaque has partially clogged the artery, reducing the
More informationBasics of fluid flow. Types of flow. Fluid Ideal/Real Compressible/Incompressible
Basics of fluid flow Types of flow Fluid Ideal/Real Compressible/Incompressible Flow Steady/Unsteady Uniform/Nonuniform Laminar/Turbulent Pressure/Gravity (free surface) 1 Basics of fluid flow (Chapter
More informationChapter Two. Basic Thermodynamics, Fluid Mechanics: Definitions of Efficiency. Laith Batarseh
Chapter Two Basic Thermodynamics, Fluid Mechanics: Definitions of Efficiency Laith Batarseh The equation of continuity Most analyses in this book are limited to onedimensional steady flows where the velocity
More informationINSTITUTE 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 : III B. Tech Year : 0 0 Course Coordinator
More informationFluid Mechanics61341
AnNajah National University College of Engineering Fluid Mechanics61341 Chapter [5] Flow of An Incompressible Fluid Dr. Sameer Shadeed 1 Fluid Mechanics2nd Semester 2010 [5] Flow of An Incompressible
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 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 informationUniversity of Engineering and Technology, Taxila. Department of Civil Engineering
University of Engineering and Technology, Taxila Department of Civil Engineering Course Title: CE201 Fluid Mechanics  I Prerequisite(s): None Credit Hours: 2 + 1 Contact Hours: 2 + 3 Text Book(s): Reference
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 informationCOURSE 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 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 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 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 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 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 informationDimensions represent classes of units we use to describe a physical quantity. Most fluid problems involve four primary dimensions
BEE 5330 Fluids FE Review, Feb 24, 2010 1 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 will form a free
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 information1.060 Engineering Mechanics II Spring Problem Set 4
1.060 Engineering Mechanics II Spring 2006 Due on Monday, March 20th Problem Set 4 Important note: Please start a new sheet of paper for each problem in the problem set. Write the names of the group members
More informationBasic equations of motion in fluid mechanics
1 Annex 1 Basic equations of motion in fluid mechanics 1.1 Introduction It is assumed that the reader of this book is familiar with the basic laws of fluid mechanics. Nevertheless some of these laws will
More informationME 3560 Fluid Mechanics
Sring 018 ME 3560 Fluid Mechanic Chater III. Elementary Fluid Dynamic The Bernoulli Equation 1 Sring 018 3.1 Newton Second Law A fluid article can exerience acceleration or deceleration a it move from
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 informationUNIT IV. Flow through Orifice and Mouthpieces and Flow through Notchs and Weirs
SIDDHARTH GROUP OF INSTITUTIONS :: PUTTUR Siddharth Nagar, Narayanavanam Road 517583 QUESTION BANK (DESCRIPTIVE) Subject with Code : FM(15A01305) Year & Sem: IIB.Tech & ISem Course & Branch: B.Tech 
More informations 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
More informationHYDRAULICS 1 (HYDRODYNAMICS) SPRING 2005
HYDRAULICS (HYDRODYNAMICS) SPRING 005 Part. FluidFlow Principles. Introduction. Definitions. Notation and fluid properties.3 Hydrostatics.4 Fluid dynamics.5 Control volumes.6 Visualising fluid flow.7
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 informationCLASS Fourth Units (Second part)
CLASS Fourth Units (Second part) Energy analysis of closed systems Copyright The McGrawHill Companies, Inc. Permission required for reproduction or display. MOVING BOUNDARY WORK Moving boundary work (P
More informationChapter 5(Section1) Friction in Solids and Liquids
Chapter 5(Section1) 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
More informationCHAPTER (13) FLOW MEASUREMENTS
CHAPTER (13) FLOW MEASUREMENTS 09/12/2010 Dr. Munzer Ebaid 1 Instruments for the Measurements of Flow Rate 1. Direct Methods: Volume or weight measurements. 2. Indirect Methods: Venturi meters, Orifices
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 informationCVE 372 HYDROMECHANICS EXERCISE PROBLEMS
VE 37 HYDROMEHNIS EXERISE PROLEMS 1. pump that has the characteristic curve shown in the accompanying graph is to be installed in the system shown. What will be the discharge of water in the system? Take
More informationChapter 6 The ImpulseMomentum Principle
Chapter 6 The ImpulseMomentum Principle 6. The Linear ImpulseMomentum Equation 6. Pipe Flow Applications 6.3 Open Channel Flow Applications 6.4 The Angular ImpulseMomentum Principle Objectives:  Develop
More informationChapter 5. Mass and Energy Analysis of Control Volumes. by Asst. Prof. Dr.Woranee Paengjuntuek and Asst. Prof. Dr.Worarattana Pattaraprakorn
Chapter 5 Mass and Energy Analysis of Control Volumes by Asst. Prof. Dr.Woranee Paengjuntuek and Asst. Prof. Dr.Worarattana Pattaraprakorn Reference: Cengel, Yunus A. and Michael A. Boles, Thermodynamics:
More informationBenha 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 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 informationWilliam В. Brower, Jr. A PRIMER IN FLUID MECHANICS. Dynamics of Flows in One Space Dimension. CRC Press Boca Raton London New York Washington, D.C.
William В. Brower, Jr. A PRIMER IN FLUID MECHANICS Dynamics of Flows in One Space Dimension CRC Press Boca Raton London New York Washington, D.C. Table of Contents Chapter 1 Fluid Properties Kinetic Theory
More informationThe ImpulseMomentum Principle
Chapter 6 /60 The ImpulseMomentum Principle F F Chapter 6 The ImpulseMomentum Principle /60 Contents 6.0 Introduction 6. The Linear ImpulseMomentum Equation 6. Pipe Flow Applications 6.3 Open Channel
More informationIntroduction to Turbomachinery
1. Coordinate System Introduction to Turbomachinery Since there are stationary and rotating blades in turbomachines, they tend to form a cylindrical form, represented in three directions; 1. Axial 2. Radial
More informationSteven 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
More informationSection 2: Lecture 1 Integral Form of the Conservation Equations for Compressible Flow
Section 2: Lecture 1 Integral Form of the Conservation Equations for Compressible Flow Anderson: Chapter 2 pp. 4154 1 Equation of State: Section 1 Review p = R g T " > R g = R u M w  R u = 8314.4126
More informationIran University of Science & Technology School of Mechanical Engineering Advance Fluid Mechanics
1. Consider a sphere of radius R immersed in a uniform stream U0, as shown in 3 R Fig.1. The fluid velocity along streamline AB is given by V ui U i x 1. 0 3 Find (a) the position of maximum fluid acceleration
More informationChapter 5. Mass and Energy Analysis of Control Volumes
Chapter 5 Mass and Energy Analysis of Control Volumes Conservation Principles for Control volumes The conservation of mass and the conservation of energy principles for open systems (or control volumes)
More informationHigher Education. Mc Grauu FUNDAMENTALS AND APPLICATIONS SECOND EDITION
FLUID MECHANICS FUNDAMENTALS AND APPLICATIONS SECOND EDITION Mc Grauu Higher Education Boston Burr Ridge, IL Dubuque, IA Madison, Wl New York San Francisco St. Louis Bangkok Bogota Caracas Kuala Lumpur
More informationChapter 5: Mass, Bernoulli, and
and Energy Equations 51 Introduction 52 Conservation of Mass 53 Mechanical Energy 54 General Energy Equation 55 Energy Analysis of Steady Flows 56 The Bernoulli Equation 51 Introduction This chapter
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 informationFigure 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