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

Size: px
Start display at page:

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

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 Work-energy 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, well-contoured 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 sharp-edged 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 U-tube 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, sharp-crested 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 U-tube as indicated in Fig. E3.6. When released from the non-equilibrium 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 3-D, unsteady (x, y, z, t; r,θ, z, t; etc) Let consider

### Chapter 3 Bernoulli Equation

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

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

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

### 주요명칭 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

### Unit C-1: 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

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

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

### 5 ENERGY EQUATION OF FLUID MOTION

5 ENERGY EQUATION OF FLUID MOTION 5.1 Introduction In order to develop the equations that describe a flow, it is assumed that fluids are subject to certain fundamental laws of physics. The pertinent laws

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

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

### Useful 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

### Objectives. Conservation of mass principle: Mass Equation The Bernoulli equation Conservation of energy principle: Energy equation

Objectives Conservation of mass principle: Mass Equation The Bernoulli equation Conservation of energy principle: Energy equation Conservation of Mass Conservation of Mass Mass, like energy, is a conserved

### Pressure in stationary and moving fluid Lab- Lab On- On Chip: Lecture 2

Pressure in stationary and moving fluid Lab-On-Chip: 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;

### Mass of fluid leaving per unit time

5 ENERGY EQUATION OF FLUID MOTION 5.1 Eulerian Approach & Control Volume In order to develop the equations that describe a flow, it is assumed that fluids are subject to certain fundamental laws of physics.

### Chapter 4 DYNAMICS OF FLUID FLOW

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

### If 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

### 3.25 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

### Chapter Four fluid flow mass, energy, Bernoulli and momentum

4-1Conservation of Mass Principle Consider a control volume of arbitrary shape, as shown in Fig (4-1). Figure (4-1): the differential control volume and differential control volume (Total mass entering

### FLUID MECHANICS PROF. DR. METİN GÜNER COMPILER

FLUID MECHANICS PROF. DR. METİN GÜNER COMPILER ANKARA UNIVERSITY FACULTY OF AGRICULTURE DEPARTMENT OF AGRICULTURAL MACHINERY AND TECHNOLOGIES ENGINEERING 1 4. ELEMENTARY FLUID DYNAMICS -THE BERNOULLI EQUATION

### 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

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

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

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

### Pressure in stationary and moving fluid. Lab-On-Chip: Lecture 2

Pressure in stationary and moving fluid Lab-On-Chip: Lecture Fluid Statics No shearing stress.no relative movement between adjacent fluid particles, i.e. static or moving as a single block Pressure at

### 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

### NPTEL Quiz Hydraulics

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

### ME3560 Tentative Schedule Spring 2019

ME3560 Tentative Schedule Spring 2019 Week Number Date Lecture Topics Covered Prior to Lecture Read Section Assignment Prep Problems for Prep Probs. Must be Solved by 1 Monday 1/7/2019 1 Introduction to

### 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

### ME3560 Tentative Schedule Fall 2018

ME3560 Tentative Schedule Fall 2018 Week Number 1 Wednesday 8/29/2018 1 Date Lecture Topics Covered Introduction to course, syllabus and class policies. Math Review. Differentiation. Prior to Lecture Read

### HOMEWORK 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 spray-guns operate by achieving a low pressure

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

SUBJECT: FLUID MECHANICS VIVA QUESTIONS (M.E 4 th SEM) Experiment- To determine the coefficient of impact for vanes. Q1. Explain impulse momentum principal. Ans1. Momentum equation is based on Newton s

### CHAPTER 3 BASIC EQUATIONS IN FLUID MECHANICS NOOR ALIZA AHMAD

CHAPTER 3 BASIC EQUATIONS IN FLUID MECHANICS 1 INTRODUCTION Flow often referred as an ideal fluid. We presume that such a fluid has no viscosity. However, this is an idealized situation that does not exist.

### 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.

### Basic Fluid Mechanics

Basic Fluid Mechanics Chapter 5: Application of Bernoulli Equation 4/16/2018 C5: Application of Bernoulli Equation 1 5.1 Introduction In this chapter we will show that the equation of motion of a particle

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

The angular momentum A control volume analysis can be applied to the angular momentum, by letting B equal to angularmomentum vector H. If O is the point about which moments are desired, the angular moment

### 2 Internal Fluid Flow

Internal Fluid Flow.1 Definitions Fluid Dynamics The study of fluids in motion. Static Pressure The pressure at a given point exerted by the static head of the fluid present directly above that point.

### EGN 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

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

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

### 10.52 Mechanics of Fluids Spring 2006 Problem Set 3

10.52 Mechanics of Fluids Spring 2006 Problem Set 3 Problem 1 Mass transfer studies involving the transport of a solute from a gas to a liquid often involve the use of a laminar jet of liquid. The situation

### 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

### EXPERIMENT No.1 FLOW MEASUREMENT BY ORIFICEMETER

EXPERIMENT No.1 FLOW MEASUREMENT BY ORIFICEMETER 1.1 AIM: To determine the co-efficient of discharge of the orifice meter 1.2 EQUIPMENTS REQUIRED: Orifice meter test rig, Stopwatch 1.3 PREPARATION 1.3.1

### BERNOULLI 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

### 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

### New 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,

### 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

### Lesson 6 Review of fundamentals: Fluid flow

Lesson 6 Review of fundamentals: Fluid flow The specific objective of this lesson is to conduct a brief review of the fundamentals of fluid flow and present: A general equation for conservation of mass

### Chapter (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

### Approximate 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

### Lecture 3 The energy equation

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

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

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

### Measurements 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.

### Chapter 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.

### CLASS SCHEDULE 2013 FALL

CLASS SCHEDULE 2013 FALL Class # or Lab # 1 Date Aug 26 2 28 Important Concepts (Section # in Text Reading, Lecture note) Examples/Lab Activities Definition fluid; continuum hypothesis; fluid properties

### 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

### Chapter 7 The Energy Equation

Chapter 7 The Energy Equation 7.1 Energy, Work, and Power When matter has energy, the matter can be used to do work. A fluid can have several forms of energy. For example a fluid jet has kinetic energy,

### UNIT I FLUID PROPERTIES AND STATICS

SIDDHARTH GROUP OF INSTITUTIONS :: PUTTUR Siddharth Nagar, Narayanavanam Road 517583 QUESTION BANK (DESCRIPTIVE) Subject with Code : Fluid Mechanics (16CE106) Year & Sem: II-B.Tech & I-Sem Course & Branch:

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

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

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

Chapter 6 INCOMPRESSIBLE INVISCID FLOW All real fluids possess viscosity. However in many flow cases it is reasonable to neglect the effects of viscosity. It is useful to investigate the dynamics of an

### !! +! 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

### CHEN 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

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

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

### Chapter 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 one-dimensional steady flows where the velocity

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

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

### Fluid Mechanics-61341

An-Najah National University College of Engineering Fluid Mechanics-61341 Chapter [5] Flow of An Incompressible Fluid Dr. Sameer Shadeed 1 Fluid Mechanics-2nd Semester 2010- [5] Flow of An Incompressible

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

Part A: 1 pts each, 10 pts total, no partial credit. 1) (Correct: 1 pt/ Wrong: -3 pts). The sum of static, dynamic, and hydrostatic pressures is constant when flow is steady, irrotational, incompressible,

### 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

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

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

### Q1 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

### COURSE NUMBER: ME 321 Fluid Mechanics I 3 credit hour. Basic Equations in fluid Dynamics

COURSE NUMBER: ME 321 Fluid Mechanics I 3 credit hour Basic Equations in fluid Dynamics Course teacher Dr. M. Mahbubur Razzaque Professor Department of Mechanical Engineering BUET 1 Description of Fluid

### CH.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

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

UNIT III FLOW THROUGH PIPES 1. List the types of fluid flow. Steady and unsteady flow Uniform and non-uniform flow Laminar and Turbulent flow Compressible and incompressible flow Rotational and ir-rotational

### BACHELOR OF TECHNOLOGY IN MECHANICAL ENGINEERING (COMPUTER INTEGRATED MANUFACTURING)

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

### 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

### Where 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

### Dimensions 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

### MASS, 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

### 1.060 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

### Basic equations of motion in fluid mechanics

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

### ME 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

### Lecture23. 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

### UNIT 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: II-B.Tech & I-Sem Course & Branch: B.Tech -

### 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

### HYDRAULICS 1 (HYDRODYNAMICS) SPRING 2005

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

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

Hydraulic Coefficient & Flow Measurements ELEMENTARY HYDRAULICS National Certificate in Technology (Civil Engineering) Chapter 3 1. Mass flow rate If we want to measure the rate at which water is flowing

### CLASS Fourth Units (Second part)

CLASS Fourth Units (Second part) Energy analysis of closed systems Copyright The McGraw-Hill Companies, Inc. Permission required for reproduction or display. MOVING BOUNDARY WORK Moving boundary work (P

### 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

### CHAPTER (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

### Experiment (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

### CVE 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

### Chapter 6 The Impulse-Momentum Principle

Chapter 6 The Impulse-Momentum Principle 6. The Linear Impulse-Momentum Equation 6. Pipe Flow Applications 6.3 Open Channel Flow Applications 6.4 The Angular Impulse-Momentum Principle Objectives: - Develop

### Chapter 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:

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

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

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

IV. DIFFERENTIAL RELATIONS FOR A FLUID PARTICLE This chapter presents the development and application of the basic differential equations of fluid motion. Simplifications in the general equations and common

### 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.

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

### The Impulse-Momentum Principle

Chapter 6 /60 The Impulse-Momentum Principle F F Chapter 6 The Impulse-Momentum Principle /60 Contents 6.0 Introduction 6. The Linear Impulse-Momentum Equation 6. Pipe Flow Applications 6.3 Open Channel

### Introduction 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

### 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

### Section 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. 41-54 1 Equation of State: Section 1 Review p = R g T " > R g = R u M w - R u = 8314.4126

### Iran 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

### Chapter 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)

### Higher Education. Mc Grauu FUNDAMENTALS AND APPLICATIONS SECOND EDITION

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

### Chapter 5: Mass, Bernoulli, and

and Energy Equations 5-1 Introduction 5-2 Conservation of Mass 5-3 Mechanical Energy 5-4 General Energy Equation 5-5 Energy Analysis of Steady Flows 5-6 The Bernoulli Equation 5-1 Introduction This chapter