Chapter 8: Flow in Pipes

Size: px
Start display at page:

Transcription

1

2 Objectives 1. Have a deeper understanding of laminar and turbulent flow in pipes and the analysis of fully developed flow 2. Calculate the major and minor losses associated with pipe flow in piping networks and determine the pumping power requirements Meccanica dei Fluidi I 2

3 Introduction Average velocity in a pipe Recall - because of the no-slip condition, the velocity at the walls of a pipe or duct flow is zero We are often interested only in V avg, which we usually call just V (drop the subscript for convenience) Keep in mind that the no-slip condition causes shear stress and friction along the pipe walls Friction force of wall on fluid Meccanica dei Fluidi I 3

4 Introduction V avg V avg For pipes of constant diameter and incompressible flow V avg stays the same down the pipe, even if the velocity profile changes Why? Conservation of Mass same same same Meccanica dei Fluidi I 4

5 Introduction For pipes with variable diameter, m is still the same due to conservation of mass, but V 1 V 2 D 1 D 2 V 1 m V 2 m 2 1 Meccanica dei Fluidi I 5

6 Laminar and Turbulent Flows Clay Institute Millennium Prize Re = Inertial forces Viscous forces Meccanica dei Fluidi I 6

7 Laminar and Turbulent Flows Definition of Reynolds number Critical Reynolds number (Re cr ) for flow in a round pipe Re < 2300 laminar 2300 Re 4000 transitional Re > 4000 turbulent Note that these values are approximate. For a given application, Re cr depends upon Pipe roughness Vibrations Upstream fluctuations and disturbances (valves, elbows, etc. that may perturb the flow) Meccanica dei Fluidi I 7

8 Osborne Reynolds ( ) Meccanica dei Fluidi I 8

9 Osborne Reynolds 1880 Experiments Re cr (??) Meccanica dei Fluidi I 9

10 Laminar and Turbulent Flows For non-round pipes, define the hydraulic diameter D h = 4A c /P A c = cross-section area P = wetted perimeter Example: open channel A c = 0.15 * 0.4 = 0.06m 2 P = = 0.7m Don t count free surface, since it does not contribute to friction along pipe walls! D h = 4A c /P = 4*0.06/0.7 = 0.343m What does it mean? This channel flow is equivalent to a round pipe of diameter 0.343m (approximately). Meccanica dei Fluidi I 10

11 The Entrance Region Consider a round pipe of diameter D. The flow can be laminar or turbulent. In either case, the profile develops downstream over several diameters called the entry length L h. L h /D is a function of Re. L h u(r,x) = 0 u = u(r) x Meccanica dei Fluidi I 11

12 Fully Developed Pipe Flow Comparison of laminar and turbulent flow There are some major differences between laminar and turbulent fully developed pipe flows Laminar Can solve exactly (Chapter 9) Flow is steady Velocity profile is parabolic Pipe roughness not important It turns out that V avg = ½ u max and u(r)= 2V avg (1 - r 2 /R 2 ) Meccanica dei Fluidi I 12

13 Fully Developed Pipe Flow Laminar = - m du/dr Ring-shaped differential volume element m d du dp (r ) = = constant r dr dr dx u(r) =, P 1 P 2 = 32 m L V avg /D 2 Meccanica dei Fluidi I 13 = constant

14 Example Oil at 20 C (r = 888 kg/m 3 and m = kg/m. s) flows steadily through a 5-cm-diameter 40-m-long pipe. The pressure at the pipe inlet and outlet are measured to be 745 and 97 kpa, respectively. 1) Determine the average velocity and the flow rate through the pipe; 2) Verify that the flow through the pipe is laminar; 3) Determine the value of the Darcy friction factor f ; 4) Determine the pumping power required to overcome the pressure drop. Definition: D P L = f L r V avg 2 D 2 f : Darcy friction factor (this definition applies to both laminar and turbulent flows) Meccanica dei Fluidi I 14

15 Fully Developed Pipe Flow Turbulent Cannot solve exactly (too complex) Flow is unsteady (3D swirling eddies), but it is steady in the mean Mean velocity profile is fuller (shape more like a top-hat profile, with very sharp slope at the wall) Pipe roughness is very important Instantaneous profiles V avg 85% of u max (depends on Re a bit) No analytical solution, but there are some good semi-empirical expressions that approximate the velocity profile shape. See text Logarithmic law (Eq. 8-46) Power law (Eq. 8-49) Meccanica dei Fluidi I 15

16 Fully Developed Pipe Flow Wall-shear stress Recall, for simple shear flows u=u(y), we had = m du/dy In fully developed pipe flow, it turns out that = -m du/dr Laminar Turbulent w w = shear stress at the wall, acting on the fluid Meccanica dei Fluidi I 16 w w,turb > w,lam

17 Fully Developed Pipe Flow Pressure drop There is a direct connection between the pressure drop in a pipe and the shear stress at the wall Consider a horizontal pipe, fully developed, and incompressible flow w Take CV inside the pipe wall P 1 V P 2 L 1 2 Let s apply conservation of mass, momentum, and energy to this CV Meccanica dei Fluidi I 17

18 Fully Developed Pipe Flow Pressure drop Conservation of Mass Conservation of x-momentum Terms cancel since 1 = 2 and V 1 = V 2 Meccanica dei Fluidi I 18

19 Fully Developed Pipe Flow Pressure drop Thus, x-momentum reduces to or Energy equation (in head form) cancel (horizontal pipe) Velocity terms cancel again because V 1 = V 2 h L = irreversible head loss; it is felt as a pressure drop in the pipe Meccanica dei Fluidi I 19

20 Fully Developed Pipe Flow Head Loss From momentum CV analysis From energy CV analysis Equating the two gives To predict head loss, we need to be able to calculate w. How? Laminar flow: solve exactly Turbulent flow: rely on empirical data (experiments) In either case, we can benefit from dimensional analysis! Meccanica dei Fluidi I 20

21 Fully Developed Pipe Flow Darcy Friction Factor w = func(r V, D, m, ) -analysis gives = average roughness of the inside wall of the pipe Meccanica dei Fluidi I 21

22 Fully Developed Pipe Flow Friction Factor Now go back to equation for h L and substitute f for w Our problem is now reduced to solving for Darcy friction factor f Recall Therefore Laminar flow: f = 64/Re (exact) Turbulent flow: Use charts or empirical equations (Moody Chart, a famous plot of f vs. Re and /D) But for laminar flow, roughness does not affect the flow unless it is huge Meccanica dei Fluidi I 22

23 Meccanica dei Fluidi I 23

24 Fully Developed Pipe Flow Friction Factor Moody chart was developed for circular pipes, but can be used for non-circular pipes using hydraulic diameter Colebrook equation is a curve-fit of the data which is convenient for computations Implicit equation for f which can be solved with an iterative numerical method Both Moody chart and Colebrook equation are accurate to ±15% due to roughness size, experimental error, curve fitting of data, etc. Meccanica dei Fluidi I 24

25 Types of Fluid Flow Problems In design and analysis of piping systems, 3 problem types are encountered 1. Determine D p (or h L ) given L, D, V (or flow rate) Can be solved directly using Moody chart and Colebrook equation 2. Determine V, given L, D, D p 3. Determine D, given L, D p, V (or flow rate) Types 2 and 3 are common engineering design problems, i.e., selection of pipe diameters to minimize construction and pumping costs. However, iterative approach required since both V and D are in the Reynolds number. Meccanica dei Fluidi I 25

26 Example Heated air at 1 atm and 35 C is to be transported in a 150-m long circular plastic duct at a rate of 0.35 m 3 /s. If the head loss in the pipe is not to exceed 20 m, determine the maximum required pumping power, the minimum diameter of the duct, average velocity, the Reynolds number and the Darcy friction factor. r = kg/m 3, n = m 2 /s Meccanica dei Fluidi I 26

27 Minor Losses Piping systems include fittings, valves, bends, elbows, tees, inlets, exits, enlargements, and contractions. These components interrupt the smooth flow of fluid and cause additional losses because of flow separation and mixing We introduce a relation for the minor losses associated with these components K L is the loss coefficient. It is different for each component. It is assumed to be independent of Re. Typically provided by manufacturer or generic table (e.g., Table 8-4 in text). Meccanica dei Fluidi I 27

28 Minor Losses The loss coefficient K L is determined by measuring the additional pressure loss the component causes, and dividing it by the dynamic pressure in the pipe The head loss at the inlet of a pipe is almost negligible for well rounded inlets Meccanica dei Fluidi I 28

29 Minor Losses Total head loss in a system is comprised of major losses (in the pipe sections) and the minor losses (in the components) i pipe sections j components If the piping system has constant diameter Meccanica dei Fluidi I 29

30 a = 2 for fully developed laminar flow a 1 for fully developed turbulent flow Meccanica dei Fluidi I 30

31 Meccanica dei Fluidi I 31

32 Head Loss at a Sharp-Edge Inlet Meccanica dei Fluidi I 32

33 Example A 9-cm-diameter horizontal water pipe contracts gradually to a 6-cm-diameter pipe. The walls of the contraction section are angled 30 from the horizontal. The average velocity and pressure of water at the exit of the contraction section are 7 m/s and 150 kpa, respectively. Determine the head loss in the contraction section and the pressure in the larger-diameter pipe. In the case of plastic pipes, determine also the friction factor for both pipes in series. 2 1 Turbulent fully developed flow at sections 1 and 2 (?), r = 998 kg/m 3, m = x 10-3 kg/(m s), K L? Meccanica dei Fluidi I 33

34 Piping Networks and Pump Selection Two general types of networks Pipes in series Volume flow rate is constant Head loss is the summation of parts Pipes in parallel Volume flow rate is the sum of the components Pressure loss across all branches is the same Meccanica dei Fluidi I 34

35 Piping Networks and Pump Selection For parallel pipes, perform CV analysis between points A and B Since D P is the same for all branches, head loss in all branches is the same Meccanica dei Fluidi I 35

36 Piping Networks and Pump Selection Head loss relationship between branches allows the following ratios to be developed so that the relative flow rates in parallel pipes are established from the requirements that the head loss in each pipe is the same Real pipe systems result in a system of non-linear equations. Note: the analogy with electrical circuits should be obvious. Flow rate (V): Pressure gradient (Dp): Head loss (h L ): current (I) electrical potential (V) resistance (R), however h L is very nonlinear Meccanica dei Fluidi I 36

37 Piping Networks and Pump Selection When a piping system involves pumps and/or turbines, pump and turbine head must be included in the energy equation The useful head of the pump (h pump,u ) or the head extracted by the turbine (h turbine,e ), are functions of volume flow rate, i.e., they are not constants. Operating point of system is where the system is in balance, e.g., where pump head is equal to the head loss (plus elevation difference, velocity head difference, etc.) Meccanica dei Fluidi I 37

38 Pump and systems curves Supply curve for h pump,u : determined experimentally by manufacturer. It is possible to build a functional relationship for h pump,u. System curve determined from analysis of fluid dynamics equations Operating point is the intersection of supply and demand curves If peak efficiency is far from operating point, pump is wrong for that application. Meccanica dei Fluidi I 38

Chapter 8: Flow in Pipes

8-1 Introduction 8-2 Laminar and Turbulent Flows 8-3 The Entrance Region 8-4 Laminar Flow in Pipes 8-5 Turbulent Flow in Pipes 8-6 Fully Developed Pipe Flow 8-7 Minor Losses 8-8 Piping Networks and Pump

Viscous Flow in Ducts

Dr. M. Siavashi Iran University of Science and Technology Spring 2014 Objectives 1. Have a deeper understanding of laminar and turbulent flow in pipes and the analysis of fully developed flow 2. Calculate

Chapter 10 Flow in Conduits

Chapter 10 Flow in Conduits 10.1 Classifying Flow Laminar Flow and Turbulent Flow Laminar flow Unpredictable Turbulent flow Near entrance: undeveloped developing flow In developing flow, the wall shear

Basic Fluid Mechanics

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

ME 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 non-circular ducts) are very common. Part 8 Viscous Flow in Pipes and Ducts These presentations are prepared

FLOW IN CONDUITS. Shear stress distribution across a pipe section. Chapter 10

Chapter 10 Shear stress distribution across a pipe section FLOW IN CONDUITS For steady, uniform flow, the momentum balance in s for the fluid cylinder yields Fluid Mechanics, Spring Term 2010 Velocity

FACULTY OF CHEMICAL & ENERGY ENGINEERING FLUID MECHANICS LABORATORY TITLE OF EXPERIMENT: MINOR LOSSES IN PIPE (E4)

FACULTY OF CHEMICAL & ENERGY ENGINEERING FLUID MECHANICS LABORATORY TITLE OF EXPERIMENT: MINOR LOSSES IN PIPE (E4) 1 1.0 Objectives The objective of this experiment is to calculate loss coefficient (K

Chapter 6. Losses due to Fluid Friction

Chapter 6 Losses due to Fluid Friction 1 Objectives ä To measure the pressure drop in the straight section of smooth, rough, and packed pipes as a function of flow rate. ä To correlate this in terms of

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

ME 305 Fluid Mechanics I. Chapter 8 Viscous Flow in Pipes and Ducts

ME 305 Fluid Mechanics I Chapter 8 Viscous Flow in Pipes and Ducts These presentations are prepared by Dr. Cüneyt Sert Department of Mechanical Engineering Middle East Technical University Ankara, Turkey

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.

Reynolds, an engineering professor in early 1880 demonstrated two different types of flow through an experiment:

7 STEADY FLOW IN PIPES 7.1 Reynolds Number Reynolds, an engineering professor in early 1880 demonstrated two different types of flow through an experiment: Laminar flow Turbulent flow Reynolds apparatus

Fluid flow in circular and noncircular pipes is commonly encountered in

cen72367_ch08.qxd /4/04 7:3 PM Page 32 FLOW IN PIPES CHAPTER 8 Fluid flow in circular and noncircular pipes is commonly encountered in practice. The hot and cold water that we use in our homes is pumped

FLUID MECHANICS PROF. DR. METİN GÜNER COMPILER

FLUID MECHANICS PROF. DR. METİN GÜNER COMPILER ANKARA UNIVERSITY FACULTY OF AGRICULTURE DEPARTMENT OF AGRICULTURAL MACHINERY AND TECHNOLOGIES ENGINEERING 1 5. FLOW IN PIPES Liquid or gas flow through pipes

Chapter 6. Losses due to Fluid Friction

Chapter 6 Losses due to Fluid Friction 1 Objectives To measure the pressure drop in the straight section of smooth, rough, and packed pipes as a function of flow rate. To correlate this in terms of the

Chapter (3) Water Flow in Pipes

Chapter (3) Water Flow in Pipes Water Flow in Pipes Bernoulli Equation Recall fluid mechanics course, the Bernoulli equation is: P 1 ρg + v 1 g + z 1 = P ρg + v g + z h P + h T + h L Here, we want to study

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

Hydraulics. B.E. (Civil), Year/Part: II/II. Tutorial solutions: Pipe flow. Tutorial 1

Hydraulics B.E. (Civil), Year/Part: II/II Tutorial solutions: Pipe flow Tutorial 1 -by Dr. K.N. Dulal Laminar flow 1. A pipe 200mm in diameter and 20km long conveys oil of density 900 kg/m 3 and viscosity

Review of pipe flow: Friction & Minor Losses

ENVE 204 Lecture -1 Review of pipe flow: Friction & Minor Losses Assist. Prof. Neslihan SEMERCİ Marmara University Department of Environmental Engineering Important Definitions Pressure Pipe Flow: Refers

HEAT TRANSFER BY CONVECTION. Dr. Şaziye Balku 1

HEAT TRANSFER BY CONVECTION Dr. Şaziye Balku 1 CONDUCTION Mechanism of heat transfer through a solid or fluid in the absence any fluid motion. CONVECTION Mechanism of heat transfer through a fluid in the

Lesson 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).

FLUID MECHANICS PROF. DR. METİN GÜNER COMPILER

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

Piping Systems and Flow Analysis (Chapter 3)

Piping Systems and Flow Analysis (Chapter 3) 2 Learning Outcomes (Chapter 3) Losses in Piping Systems Major losses Minor losses Pipe Networks Pipes in series Pipes in parallel Manifolds and Distribution

Friction Factors and Drag Coefficients

Levicky 1 Friction Factors and Drag Coefficients Several equations that we have seen have included terms to represent dissipation of energy due to the viscous nature of fluid flow. For example, in the

FE Exam Fluids Review October 23, Important Concepts

FE Exam Fluids Review October 3, 013 mportant Concepts Density, specific volume, specific weight, specific gravity (Water 1000 kg/m^3, Air 1. kg/m^3) Meaning & Symbols? Stress, Pressure, Viscosity; Meaning

PIPING SYSTEMS. Pipe and Tubing Standards Sizes for pipes and tubes are standardized. Pipes are specified by a nominal diameter and a schedule number.

PIPING SYSTEMS In this chapter we will review some of the basic concepts associated with piping systems. Topics that will be considered in this chapter are - Pipe and tubing standards - Effective and hydraulic

Applied Fluid Mechanics

Applied Fluid Mechanics 1. The Nature of Fluid and the Study of Fluid Mechanics 2. Viscosity of Fluid 3. Pressure Measurement 4. Forces Due to Static Fluid 5. Buoyancy and Stability 6. Flow of Fluid and

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.

ME 309 Fluid Mechanics Fall 2010 Exam 2 1A. 1B.

Fall 010 Exam 1A. 1B. Fall 010 Exam 1C. Water is flowing through a 180º bend. The inner and outer radii of the bend are 0.75 and 1.5 m, respectively. The velocity profile is approximated as C/r where C

When water (fluid) flows in a pipe, for example from point A to point B, pressure drop will occur due to the energy losses (major and minor losses).

PRESSURE DROP AND OSSES IN PIPE When water (luid) lows in a pipe, or example rom point A to point B, pressure drop will occur due to the energy losses (major and minor losses). A B Bernoulli equation:

Mechanical Engineering Programme of Study

Mechanical Engineering Programme of Study Fluid Mechanics Instructor: Marios M. Fyrillas Email: eng.fm@fit.ac.cy SOLVED EXAMPLES ON VISCOUS FLOW 1. Consider steady, laminar flow between two fixed parallel

where = rate of change of total energy of the system, = rate of heat added to the system, = rate of work done by the system

The Energy Equation for Control Volumes Recall, the First Law of Thermodynamics: where = rate of change of total energy of the system, = rate of heat added to the system, = rate of work done by the system

Pipe Flow. Lecture 17

Pipe Flow Lecture 7 Pipe Flow and the Energy Equation For pipe flow, the Bernoulli equation alone is not sufficient. Friction loss along the pipe, and momentum loss through diameter changes and corners

Fluid Mechanics II 3 credit hour. Fluid flow through pipes-minor losses

COURSE NUMBER: ME 323 Fluid Mechanics II 3 credit hour Fluid flow through pipes-minor losses Course teacher Dr. M. Mahbubur Razzaque Professor Department of Mechanical Engineering BUET 1 Losses in Noncircular

MYcsvtu Notes HEAT TRANSFER BY CONVECTION

www.mycsvtunotes.in HEAT TRANSFER BY CONVECTION CONDUCTION Mechanism of heat transfer through a solid or fluid in the absence any fluid motion. CONVECTION Mechanism of heat transfer through a fluid in

Hydraulics and hydrology

Hydraulics and hydrology - project exercises - Class 4 and 5 Pipe flow Discharge (Q) (called also as the volume flow rate) is the volume of fluid that passes through an area per unit time. The discharge

Chapter 10: Flow Flow in in Conduits Conduits Dr Ali Jawarneh

Chater 10: Flow in Conduits By Dr Ali Jawarneh Hashemite University 1 Outline In this chater we will: Analyse the shear stress distribution across a ie section. Discuss and analyse the case of laminar

Chapter (3) Water Flow in Pipes

Chapter (3) Water Flow in Pipes Water Flow in Pipes Bernoulli Equation Recall fluid mechanics course, the Bernoulli equation is: P 1 ρg + v 1 g + z 1 = P ρg + v g + z h P + h T + h L Here, we want to study

1-Reynold s Experiment

Lect.No.8 2 nd Semester Flow Dynamics in Closed Conduit (Pipe Flow) 1 of 21 The flow in closed conduit ( flow in pipe ) is differ from this occur in open channel where the flow in pipe is at a pressure

STEADY FLOW THROUGH PIPES DARCY WEISBACH EQUATION FOR FLOW IN PIPES. HAZEN WILLIAM S FORMULA, LOSSES IN PIPELINES, HYDRAULIC GRADE LINES AND ENERGY

STEADY FLOW THROUGH PIPES DARCY WEISBACH EQUATION FOR FLOW IN PIPES. HAZEN WILLIAM S FORMULA, LOSSES IN PIPELINES, HYDRAULIC GRADE LINES AND ENERGY LINES 1 SIGNIFICANCE OF CONDUITS In considering the convenience

Liquid or gas flow through pipes or ducts is commonly used in heating and

cen58933_ch08.qxd 9/4/2002 11:29 AM Page 419 INTERNAL FORCED CONVECTION CHAPTER 8 Liquid or gas flow through pipes or ducts is commonly used in heating and cooling applications. The fluid in such applications

Principles of Convection

Principles of Convection Point Conduction & convection are similar both require the presence of a material medium. But convection requires the presence of fluid motion. Heat transfer through the: Solid

LOSSES DUE TO PIPE FITTINGS

LOSSES DUE TO PIPE FITTINGS Aim: To determine the losses across the fittings in a pipe network Theory: The resistance to flow in a pipe network causes loss in the pressure head along the flow. The overall

OE4625 Dredge Pumps and Slurry Transport. Vaclav Matousek October 13, 2004

OE465 Vaclav Matousek October 13, 004 1 Dredge Vermelding Pumps onderdeel and Slurry organisatie Transport OE465 Vaclav Matousek October 13, 004 Dredge Vermelding Pumps onderdeel and Slurry organisatie

EXPERIMENT II - FRICTION LOSS ALONG PIPE AND LOSSES AT PIPE FITTINGS

MM 30 FLUID MECHANICS II Prof. Dr. Nuri YÜCEL Yrd. Doç. Dr. Nureddin DİNLER Arş. Gör. Dr. Salih KARAASLAN Arş. Gör. Fatih AKTAŞ EXPERIMENT II - FRICTION LOSS ALONG PIPE AND LOSSES AT PIPE FITTINGS A. Objective:

Major and Minor Losses

Abstract Major and Minor Losses Caitlyn Collazo, Team 2 (1:00 pm) A Technovate fluid circuit system was used to determine the pressure drop across a pipe section and across an orifice. These pressure drops

UNIT II Real fluids. FMM / KRG / MECH / NPRCET Page 78. Laminar and turbulent flow

UNIT II Real fluids The flow of real fluids exhibits viscous effect that is they tend to "stick" to solid surfaces and have stresses within their body. You might remember from earlier in the course Newtons

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,

Sourabh V. Apte. 308 Rogers Hall

Sourabh V. Apte 308 Rogers Hall sva@engr.orst.edu 1 Topics Quick overview of Fluid properties, units Hydrostatic forces Conservation laws (mass, momentum, energy) Flow through pipes (friction loss, Moody

ACCOUNTING FOR FRICTION IN THE BERNOULLI EQUATION FOR FLOW THROUGH PIPES

ACCOUNTING FOR FRICTION IN THE BERNOULLI EQUATION FOR FLOW THROUGH PIPES Some background information first: We have seen that a major limitation of the Bernoulli equation is that it does not account for

Chapter 3 NATURAL CONVECTION

Fundamentals of Thermal-Fluid Sciences, 3rd Edition Yunus A. Cengel, Robert H. Turner, John M. Cimbala McGraw-Hill, 2008 Chapter 3 NATURAL CONVECTION Mehmet Kanoglu Copyright The McGraw-Hill Companies,

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

Chapter 1: Basic Concepts

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

150A Review Session 2/13/2014 Fluid Statics. Pressure acts in all directions, normal to the surrounding surfaces

Fluid Statics Pressure acts in all directions, normal to the surrounding surfaces or Whenever a pressure difference is the driving force, use gauge pressure o Bernoulli equation o Momentum balance with

Chapter 3 Water Flow in Pipes

The Islamic University o Gaza Faculty o Engineering Civil Engineering Department Hydraulics - ECI 33 Chapter 3 Water Flow in Pipes 3. Description o A Pipe Flow Water pipes in our homes and the distribution

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

LECTURE 6- ENERGY LOSSES IN HYDRAULIC SYSTEMS SELF EVALUATION QUESTIONS AND ANSWERS

LECTURE 6- ENERGY LOSSES IN HYDRAULIC SYSTEMS SELF EVALUATION QUESTIONS AND ANSWERS 1. What is the head loss ( in units of bars) across a 30mm wide open gate valve when oil ( SG=0.9) flow through at a

PIPE FLOW. General Characteristic of Pipe Flow. Some of the basic components of a typical pipe system are shown in Figure 1.

PIPE FLOW General Characteristic of Pipe Flow Figure 1 Some of the basic components of a typical pipe system are shown in Figure 1. They include the pipes, the various fitting used to connect the individual

Signature: (Note that unsigned exams will be given a score of zero.)

Neatly print your name: Signature: (Note that unsigned exams will be given a score of zero.) Circle your lecture section (-1 point if not circled, or circled incorrectly): Prof. Dabiri Prof. Wassgren Prof.

Atmospheric pressure. 9 ft. 6 ft

Name CEE 4 Final Exam, Aut 00; Answer all questions; 145 points total. Some information that might be helpful is provided below. A Moody diagram is printed on the last page. For water at 0 o C (68 o F):

FLUID MECHANICS. Dynamics of Viscous Fluid Flow in Closed Pipe: Darcy-Weisbach equation for flow in pipes. Major and minor losses in pipe lines.

FLUID MECHANICS Dynamics of iscous Fluid Flow in Closed Pipe: Darcy-Weisbach equation for flow in pipes. Major and minor losses in pipe lines. Dr. Mohsin Siddique Assistant Professor Steady Flow Through

Chapter 8 Flow in Conduits

57:00 Mechanics of Fluids and Transport Processes Chapter 8 Professor Fred Stern Fall 013 1 Chapter 8 Flow in Conduits Entrance and developed flows Le = f(d, V,, ) i theorem Le/D = f(re) Laminar flow:

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

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

External Flow and Boundary Layer Concepts

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

PIPE FLOW. The Energy Equation. The first law of thermodynamics for a system is, in words = +

The Energy Equation PIPE FLOW The first law of thermodynamics for a system is, in words Time rate of increase of the total storage energy of the t Net time rate of energy addition by heat transfer into

FLUID MECHANICS D203 SAE SOLUTIONS TUTORIAL 2 APPLICATIONS OF BERNOULLI SELF ASSESSMENT EXERCISE 1

FLUID MECHANICS D203 SAE SOLUTIONS TUTORIAL 2 APPLICATIONS OF BERNOULLI SELF ASSESSMENT EXERCISE 1 1. A pipe 100 mm bore diameter carries oil of density 900 kg/m3 at a rate of 4 kg/s. The pipe reduces

Water Circuit Lab. The pressure drop along a straight pipe segment can be calculated using the following set of equations:

Water Circuit Lab When a fluid flows in a conduit, there is friction between the flowing fluid and the pipe walls. The result of this friction is a net loss of energy in the flowing fluid. The fluid pressure

Uniform Channel Flow Basic Concepts. Definition of Uniform Flow

Uniform Channel Flow Basic Concepts Hydromechanics VVR090 Uniform occurs when: Definition of Uniform Flow 1. The depth, flow area, and velocity at every cross section is constant 2. The energy grade line,

Applied Fluid Mechanics

Applied Fluid Mechanics 1. The Nature of Fluid and the Study of Fluid Mechanics 2. Viscosity of Fluid 3. Pressure Measurement 4. Forces Due to Static Fluid 5. Buoyancy and Stability 6. Flow of Fluid and

Lecture 30 Review of Fluid Flow and Heat Transfer

Objectives In this lecture you will learn the following We shall summarise the principles used in fluid mechanics and heat transfer. It is assumed that the student has already been exposed to courses in

F L U I D S Y S T E M D Y N A M I C S

F L U I D S Y S T E M D Y N A M I C S T he proper design, construction, operation, and maintenance of fluid systems requires understanding of the principles which govern them. These principles include

Heat Transfer Convection

Heat ransfer Convection Previous lectures conduction: heat transfer without fluid motion oday (textbook nearly 00 pages) Convection: heat transfer with fluid motion Research methods different Natural Convection

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

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

The effect of geometric parameters on the head loss factor in headers

Fluid Structure Interaction V 355 The effect of geometric parameters on the head loss factor in headers A. Mansourpour & S. Shayamehr Mechanical Engineering Department, Azad University of Karaj, Iran Abstract

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

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

Sizing of Gas Pipelines

Sizing of Gas Pipelines Mavis Nyarko MSc. Gas Engineering and Management, BSc. Civil Engineering Kumasi - Ghana mariiooh@yahoo.com Abstract-In this study, an effective approach for calculating the size

Compressible Duct Flow with Friction

Compressible Duct Flow with Friction We treat only the effect of friction, neglecting area change and heat transfer. The basic assumptions are 1. Steady one-dimensional adiabatic flow 2. Perfect gas with

An-Najah National University Civil Engineering Department. Fluid Mechanics. Chapter 1. General Introduction

1 An-Najah National University Civil Engineering Department Fluid Mechanics Chapter 1 General Introduction 2 What is Fluid Mechanics? Mechanics deals with the behavior of both stationary and moving bodies

Fluid Mechanics Prof. T.I. Eldho Department of Civil Engineering Indian Institute of Technology, Bombay. Lecture - 17 Laminar and Turbulent flows

Fluid Mechanics Prof. T.I. Eldho Department of Civil Engineering Indian Institute of Technology, Bombay Lecture - 17 Laminar and Turbulent flows Welcome back to the video course on fluid mechanics. In

Hydraulics for Urban Storm Drainage

Urban Hydraulics Hydraulics for Urban Storm Drainage Learning objectives: understanding of basic concepts of fluid flow and how to analyze conduit flows, free surface flows. to analyze, hydrostatic pressure

UNIT II CONVECTION HEAT TRANSFER

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

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

ME19b. FINAL REVIEW SOLUTIONS. Mar. 11, 2010.

ME19b. FINAL REVIEW SOLTIONS. Mar. 11, 21. EXAMPLE PROBLEM 1 A laboratory wind tunnel has a square test section with side length L. Boundary-layer velocity profiles are measured at two cross-sections and

SENTHIL SELIYAN ELANGO ID: UB3016SC17508 AIU HYDRAULICS (FLUID DYNAMICS)

SENTHIL SELIYAN ELANGO ID: UB3016SC17508 AIU HYDRAULICS (FLUID DYNAMICS) ATLANTIC INTERNATIONAL UNIVERSITY INTRODUCTION Real fluids The flow of real fluids exhibits viscous effect, which are they tend

We will assume straight channels with simple geometries (prismatic channels) and steady state flow (in time).

56 Review Drag & Lift Laminar vs Turbulent Boundary Layer Turbulent boundary layers stay attached to bodies longer Narrower wake! Lower pressure drag! 8. Open-Channel Flow Pipe/duct flow closed, full,

Hydraulic Design Of Polyethylene Pipes

Hydraulic Design Of Polyethylene Pipes Waters & Farr polyethylene pipes offer a hydraulically smooth bore that provides excellent flow characteristics. Other advantages of Waters & Farr polyethylene pipes,

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

M E 320 Professor John M. Cimbala Lecture 24

M E 30 Professor John M. Cimbala Lecture 4 Today, we will: Discuss pump performance curves Discuss how to match a pump and a piping system, and do some example problems. Pump Performance a. Pump performance

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

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

REE 307 Fluid Mechanics II. Lecture 1. Sep 27, Dr./ Ahmed Mohamed Nagib Elmekawy. Zewail City for Science and Technology

REE 307 Fluid Mechanics II Lecture 1 Sep 27, 2017 Dr./ Ahmed Mohamed Nagib Elmekawy Zewail City for Science and Technology Course Materials drahmednagib.com 2 COURSE OUTLINE Fundamental of Flow in pipes

Analysis of Fully Developed Turbulent Flow in a AXI-Symmetric Pipe using ANSYS FLUENT Software

Analysis of Fully Developed Turbulent Flow in a AXI-Symmetric Pipe using ANSYS FLUENT Software Manish Joshi 1, Priyanka Bisht, Dr. Anirudh Gupta 3 1 M. Tech Scholar, M. Tech Scholar, 3 Associate Professor

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

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

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

ρg 998(9.81) LV 50 V. d2g 0.062(9.81)

6.78 In Fig. P6.78 the connecting pipe is commercial steel 6 cm in diameter. Estimate the flow rate, in m 3 /h, if the fluid is water at 0 C. Which way is the flow? Solution: For water, take ρ = 998 kg/m

Chapter 8 INTERNAL FORCED CONVECTION

Heat Transfer Chapter 8 INTERNAL FORCED CONVECTION Universitry of Technology Materials Engineering Department MaE216: Heat Transfer and Fluid bjectives Obtain average velocity from a knowledge of velocity