# Fox and McDonald's Introduction to Fluid Mechanics; 2015, 9th Edition by Philip J. Pritchard

SI Units and PrefixesaSI Units Quantity Unit SI Symbol ulaSI base units Length meter m Mass kilogram kg Time second s Temperature kelvin K SI supplementary unit Plane angle radian rad SI derived units Energy joule J NC1mForce newton N kgC1m/s2Power watt W J/sPressure pascal Pa N/m2Work joule J NC1mSI prefixes Multiplication Factor Prefix SI Symbol1 000 000 000 000 1012tera T1 000 000 000 109giga G1 000 000 106mega M1 000 103kilo k0.01 102centibc0.001 103milli m0.000 001 106micro 0.000 000 001 109nano n0.000 000 000 001 1012pico paSource ASTM SI10-10, IEEE/ASTM SI 10 American National Standard for Metric Practice, ASTM International,West Conshohocken, PA, 2010, www.astm.orgbTo be avoided where possible.Conversion Factors and DefinitionsFundamental Dimension English Unit Exact SI Value Approximate SI ValueLength 1 in. 0.0254 m Mass 1 lbm 0.453 592 37 kg 0.454 kgTemperature 1C14F 5/9 K DefinitionsAcceleration of gravity g98066ms232174fts2Energy Btu British thermal unit amount of energy required to raise the temperature of 1 lbmof water 1C14F 1 Btu 778.2 ftC1lbfkilocalorie amount of energy required to raise the temperature of 1 kg of water1 K1 kcal 4187 JLength 1 mile 5280 ft; 1 nautical mile 6076.1 ft 1852 m exactPower 1 horsepower 550 ftC1lbf/sPressure 1 bar 105PaTemperature degree Fahrenheit, TF95TC32 where TCis degrees Celsiusdegree Rankine, TRTF45967Kelvin, TKTC27315 exactViscosity 1 Poise 0.1 kg/mC1s1 Stoke 0.0001 m2/sVolume 1 gal 231 in.31 ft3 7.48 galUseful Conversion FactorsLength 1 ft 0.3048 m1 in. 25.4 mmMass 1 lbm 0.4536 kg1 slug 14.59 kgForce 1 lbf 4.448 N1 kgf 9.807 NVelocity 1 ft/s 0.3048 m/s1 ft/s 15/22 mph1 mph 0.447 m/sPressure 1 psi 6.895 kPa1 lbf/ft2 47.88 Pa1 atm 101.3 kPa1 atm 14.7 psi1 in. Hg 3.386 kPa1 mm Hg 133.3 PaEnergy 1 Btu 1.055 kJ1ftC1lbf 1.356 J1 cal 4.187 JPower 1 hp 745.7 W1ftC1lbf/s 1.356 W1 Btu/hr 0.2931 WArea 1 ft2 0.0929 m21 acre 4047 m2Volume 1 ft3 0.02832 m31 gal US 0.003785 m31 gal US 3.785 LVolume flow rate 1 ft3/s 0.02832 m3/s1 gpm 6.309 10 5m3/sViscosity dynamic 1 lbfC1s/ft2 47.88 NC1s/m21 g/cmC1s 0.1 NC1s/m21 Poise 0.1 NC1s/m2Viscosity kinematic 1 ft2/s 0.0929 m2/s1 Stoke 0.0001 m2/sFor more ination, visit WileyPLUS builds students confidence because it takes the guesswork out of studying by providing students with a clear roadmap what to do how to do it if they did it rightIt offers interactive resources along with a complete digital textbook that help students learn more. With WileyPLUS, students take more initiative so youll have greater impact on their achievement in the classroom and beyond.WileyPLUS is a research-based online environment for effective teaching and learning.Now available forALL THE HELP, RESOURCES, AND PERSONAL SUPPORT YOU AND YOUR STUDENTS NEED Support 24/7FAQs, online chat,and phone support from an experienced student userCollaborate with your colleagues,find a mentor, attend virtual and liveevents, and view resources2-Minute Tutorials and allof the resources you and yourstudents need to get startedYour WileyPLUS Account Manager, providing personal training and supportwww.WhereFacultyCPre-loaded, ready-to-use assignments and presentationscreated by subject matter expertsStudentPartnerProgramQuickStart Courtney Keating/iStockphotoFOX AND MCDONALD SIntroduction to Fluid Mechanics9th editionPhilip J. Pritchard Manhattan CollegeJohn W. Mitchell University of Wisconsin-MadisonWith special contributions fromJohn C. Leylegian Manhattan CollegeAll modern racing cars, such as the ones shown on the cover, are aerodynamically designed to minimizedrag and generate a downforce. As shown in the photograph, there are front and rear wings that, differentfrom an airplane, produce a downward force rather than lift. This aerodynamic downforce improvestraction without adding significant weight to the car. Although you cannot see it, the undercarriage ofthe vehicle is also designed to route the airflow carefully and develop an additional downforce. Usingdownforce allows high cornering speeds on the twisting, turning road courses typical of ula 1races. The maximum downforce can exceed twice the weight of the car at 200 mph straightawayspeeds The aerodynamic drag is reduced by the careful design of the fuselage, the drivers helmet, thesteering linkages, and all of the other parts of the car exposed to airflow that might cause turbulence.There is a tradeoff between in that a high downforce also increases the drag somewhat, which reducesstraightaway speed. Racing cars are designed to optimize this tradeoff for each type of racing course.VICE PRESIDENT AND CUTIVE PUBLISHER Don FowleyCUTIVE EDITOR Linda RattsSPONSORING EDITOR Mary OSullivanPROJECT EDITOR Ellen KeohaneEDITORIAL PROGRAM ASSISTANT Emily MeussnerMARKETING MANAGER Christopher RuelSENIOR PRODUCT DESIGNER Jennifer WelterDESIGN DIRECTOR Harold NolanSENIOR DESIGNER Madelyn LesureSENIOR PHOTO EDITOR Billy RaySENIOR CONTENT MANAGER Ellinor WagnerSENIOR PRODUCTION EDITOR Timothy LindnerCOVER DESIGN Madelyn LesureThis book was set in 10/12 STIX. The book was set by Laserwords Pvt. Ltd. and printed and bound by Courier/Kendallville. Thecover was printed by Courier/Kendallville.This book is printed on acid-free paper.Founded in 1807, John Wiley previousstudies had put that multiple at about seven times In the lower48 states, the potential from wind power is 16 times more thantotal electricity demand in the United States, the researcherssuggested,againmuchhigherthana2008DepartmentofEnergystudy that projected wind could supply a fifth of all electricity inthe country by 2030. The findings indicate the validity of theoften made claim that “the United States is the Saudi Arabia ofwind.” The new estimate is based the idea of deploying 2.5- to3-megawatt MW wind turbines in rural areas that are neitherfrozen nor forested and also on shallow offshore locations, anditincludesaconservative20percentestimateforcapacityfactor,which is a measure of how much energy a given turbine actuallyproduces. It has been estimated that the total power from thewind that could conceivably be extracted is about 72 terawattsTW 721012watts. Bearing in mind that the total power con-sumption by all humans was about 16 TW as of 2006, it is clearthat wind energy could supply all the worlds needs for the fore-seeable futureOne reason for the new estimate is due to the increasinglycommon use of very large turbines that rise to almost 100m,where wind speeds are greater. Previous wind studies werebased on the use of 50- to 80-m turbines. In addition, to reacheven higher elevations and hence wind speed, two approacheshave been proposed. In a recent paper, Professor Archer atCalifornia State University and Professor Caldeira at theCarnegie Institution of Washington, Stanford, discussed somepossibilities. One of these is a design of KiteGen shown in thefigure, consisting of tethered airfoils kites manipulated by acontrolunitandconnectedtoaground-based,carousel-shapedgenerator; the kites are maneuvered so that they drive thecarousel, generating power, possibly as much as 100 MW. Thisapproach would be best for the lowest few kilometers of theatmosphere. An approach using further increases in elevationCourtesy of Ben Shepard and Archer however, you will have devel-oped a good understanding of the concepts behind all of these, and many other applications, and havemade significant progress toward being ready to work on such state-of-the-art fluid mechanics projects.To start toward this goal, in this chapter we cover some very basic topics a case study, what fluidmechanics encompasses, the standard engineering definition of a fluid, and the basic equations ands of analysis. Finally, we discuss some common engineering student pitfalls in areas such as unitsystems and experimental analysis.Note to StudentsThis is a student-oriented book We believe it is quite comprehensive for an introductory text, and astudent can successfully self-teach from it. However, most students will use the text in conjunction withone or two undergraduate courses. In either case, we recommend a thorough reading of the relevantchapters. In fact, a good approach is to read a chapter quickly once, then reread more carefully a secondand even a third time, so that concepts develop a context and meaning. While students often find fluidmechanics quite challenging, we believe this approach, supplemented by your instructors lectures thatwill hopefully amplify and expand upon the text material if you are taking a course, will reveal fluidmechanics to be a fascinating and varied field of study.Othersources ofinationonfluidmechanicsarereadilyavailable.Inadditiontoyourprofessor,there are many other fluid mechanics texts and journals as well as the Internet a recent Google searchfor “fluid mechanics” yielded 26.4 million links, including many with fluid mechanics calculators andanimations.Therearesomeprerequisitesforreadingthistext.Weassumeyouhavealreadystudiedintroductorythermodynamics,aswellasstatics,dynamics,andcalculus; however,asneeded,wewillreviewsomeofthis material.It is our strong belief that one learns best by doing. This is true whether the subject under study isfluid mechanics, thermodynamics, or soccer. The fundamentals in any of these are few, and mastery ofthem comes through practice. Thus it is extremely important that you solve problems. The numerousproblems included at the end of each chapter provide the opportunity to practice applying fundamentalsto the solution of problems. Even though we provide for your convenience a summary of useful equa-tions at the end of each chapter except this one, you should avoid the temptation to adopt a so-calledplug-and-chug approach to solving problems. Most of the problems are such that this approach simplywill not work. In solving problems we strongly recommend that you proceed using the following log-ical steps1 State briefly and concisely in your own words the ination given.2 State the ination to be found.3 Draw a schematic of the system or control volume to be used in the analysis. Be sure to label theboundaries of the system or control volume and label appropriate coordinate directions.4 Give the appropriate mathematical ulation of the basic laws that you consider necessary to solvethe problem.5 List the simplifying assumptions that you feel are appropriate in the problem.is to generateelectricityaloftandthentransmit it tothe surfacewith a tether. In the design proposed by Sky Windpower, fourrotors are mounted on an airframe; the rotors both provide liftfor the device and power electricity generation. The aircraftwould lift themselves into place with supplied electricity toreach the desired altitude but would then generate up to40 MW of power. Multiple arrays could be used for large-scaleelectricity generation.2 Chapter 1 Introduction6 Complete the analysis algebraically before substituting numerical values.7 Substitute numerical values using a consistent set of units to obtain a numerical answer.a Reference the source of values for any physical properties.b Be sure the significant figures in the answer are consistent with the given data.8 Check the answer and review the assumptions made in the solution to make sure they are reasonable.9 Label the answer.In your initial work this problem at may seem unnecessary and even long-winded. However, it isour experience that this approach to problem solving is ultimately the most efficient; it will also prepareyou to be a successful professional, for which a major prerequisite is to be able to communicate infor-mation and the results of an analysis clearly and precisely. This at is used in all examples presentedin this text; answers to examples are rounded to three significant figures.Finally, we strongly urge you to take advantage of the many Excel tools available for this book onthe text website for use in solving problems. Many problems can be solved much more quickly usingthese tools; occasional problems can only be solved with the tools or with an equivalent computerapplication.Scope of Fluid MechanicsAs the name implies, fluid mechanics is the study of fluids at rest or in motion. It has traditionally beenappliedinsuchareasasthedesignofcanal,levee,anddamsystems;thedesignofpumps,compressors,andpiping and ducting used in the water and air conditioning systems of homes and businesses, as well as thepiping systems needed in chemical plants; the aerodynamics of automobiles and sub- and supersonic air-planes; and the development of many different flow measurement devices such as gas pump meters.While these are still extremely important areas witness, for example, the current emphasis onautomobile streamlining and the levee failures in New Orleans in 2005, fluid mechanics is truly a“high-tech” or “hot” discipline, and many exciting areas have developed in the last quarter-century.Some examples include environmental and energy issues e.g., containing oil slicks, large-scale windturbines, energy generation from ocean waves, the aerodynamics of large buildings, and the fluidmechanicsoftheatmosphereandoceanandofphenomenasuchastornadoes,hurricanes,andtsunamis;biomechanics e.g., artificial hearts and valves and other organs such as the liver; understanding of thefluid mechanics of blood, synovial fluid in the joints, the respiratory system, the circulatory system, andthe urinary system; sport design of bicycles and bicycle helmets, skis, and sprinting and swimmingclothing, and the aerodynamics of the golf, tennis, and soccer ball; “smart fluids” e.g., in automobilesuspension systems to optimize motion under all terrain conditions, military unis containing a fluidlayer that is “thin” until combat, when it can be “stiffened” to give the soldier strength and protection,andfluidlenseswithhumanlikeproperties foruseincamerasandcellphones;andmicrofluidse.g.,forextremely precise administration of medications.These are just a small sampling of the newer areas of fluid mechanics. They illustrate how the dis-cipline is still highly relevant, and increasingly diverse, even though it may be thousands of years old.Definition of a FluidWealreadyhaveacommon-senseideaofwhenweareworkingwithafluid,asopposedtoasolidFluidstendtoflowwhenweinteractwiththeme.g.,whenyoustiryourmorningcoffee; solidstendtodeorbende.g.,whenyoutypeonakeyboard,thespringsunderthekeyscompress.Engineersneedamoreal and precise definitionofafluidA fluid is asubstance that des continuouslyunder theappli-cationofasheartangentialstressnomatterhowsmalltheshearstressmaybe.Becausethefluidmotioncontinues under the application of a shear stress, we can also defi