Introduction to Agricultural Engineering Technology: A Problem Solving Approach PDF
Preview Introduction to Agricultural Engineering Technology: A Problem Solving Approach
P1:OTE/SPH P2:OTE SVNY306-Field&Solie April15,2007 8:40 Introduction to Agricultural Engineering Technology i P1:OTE/SPH P2:OTE SVNY306-Field&Solie April15,2007 8:40 Introduction to Agricultural Engineering Technology A Problem Solving Approach Third Edition Harry L. Field and John B. Solie OklahomaStateUniversity Stillwater,OK,USA iii P1:OTE/SPH P2:OTE SVNY306-Field&Solie April15,2007 8:40 HarryL.Field JohnB.Solie OklahomaStateUniversity,Stillwater,OK, OklahomaStateUniversity,Stillwater,OK, USA USA 111AgriculturalHall 111AgriculturalHall Stillwater74078 Stillwater74078 [email protected] [email protected] LibraryofCongressControlNumber:2006930107 ISBN-10:0-387-36913-9 e-ISBN-10:0-387-36915-5 ISBN-13:978-0-387-36913-6 e-ISBN-13:978-0-387-36915-0 Printedonacid-freepaper. (cid:2)C 2007SpringerScience+BusinessMedia,LLC Allrightsreserved.Thisworkmaynotbetranslatedorcopiedinwholeorinpartwithoutthewritten permissionofthepublisher(SpringerScience+BusinessMedia,LLC233SpringStreet,NewYork, NY10013,USA),exceptforbriefexcerptsinconnectionwithreviewsorscholarlyanalysis.Use in connection with any form of information storage and retrieval, electronic adaptation, computer software,orbysimilarordissimilarmethodologynowknownorhereafterdevelopedisforbidden. Theuseinthispublicationoftradenames,trademarks,servicemarks,andsimilarterms,evenifthey arenotidentifiedassuch,isnottobetakenasanexpressionofopinionastowhetherornottheyare subjecttoproprietaryrights. 9 8 7 6 5 4 3 2 1 springer.com iv P1:OTE/SPH P2:OTE SVNY306-Field&Solie April15,2007 8:40 Contents 1. ProblemSolving................................................................ 1 2. SignificantFiguresandStandardForm.................................. 17 3. CommonUnitsofMeasure.................................................. 23 4. SimpleMachines............................................................... 36 5. InternalCombustionEngines............................................... 49 6. PowerTrains.................................................................... 61 7. TractorsandPowerUnits.................................................... 80 8. MachineryCalibration....................................................... 93 9. EquipmentEfficiencyandCapacity....................................... 118 10. EconomicsofAgriculturalMachinery.................................... 129 11. SoundandNoise................................................................ 152 12. MeasuringDistance............................................................ 159 13. AnglesandAreas............................................................... 175 14. LandDescription............................................................... 196 15. DifferentialandProfileLeveling........................................... 204 16. Weather........................................................................... 221 v P1:OTE/SPH P2:OTE SVNY306-Field&Solie April15,2007 8:40 vi Contents 17. WaterRunoff.................................................................... 234 18. ErosionandErosionControl................................................ 244 19. Irrigation......................................................................... 253 20. Handling,MoistureManagement,andStorageof BiologicalProducts............................................................ 266 21. AnimalWasteManagement................................................. 279 22. InsulationandHeatFlow.................................................... 286 23. Heating,Ventilation,andAir-Conditioning............................. 293 24. SelectionofStructuralMembers........................................... 319 25. PrinciplesofElectricity....................................................... 326 26. SeriesandParallelCircuits.................................................. 331 27. SizingConductors.............................................................. 340 28. ElectricMotors................................................................. 347 Appendices 356 Index 371 P1:GFZ SVNY306-Field&Solie March28,2007 8:35 1 Problem Solving 1.1. Objectives 1. Beabletodefineproblemsolving. 2. Beabletodescribethecommonproblem-solvingmethods. 3. Beabletoselecttheappropriatemethodforsolvingaproblem. 4. Understandthefunctionanduseofspreadsheets. 5. Understandtheuseofandcommonsymbolsforflowcharts. 1.2. Introduction Problem solving is a part of living. We are faced with a host of problems on a dailybasis.Someoftheseproblemsinvolvepeopleandhumanrelations,whereas othersrequireamathematicalsolution.Inthischapterwewilldealwithproblems involvingmathematicalsolutions,andseveralwaysinwhichtheseproblemscan beapproached. 1.3. Mathematical Problem Solving Mathematicalproblemsolvingistheprocessbywhichanindividualusesprevi- ouslyacquiredknowledge,skills,andunderstandingtosatisfythedemandsofan unfamiliarsituation.Theessenceoftheprocessistheabilitytouseinformation andfactstoarriveatasolution.Therearetwocharacteristicsofproblemsolving thatmustberememberedwhensolvingproblemsusingmathematicalprocesses. 1. The mathematical process does not always give you the answer—just more informationsothatyoucanmakeamoreinformeddecision.Gooddecision-making requiresgoodinformation. 2. Wheneverperfectionisnotpossibleorexpected,levelsorintervalsofaccept- abilitymustbeestablished.Whenperfectionisnotpossiblesomeonemustdeter- minetheamountoferrorthatisacceptable.Theacceptableleveloferrormaybe 1 P1:GFZ SVNY306-Field&Solie March28,2007 8:35 2 1. ProblemSolving determinedbystandards,manufacturers’recommendations,comparisontoanother situationsormachinesorpersonalexperience. Bothofthesecharacteristicswillbeutilizedandexplainedinmoredetailinlater chaptersbyusingexamples. Problemscanbesolvedindifferentways.Oneoftheobjectivesofthischapter istoincreasethereader’sknowledgeofproblem-solvingmethods.Sevendifferent approaches to solving mathematical problems will be discussed: diagrams and sketches,patterns,equationsandformulas,unitscancellation,intuitivereasoning, spreadsheets,andflowcharts. 1.3.1. Diagrams and Sketches Someproblemsinvolvethedeterminationofaquantityofitems,suchasthenumber of nails per sheet of plywood or the number of studs in a wall. In solving these typesofproblemsitusuallyishelpfultodrawasketchoradiagram. Problem: Howmanypostsareneededtobuildafence100ftlongwithposts10ft apart? Solution: Formanypeoplethefirstresponsewouldbe10: 100ft Posts= =10posts 10.0ft/post butadiagram,Figure1.1showsthatthecorrectnumberofpostsis11. This is an example of a situation where a wrong answer is possible if you do notinterprettheproblemcorrectly.Inthisexample,10isthenumberofspaces, notthenumberofposts. FIGURE1.1. Numberofposts. 1.3.2. Patterns Thesolutiontosomeproblemsmaydependuponone’sbeingabletodiscovera patterninanarrayofnumbersorvalues.Frequently,itisconvenienttoexaminethe patternsinasampleratherthantheentirepopulation.Onceapatternisdiscovered andshowntobeconsistentforthesample,itcanbeusedtopredictthesolution fortheentirepopulation. P1:GFZ SVNY306-Field&Solie March28,2007 8:35 MathematicalProblemSolving 3 TABLE1.1. Patternsinnumbers,firstsample. Cownumber Ration Child 1 2 3 4 5 6 7 8 9 10 Grain 1 N N N N N N N N N N Mineral 2 Y Y Y Y Y Hay 3 Y Y Y Silage 4 Y Y Water 5 Y Y Problem: Adairyfarmerhasfivechildren.Eachchildisresponsibleforonepart ofthedailyfeedrationforthefamily’s100dairycows.Theoldestisresponsible forthegrain,thesecondfortheminerals,thethirdforthehay,thefourthforthe silage,andthefifthforwater.Insteadoffeedingeachcow,thefirstchilddecides shewillnotfeedthecowsatallthatday.Thesecondchilddecidesjusttofeedevery other cow, the third child feeds every third cow, and so on. Dad soon discovers howthecowswerefed,andneedstoknowwhichcowsdidnotreceiveanyfeed orwater. Solution: Whenoneisfacedwiththistypeofproblem,itisusuallyhelpfultoset upatable.Inthiscase,itwouldbeverytime-consumingtosetupatableforall100 cows.Instead,selectasampleofthecows.Ifapatternistrueforthesample,there is a high probability that the pattern will be true for a large group. Determining thesizeofasampleisnotalwayseasy.Pickone,andifaclearpatterndoesnot appear, increase the size until a pattern develops. We will start with the first 10 cows,Table1.1. Inthissample,cows#1and#7didnotreceiveanygrain,mineral,hay,silage, orwater.Isthisenoughinformationtoestablishapattern?Wewillpredictthatthe nextcowthatdidnotreceiveanyfeedorwateris#11.Why?Totestthisprediction, thesamplesizemustbeextendedtoincludealargernumberofcows. Table 1.2 shows that the prediction was right; cow #11, along with #13, #17, and#19,didnotreceiveanygrain,minerals,hay,silage,orwater.Itisnowsafeto considerthatthepredictioncouldbeusedtoidentifyalloftheanimalswithinthe herdthatdidnotreceiveanygrain,minerals,hay,silage,orwater(thoseanimals representedbyprimenumbers,thatis,anumberdivisibleonlybyitselfandone). TABLE1.2. Patternsinnumbers,secondsample. Cownumber Ration Child 11 12 13 14 15 16 17 18 19 20 Grain 1 N N N N N N N N N N Mineral 2 Y Y Y Y Y Hay 3 Y Y Y Silage 4 Y Y Y Water 5 Y Y P1:GFZ SVNY306-Field&Solie March28,2007 8:35 4 1. ProblemSolving 1.3.3. Equations and Formulas Equationsandformulasareverysimilarproblem-solvingtools.Sometextsstudy themseparately,butinthissectiontheywillbecombined.Equationsareawayof showingtherelationshipbetweendifferentvariablesinaproblemandareusually derivedasneededforeachproblem.Formulasareequationsthatareusedfrequently enoughoraresomehowuniqueenoughthattheyarerememberedandusedwithout aderivation. 1.3.3.1. Equations Thesolutiontosomeproblemsrequiresthederivationofamathematicalequation based on a pattern or another type of relationship between the numbers. These equationswillbeuniqueforeachproblem. Problem: Howmuchwireisneededtobuildasinglewirefencearoundarectan- gularfieldmeasuring450ftlongand350ftwide? Solution: Inthisexampletherearethreequantities:length,width,andperimeter. It should be obvious that the perimeter is a function of the other two. Begin by assigning the variables L to represent the length, W to represent the width, and Prtorepresenttheperimeter.Then,becausearectanglehastwolengthsandtwo widths,theperimetercanbefoundasfollows: Pr=(L+L)+(W +W) Pr=(450ft+450ft)+(350ft+350ft) =900ft+700ft =1,600ft 1.3.3.2. Formulas Forsomeproblemstherelationshipsofthevariablesarefixedandconstant,sothe equationforthatproblemisrememberedandused.Theseequationsaresometimes calledformulas.Anothercharacteristicofformulasisthattheyusuallycontaina constant.Oneexampleistheareaofacircle:A=πr2.Thevariableπisaconstant. Thereareatleasttwoimportantconsiderationsinusingformulas. 1. Youmustenterthenumberswiththecorrectunitsofmeasure.Allformulasare designedwithspecificunitsforthenumbers,especiallyiftheyhaveaconstant.If the units are incorrect, the answer will be incorrect. An example is the equation usedtodeterminetheapplicationrateofaboomtypesprayer: gal 5,940×Flowrate(gal/min) Applicationrate = ac Speed(mi/hr)×nozzlespacing(in) It should be obvious that the units in the equation do not work (the units when combineddonotresultintheunitsforapplicationrate,gal/min).Thisequationis anexampleofasituationinwhichunitsconversionvalues,thatarealwaysused P1:GFZ SVNY306-Field&Solie March28,2007 8:35 MathematicalProblemSolving 5 eachtimetheproblemisworked,arecombinedintoaunitsconversionconstant (5,940). If any one of the values is entered in different units, the answer will be incorrect. When we solve for the application rate using units cancellation and conversionvalues,thesourceoftheconstantbecomesapparent. gal gal 60min 1hr 1mi = × × × ac min 1hr 1mi 5,280ft 43,560ft2 12in 1 × × × 1ac 1ft 1in 31,363,200 = 5,280 gal =5,940 min 2. You must be able to rearrange the formula to solve for the unknown value. Forexample,theapplicationrateequationcouldberearrangedtosolvefornozzle spacingininches(nsi): 5,940×Flowrate(gal/min) Nozzlespacing(nsi)= Speed(mi/hr)×Applicationrate(gal/ac) For the remainder of this text the terms equation and formula will be used as synonyms. 1.3.4. Units Cancellation Someproblemsaremorecomplexthantheexampleswehaveused,andmanydonot havepatternsorpreviouslydevelopedequations.Equationscanbedevelopedfor someoftheseproblems,butanalternativeapproachisunitscancellation.Problems ofthistypewillusuallyinvolveseveralquantities.Allofthesequantities,except π, will have a unit such as feet, pounds, gallons, and so on. Units cancellation followstwomathematicalprinciples:(1)theunitsofmeasureassociatedwiththe numbers (feet, gallons, minutes, etc.) follow the same mathematical rules as the numbers;(2)theunitsofthenumbersbehaveaccordingtotherulesoffractions. Forexample: 2×2=4or22 Withunitsoffeetthesameequationis: 2ft ×2ft=2×2andft×ftor4ft2 Toreviewtherulesoffractionsstudythefollowingexample: 3 4 3×4 3 × = = 4 5 4×5 5 Inthisexample,the4’sinthenumeratoranddenominatorcancelout(4/4=1).
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