Introduction to Agricultural Engineering Technology: A Problem Solving Approach

394 Pages·2007·8.09 MB·English

by  Harry L. Field

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Introduction to Agricultural
Engineering Technology
i
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Introduction to Agricultural
Engineering Technology
A Problem Solving Approach
Third Edition
Harry L. Field and John B. Solie
OklahomaStateUniversity
Stillwater,OK,USA
iii
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HarryL.Field JohnB.Solie
OklahomaStateUniversity,Stillwater,OK, OklahomaStateUniversity,Stillwater,OK,
USA USA
111AgriculturalHall 111AgriculturalHall
Stillwater74078 Stillwater74078
[e-mail] [e-mail]
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
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iv
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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
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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
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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
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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.
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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
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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
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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).