Table Of ContentXian Wen Ng
Engineering
Problems for
Undergraduate
Students
Over 250 Worked Examples with
Step-by-Step Guidance
Engineering Problems for Undergraduate Students
Xian Wen Ng
Engineering Problems
for Undergraduate Students
Over 250 Worked Examples
with Step-by-Step Guidance
XianWenNg
Singapore,Singapore
ISBN978-3-030-13855-4 ISBN978-3-030-13856-1 (eBook)
https://doi.org/10.1007/978-3-030-13856-1
LibraryofCongressControlNumber:2019935805
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Preface
Engineering Problems for Undergraduate Students contains over 250 example
problems covering key topics in engineering courses. Step-by-step solutions are
presented with clear and detailed explanations. This book will support a thorough
understanding of fundamental concepts in engineering for tertiary-level students.
The problems in this book are quality examples which were carefully selected to
demonstrate the application of abstract concepts in solving practical engineering
problems, with comprehensive guidance provided in the explanations that follow
eachstepofthesolutions.
Topics included in this book are fundamental in the engineering discipline.
Hence,theyareversatileintheiroverarchingapplicationacrossvariousengineering
sub-specializations.Thesetopicsincludethermodynamics,fluidmechanics,separa-
tionprocesses(e.g., flashdistillation), reactordesignandkinetics(includingbiore-
actor concepts), and engineering mathematics (e.g., Laplace transform,
differentiationandintegration,Fourierseries,statistics).
Thereisalsoasectionincludedwhichsummarizeskeymathematicalformulaand
other useful data commonly referred to when solving engineering problems. This
book will support step-by-step learning for students taking first or second-year
undergraduatecoursesinengineering.
Singapore XianWenNg
v
Acknowledgments
MyheartfeltgratitudegoestotheteamatSpringerfortheirunrelentingsupportand
professionalismthroughoutthepublicationprocess.SpecialthankstoMichaelLuby,
Nicole Lowary, and Brian Halm for their kind effort and contributions toward
making this publication possible. I am also deeply appreciative of the reviewers
formymanuscriptwhohadprovidedexcellentfeedbackandnumerousenlightening
suggestionstohelpimprovethebook’scontents.
Finally,Iwishtothankmylovedoneswhohave,asalways,offeredonlypatience
andunderstandingthroughouttheprocessofmakingthisbookareality.
vii
Contents
Mathematics. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
UsefulMathematicalFormula. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
ComplexNumbers. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
HyperbolicTrigonometricFunctions. . . . . . . . . . . . . . . . . . . . . . . . . . 2
TrigonometricFormulaeandIdentities. . .. . . .. . . .. . . .. . . . .. . . .. 3
GraphicalTransformationsandCommonFunctions. . . . . . . . . . . . . . . 4
PowerSeries. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
FourierSeries. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
DifferentiationTechniques. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
IntegrationTechniques. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
UsefulIntegrals. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
PartialFractions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
DifferentiationandIntegration. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
LaplaceTransformandTransferFunctions. . . . . . . . . . . . . . . . . . . . . . . 55
MultipleIntegrals. . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79
FourierSeries. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85
Statistics. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 100
EigenfunctionsandEigenvalues. .. . . . .. . . .. . . . .. . . .. . . . .. . . . .. 113
Thermodynamics. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 127
SeparationProcesses. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 211
ReactorKinetics. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 419
FluidMechanics. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 579
Index. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 729
ix
About the Author
Xian Wen Ng graduated with First-Class Honors from the University of Cam-
bridge,UK,withaMaster’sDegreeinChemicalEngineeringandBachelorofArts
in2011andwassubsequentlyconferredaMasterofArtsin2014.Shewasranked
second in her graduating class and was the recipient of a series of college scholar-
ships, including the Samuel Taylor Scholarship, Thomas Ireland Scholarship, and
British Petroleum Prize in Chemical Engineering, for top performance in consecu-
tive years of academic examinations. Ng was also one of two students from
CambridgeUniversityselectedfortheCambridge-MassachusettsInstituteofTech-
nology (MIT) exchange program in Chemical Engineering, which she completed
withHonorswithacumulativeGPAof4.8(5.0).DuringhertimeatMIT,shewas
alsoapart-timetutorforjuniorclassesinengineeringandpursuedotherdisciplines
includingeconomics,realestatedevelopment,andfinanceatMITaswellastheJohn
F.KennedySchoolofGovernmentatHarvardUniversity.Upongraduation,Ngwas
electedbyherCollegeFellowshiptotheTitleofScholar,asamarkofheracademic
distinction.
Since graduation, Ng has been keenly involved in teaching across various
academic levels, doing so both in schools and with smaller groups as a private
tutor.Ng’stopicsofspecializationrangefromsecondary-levelMathematics,Phys-
ics,andChemistrytotertiary-levelMathematicsandEngineeringsubjects.
xi
Mathematics
Useful Mathematical Formula
Before we begin to tackle mathematics, we should familiarize ourselves with
mathematicalformulaeoridentitiesthathelpusobservepatternsinproblems
andhencededucemoreefficientapproachestosolutions.Ihavelistedbelowa
collectionofusefulidentitiesandformulaethatareworthremembering.
Complex Numbers
Thecomplexnumberzcanbeexpressedinthefollowingforms,wherei2¼(cid:2)1.
©SpringerNatureSwitzerlandAG2019 1
X.W.Ng,EngineeringProblemsforUndergraduateStudents,
https://doi.org/10.1007/978-3-030-13856-1_1
2 Mathematics
InCartesianform,wherez*isthecomplexconjugateofz.
z¼xþiy; z(cid:3) ¼x(cid:2)iy
jzj¼x2þy2 ¼zz(cid:3)
Inpolarform,whereθistheargumentofz.
z¼reiðθþ2nπÞ
jzj¼r
x¼rcosθ; y¼rsinθ
Intrigonometricform
z¼rðcosθþisinθÞ
(cid:1) (cid:3)
1
cosθ¼ eiθþe(cid:2)iθ
2
(cid:1) (cid:3)
1
sinθ¼ eiθ(cid:2)e(cid:2)iθ
2i
DeMoivre’sTheorem
ðcosθþisinθÞn ¼einθ ¼ cosnθþisinnθ
Hyperbolic Trigonometric Functions
coshz¼ cosiz
isinhz¼ siniz
itanhz¼ taniz
