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INTRODUCTION
REFERENSI
1. C.J. GEANKOPLIS : “TRANSPORT PROCESSES AND UNIT
OPERATIONS”, EDISI 3, PRENTICE HALL INTERNATIONAL,
1995
2. N. de NEVERS : “FLUID MECHANICS FOR CHEMICAL
ENGINEERS”, EDISI 2, McGRAW HILL INTERNATIONAL,1991
3. R.S. BRODKEY & H.C. HERSHEY: “TRANSPORT PHENOMENA,
A UNIFIED APPROACH”, INTERNATIONAL EDITION, McGRAW
HILL, 1989
4. J.M. WELTY, C.E. WICKS & R.E. WILSON: “FUNDAMENTAL OF
MOMENTUM, HEAT, AND MASS TRANSFER”, EDISI 4, JOHN
WILEY & SONS, 2001
MOMENTUM
TRANSFER or
FLUID MECHANICS
Sir Isaac Newton
1642-1727
MECHANICS AND GRAVITATION
According to the well-known story, it was on seeing an apple fall in his orchard at some time during 1665
or 1666 that Newton conceived that the same force governed the motion of the Moon and the apple. He
calculated the force needed to hold the Moon in its orbit, as compared with the force pulling an object
to the ground. He also calculated the centripetal force needed to hold a stone in a sling, and the relation
between the length of a pendulum and the time of its swing. These early explorations were not soon
exploited by Newton, though he studied astronomy and the problems of planetary motion.
Correspondence with Hooke (1679-1680) redirected Newton to the problem of the path of a body
subjected to a centrally directed force that varies as the inverse square of the distance; he determined
it to be an ellipse, so informing Edmond Halley in August 1684. Halley's interest led Newton to
demonstrate the relationship afresh, to compose a brief tract on mechanics, and finally to write the
Principia.
Book I of the Principia states the foundations of the science of mechanics, developing upon them the
mathematics of orbital motion round centres of force. Newton identified gravitation as the fundamental
force controlling the motions of the celestial bodies. He never found its cause. To contemporaries who
found the idea of attractions across empty space unintelligible, he conceded that they might prove to be
caused by the impacts of unseen particles.
Book II inaugurates the theory of fluids: Newton solves problems of fluids in movement and of motion
through fluids. From the density of air he calculated the speed of sound waves.
Book III shows the law of gravitation at work in the universe: Newton demonstrates it from the
revolutions of the six known planets, including the Earth, and their satellites. However, he could never
quite perfect the difficult theory of the Moon's motion. Comets were shown to obey the same law; in
later editions, Newton added conjectures on the possibility of their return. He calculated the relative
masses of heavenly bodies from their gravitational forces, and the oblateness of Earth and Jupiter,
already observed. He explained tidal ebb and flow and the precession of the equinoxes from the forces
exerted by the Sun and Moon. All this was done by exact computation.
Newton's work in mechanics was accepted at once in Britain, and universally after half a century. Since
then it has been ranked among humanity's greatest achievements in abstract thought. It was extended
and perfected by others, notably Pierre Simon de Laplace, without changing its basis and it survived into
the late 19th century before it began to show signs of failing. See Quantum Theory; Relativity.
TRANSPORT PHENOMENA ?
• TRANSPORT PHENOMENA = FENOMENA
PERPINDAHAN = PERISTIWA PERPINDAHAN
• TRANSPORT PHENOMENA MELIBATKAN 3
(TIGA) PROSES PERPINDAHAN :
•PERPINDAHAN MASSA
•PERPINDAHAN PANAS
•PERPINDAHAN MOMENTUM
• PROSES PERPINDAHANNYA SERING TERJADI
SECARA SIMULTAN DENGAN ANALOGI SAMA
MEKANISME TRANSFER
• MEKANISME TRANSFER MOLEKULER (MTM)
• MEKANISME TRANSFER TURBULENSI (MTB)
MEKANISME TRANSFER PANAS
MOLEKULER
BENTUK
ANALOGI
Driving force
Rate 
Resistance
HEAT FLOW
HEAT TRANSFER
FIRE
Fluks
panas
J/s.m2
HK FOURIER
d c pT 
qz
 
A
dz
Difusivitas
panas,
m2/s
Kons.
panas
J/m3
MEKANISME TRANSFER MASSA
MOLEKULER
BENTUK
ANALOGI
N2
O2
MASS TRANSFER
Fluks
massa A
mol/s.m2
Driving force
Rate 
Resistance
HUKUM FICK
J
*
Az
dcA
  DAB
dz
Difusivitas
molekul A dlm
B, m2/s
Kons.
massa A
mol/m3
MEKANISME TRANSFER MOMENTUM
MOLEKULER
BENTUK
ANALOGI
LAMINAR FLOW
z
x
MOMENTUM TRANSFER
Fluks mom arah z
akibat komponen
kecepatan x
(kg.m/s)/s.m2
Driving force
Rate 
Resistance
HK NEWTON VISKOSITAS
d vx  
 zx  
dz
Difusivitas
momentum,
 m/
m2/s
Arah
perpindahan
momentum
MOMENTUM TRANSFER ?
MOMENTUM TRANSFER = FLUID MECHANICS
MOMENTUM TRANSFER :
THE STUDY OF FORCE AND MOTION OF
FLUIDS
PENTINGNYA MEKANIKA FLUIDA?
(1)
• PROCESS INDUSTRIES: BEBERAPA MATERIAL
ADALAH DALAM BENTUK FLUIDA DAN HARUS
DISIMPAN, DIHANDLING, DIPOMPA.
• HYDRAULICS: PIPE FLOW, PUMPS, TURBINES
• PARTICLE DYNAMICS : FLOW AROUND PARTICLE,
INTERACTION OF PARTICLES AND FLUIDS
(SETTLING, SLURRIES, PNEUMATIC TRANSPORT,
FLUIDIZED BED, AIR POLLUTANT PARTICLE)
• MULTIPHASE FLOW: COMBUSTION, SPRAYS, FLOW
IN REACTOR, DISTILATION COULOMN
PENTINGNYA MEKANIKA FLUIDA?
• METEREOLOGY: FLOW OF THE ATMOSPHERE
• HYDROLOGY: FLOW WATER IN THE GROUND
• VISCOUS FLOWS : LUBRICATION, INJECTION
MOLDING, EKSTRUKSI POLIMER, DLL
(2)
IDE DASAR dalam MEKANIKA FLUIDA (1)
• 4 PRINCIPLES:
•
•
•
•
CONSERVATION OF MASS
CONSERVATION OF ENERGY= FIRST LAW OF THERMO
SECOND NEWTON’S LAW=SECOND LAW THERMO
NEWTON’S LAW OF MOTION
• SIMPLE FLOWS : BILA 4 PRINSIP DASAR TERSEBUT DAN
SIFAT FISIK TERUKUR DAPAT DISELESAIKAN LANGSUNG
SECARA MATEMATIKA  GAYA, KECEPATAN, DLL
• COMPLEK FLOWS : BILA 4 PRINSIP TERSEBUT HANYA
DAPAT DISELESAIKAN DENGAN EKSPERIMEN, ANALISIS DIMENSI
& SIMULASI CFD
EXAMPLE OF COMPLEX FLOWS
ARROUND A SUBMERGED OBJECT
EXAMPLE OF COMPLEX FLOWS IN
STIRRED TANK ANALYZED BY CFD
Fluid velocity vector
2.50e+00
2.29e+00
2.08e+00
1.87e+00
1.66e+00
1.46e+00
1.25e+00
1.04e+00
8.35e-01
6.27e-01
4.19e-01
Y
2.12e-01
4.17e-03
Z
X
Solid concentration contour
0,08
0,019
0,16
1
0,03
0,20
1
0,046
0,18
1
0,035
0,047
0,041
0,181
0,052
0,046
0,052
0,20
1
0,057
0,22
1
0,063
0,081
0,068
Cav = 5%
0,24
1
0,28
1
Cav = 20%
Local gas hold up at several position from
baffle
00
10
450
EXAMPLE OF COMPLEX FLOWS IN
COMBUSTION ANALYZED BY CFD
Vektor Kecepatan dalam Ruang Bakar
Distribusi Suhu dalam Ruang Bakar
Distribusi Suhu dalam Ruang Bakar
Distribusi CO2 dalam Ruang Bakar
(a)
Distribusi O2 dalam Ruang Bakar