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=
dV/dt=A. P/R
c
Lc
=SV/A
.
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=
Lc =thicknessofaccumulatedsolidinthefiltercake(m)
r=specificresistanceofthefiltercake(kg/m)
V=volumethathaspassedthroughthefilterwith
P=pressuredropacrossthefilter(kg/ms2)
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V/t=A. P/{ r([SV/A]+L)}
negligible:
= 2 2
inmanysituations,canbeusedtopredictpressure
dro re uirementsforafilterdurin theearl sta es
oftheprocess
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Exam leAnairfilterisusedtoremovesmallparticlesfromanair
. . .
Ns/m2)issuppliedatarateof0.5m3/sthroughanairfilter
with a 0.5 m2 crosssection. If the ressure dro across the
filteris0,25cmofwater(=24.52Pa)after1hrofuse,
determinethelifeofthefilterifafilterchangeisrequiredwhenthepressuredropis2.5cmofwater(=245.16Pa).
*Duetothenatureofairfiltration,constantratefiltration
canbeassumedandthefiltermediumthicknessis
neg g e
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CENTRIFUGATIONTheuseofcentrifugalforcetoaccelerateseparation
Fc=mr 2
= /r Fc=(m 2)/r
=2N/60 Fc=0.011mrN2
Fc=centrifugalforce
m=particlemass
r=radiusofthepath
(omega)=angularvelocityoftheparticle
(upsilon)=tangentialvelocityoftheparticle
N=rotationalspeed(revolutionspermin)
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F = m 0.011 r N2
ComparedwithFg =mg
thecentrifugalforceisoftenexpressedforcomparativepurposesassomanyg
Example:
Howmanygcanbeobtainedinacentrifugewhichcan
spinaliquidat2000rev/minatamaximumradiusof
10cm?
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Velocityofsphericalparticlesina
centri uga orce ie
2 2 c p s
c =rateofseparation=velocity
N=speedofrotation
(p s)=densitydifferencebetweenphase
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separatedbycentrifugalforce.Theparticlesare100micronsindiameterwithadensityof800kg/m3.Theliquidiswater
(viscosity=5.95.104 kg/ms;density=993kg/m3).The
effectiveradiusforseparationis7.5cm.Iftherequiredve oc y
orsepara on s . m s, e erm ne erequ re
rotationspeedforthecentrifuge.
