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Unformatted text preview: 492 PHYSICAL TREATMENT METHODS 0
E
O
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.0
.5 Outlet zone Spherical
particle FIGURE 12.15 Definition sketch for a spheried particle settling in (a) m idediud rectangular
horizontdﬂow settling tank and (b) a ﬂuid whim to the form of buoyancy,
gravity, and drag. balance can be written for a discrete particle that is settling:
d ,
mfﬁf=rg—I;—rb 022» where m p = mass of settling particle, kg
vs = particle settling velocity, m/s
FG = gravitational force, N
F, = buoyant force, N
F D = drag force, N
The net gravitational force is given by
Fa—Fa= (10,, Pw)ng (12.23)
where
pp = density of particle, kg/m3
pw = density of water, kg/m3
g = acceleration due to gravity, m/s2
VP = volume of particle (1rd 3 /6), m3
d p = diameter of particle, m
The drag force is a function of the crosssectional area of the particle, the settling velocity of the particle, the liquid density, and the coeﬂicient
of drag: 2
5=g¢ag (um 12.7 SEDIMENTATION 493 where CD = coeﬂicient of drag A p = crosssectional area of particle (adj/4), m2 pw = density of water, kg/m3
vs = particle settling velocity, m/s For spherical particles, the coefﬁcient of drag can be estimated using
the following relationship: CD=24.+ 3 Nkﬁv: + 0.34 (1225) where
N R = Reynolds number, dimensionless
v: d p pw p.
p. = liquid viscosity, kg/ m  s and other terms are as deﬁned previously. In the ideal system, the terminal settling velocity is attained quickly,
and the acceleration term can be assumed to be negligible. Thus, Eq.
(12.22) can be rewritten as F0 — FB = FD (12.26) Substituting Eq. (12.23) for F6 — F3 and Eq. (12.24) for FD and solving
for the settling velocity 03 yields u, = — —— (12.27) where d p is the diameter of the particle, in meters, and the other terms
are as deﬁned previously. When NR < 0.3, the ﬁrst term of Eq. (12.25)
predominates, and the discrete particle settling rate becomes (Stokes’ law)
g( p,  Md}
Us _ 18” (12.28)
where pp = particle density, kg/m3
)1 = liquid viscosity, kg/ m  s Particle densities in water and wastewater treatment vary consider
ably, but fall into distinct bands. Organic materials (bacteria, food
particles, and fecal particles) usually have densities in the 1030 to 1100
kg/m3 range. Chemical ﬂocs produced in precipitation reactions have WATER QUALITY MANAGEMENT WATER]
[Mil W CHARACTERISTICS  MODELING  MODIFICATION George Tchobanoglous
Edward D. Schroeder UNIVERSITY OF CALIFORNIA AT DAVIS Addison I a] W isley 1 Longman Reading, Massachusetts I Menlo Park, California Don Mills, Ontario I Wokingham, England I Amsterdam I Sydney
Singapore I Tokyo I Mexico City I Bogota Santiago I San Juan ...
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This note was uploaded on 05/20/2010 for the course EVEG 3110 taught by Professor Malone during the Spring '10 term at LSU.
 Spring '10
 Malone

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