Post on 07-Apr-2022
CEE 633 Physical & Chemical TreatmentLecture 18. Ch. 10
Prof. Albert S. Kim
Civil and Environmental Engineering, University of Hawaii at Manoa
Thursday, October 18, 2011
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Circular Sedimentation Tankh 0
r0
ri
vf
The fluid velocity vf
vf =Q
2π (r − ri)h0
as r → r0, vf (↓). The distance a particle has set-tled
h = t · vc =(r2 − r2i
)h0
Qvc
where t is the settling time. The particle travelingvelocity vc is equal to overflow rate (OR)
vc =h0τ
= h0Q
π(r20 − r2i
)h0
=Q
π(r20 − r2i
) =Q
A= OR
Particles of settling velocity greater than or equal to vc are all removed.
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Therefore,
h =π(r2 − r2i
)h0
Q
Q
π(r20 − r2i
) =
(r2 − r2ir20 − r2i
)h0
In other wordsh
r2 − r2i=
h0r20 − r2i
Interpretation,1 Given h, if the particle’s radial distance < r,⇒ settled.2 Given r, if the particle’s depth > h,⇒ settled.
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Basin ConditionsCritical scour velocity by Camp
vsc =
√8k
fg
(ρp − ρfρf
)dp
The width-to-length ratio of a basin is related to the travel velocity of thewater for excess velocity values that would result in scour.
Horizontal velocity to cause scouring
k =
{0.04 mono-dispersed0.06 sticky
f = Darcy Weisbach friction factor ~ 0.03For a basin with length/width≥ 5
horizontal velocity < 18m/h = 5mm/sec.Since scour velocity is usually of ' O(0.1)m/s = O(100)mm/s
Conditions1 overflow rate = settling velocity of particles (to be removed)2 The horizontal fluid velocity < scour velocity
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10-3 Flocculant settling in sedimentation basins
Type I: Individual (stabilized) particle (low concentration water surface)
Type II:
particle flocs formed (orthokinetic or differential settling)Settling velocity (↑) as time (↑) by adding coagulant (slow→ fast settling)Capturing of small/tiny particles (or aggregates) by big aggregates. Tinyparticles (which did not participate in initial aggregation) are effectivelyremoved due to
1 Fast settling velocity (↑) due to increased mass (↑) by capturing2 Sweeping effects: scavenging
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Type III:1 hindered settling - near the bottom of basin2 blanket of particles formed , which traps particles below it as it settles (i.e.,
clear-cut interface between turbid and clean regions)3 called zone-settling when the particle settling velocities are affected by
presence of other particles4 concentration is high enough to provide strong drag forces on settling flocs5 settling velocity (↓) as concentration (↑) near the bottom of a basin
Type IV:1 compression settling at high concentration2 particle suspension is consolidated: phase transition from liquid to solid,
e.g., in sludge thickening dewatering processes.3 Water passes through a mat of particles near underdrain.
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Solid flux analysis
Solid fluxGT = Gs +Gb
whereGT = total solid flux toward underdrain [kg/m2 · s]Gs = settling flux in basin due to gravity [kg/m2 · s]Gb = bulk fluid flux due to underflow [kg/m2 · s]
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Settling flux1. Calculation of Gs (with initial particle concentration, Ci )
Settling velocity is defined as
vi =ddblanket
dt|t=0
where dblanket is the (measured) depth of the blanket as a function of time.Then, the settling flux is a product of settling velocity (i.e., downward velocityof the blanket) and the initial concentration Ci: Gs = viCi
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Bulk flux and Total flux2. Calculation of Gb
Qb
A
A'
Qu, C
u
The bulk flux is
Gb =QCi
A=Qu
ACi = ubCi
where ub is the bulk downward velocity.
Because Qb = Qu, ubA = uuA′, because
A > A′ ⇒ ub < uu
3. Then, the total flux is a sum of settling and bulk fluxes:
GT = Gs +Gb = (vi + vb)Ci
where vi and vb are settling velocities of flocs (blanket) and suspension,respectively.
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Settling velocity and solid flux values
Table 10-1. p 801.
Figure: Settling velocity
The solid flux, Gs is a product of solid concentration Ci and initial settlingvelocity vi [m/s].
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Limiting Flux RateIf solid loading > limiting flux rate, then solid will accumulate & overflow
1 Select Cu, the underdrain solidconcentration due to the requirementsof downstream residuals.
2 Obtain GL by drawing a tangent line3 Calculate the downward velocity at
bulk fluid: ub = GL/Cu
Required area for settling: because ub =Q
A=Qu
A=GL
Cu, the area is
A=QuCu
GL
(See Example 10-6, p. 803)12 / 12