Week # 3 MR Chapter 3 Tutorial #3 MR #3.1, 3.5, 3.9, 3.12. To be discussed on Feb 4, 2015. By either...
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Transcript of Week # 3 MR Chapter 3 Tutorial #3 MR #3.1, 3.5, 3.9, 3.12. To be discussed on Feb 4, 2015. By either...
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Week # 3MR Chapter 3
• Tutorial #3• MR #3.1, 3.5, 3.9, 3.12.
• To be discussed on Feb 4, 2015.
• By either volunteer or class list.
MARTIN RHODES (2008) Introduction to Particle Technology , 2nd Edition. Publisher John Wiley & Son, Chichester, West Sussex, England.
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Settling of a suspension of particles
Equation (3.5)
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Ufs
Equation (3.6)
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Batch settling
Re < 0.3:
Re > 500:
Equation (3.20)
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Khan & Richardson
Archimedes number, Ar:
Equation (*): A maximum is observed at = (n/(n+1);Inflection point at = (n-1)/(n+1)
(*)
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• Sharp interfaces in sedimentation
Variation of dimensionless setting flux with suspension concentration ReP<0.3, n=4.65
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Concentration interface in sedimentation
UPS1, UPS2 are particle volumetric flux Ups = Up * C =Up * (1-)
(a) The gradient of the curve at concentration C is the velocity of a layer of suspension of this concentration.(b) The slope of a chord joining two points at concentration C1 and C2 is the velocity of discontinuity or interface between suspensions of these concentrations.
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• The batch settling test
Determination of interface and layer velocities from a batch flux plot
C2
C3C2
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Type 1 batch settling. Zones A, B and S are zones of constant concentration.Zone A is a clear liquid; zone B is a suspension of concentration equal to the initial
suspension concentration; zone S is a suspension of settled bed or sediment concentration
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Change in positions of interface AB, BS and AS with time in Type 1 batch settling
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Type 2 batch settling. Zones A, B and S are zones of constant concentration.Zone A is clear liquid; zone B is a suspension of concentration equal to the initial
suspension concentration; zone S is a suspension of settled bed concentration. ZoneE is a zone of variable concentration.
S
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Change in positions of interface AB, BEmin, EmaxS and AS with time in Type 2 batch settling
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Determining if settling will be Type 1 or Type 2. A line through CS tangent to the flux curve gives CB1 and CB2. Type 2 settling occurs when initial
suspension concentration is between CB1 and CB2.
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• Relationship between the Height-Time curve and the flux plot
Analysis of batch settling test
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Analysis of batch settling; relative velocities of a plane of concentration C and the particles in the plane
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Volume of particles which have passed through this plane in time t
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Continuous settling
• Settling of a suspension in a flowing fluid
Continuous settling; downflow only
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** Upward flow of a particle suspension in a vessel gives total downward particle flux.
**(1-)
Equation (3.41)
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Total flux plot for settling in downward flow
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Total flux plot for settling in upward flow
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• A real thickener (with upflow and downflow sections)
A real thickener, combining upflow and downflow (F, L and V are volumes; CF, CL and CV are concentrations)
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Total flux plot for a thickener at
critical loading
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Total flux plot for an underloaded
thickener
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Total flux plot for an overloaded thickener
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Alternative total flux plot shape;
thickener at critical loading
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Alternative total flux plot shape;
Overloaded thickener
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