Chapter 4 Stokes Law
Chapter 4 Stokes Law
Chapter 4 Stokes Law
where
vs
g
s
dp
Cd
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Reynolds Number
In fluid mechanics, the Reynolds Number, Re (or NR), is a dimensionless
number that is the ratio of inertial forces to viscous forces.
It quantifies the relative importance of these two types of forces for a
given set of flow conditions.
where:
v = mean velocity of an object relative to a fluid (m/s)
L = characteristic dimension, (length of fluid; particle diameter) (m)
= dynamic viscosity of fluid (kg/(ms))
= kinematic viscosity ( = /) (m/s)
= fluid density (kg/m)
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Temperature
Fluid Density
Particle Density
Particle Size
Particle Shape
Degree of Turbulence
Volume fraction of solids
Solid surface charge and pulp chemistry
Magnetic and electric field strength
Vertical velocity of fluid
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For a sphere:
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Vh/V = (1 - Cv)4.65
where
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McGhee, T.J., 1991. Water Resources and Environmental Engineering. Sixth Edition. McGraw-Hill, New York.
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Retention Time
Average time spent in the vessel by an element
of the suspension
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The Significance of H
Side view
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The Significance of H
Only a fraction of particles with a settling velocity vx
(less than vo) will settle out. The fraction Fx of particles
dx (with velocity vx) that settle out is:
The Significance of H
Only a fraction of particles with a settling velocity vx
(less than vo) will settle out. The fraction Fx of particles
dx (with velocity vx) that settle out is:
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Fraction of particles
with a velocity below vs
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Sedimentation Thickener/Clarifier
Top view
Side view
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where
ub = bulk velocity of slurry
Qu = volumetric flow rate of thickener underflow
A = Surface area of thickener
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where
A = cross-sectional area (m2)
F = feed pulp liquid/solids ratio
L = underflow pulp liquid/solid ratio
s = solids density (g/cm3)
Vm = settling velocity (m/hr)
dw/dt = dry solids production rate (g/hr)
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3-5 m
Diameter (m)
3 - 170 m
Bottom Slope
Rotation Speed
of rake arm
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