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A
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common
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parameter
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used
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to
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describe
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sedimentation
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is
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the
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capture
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velocity.
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Capture
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velocity
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is
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the
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velocity
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of
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the
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floc
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that
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is
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only
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barely
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settled-out,
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or
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"captured",
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during
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the
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sedimentation
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process.
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To
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gain
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a
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more
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profound
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understanding
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of
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this
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crucial
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parameter,
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we
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will
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walk
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through
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the
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derivation
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of
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the
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capture
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velocity
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equation.
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The
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figure
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below
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illustrates
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the
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longest
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path
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that
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a
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floc
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is
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able
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to
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travel
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in
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a
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sedimentation
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tube
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and
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still
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be
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captured.
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Figure 1.
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Longest
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possible
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path
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of
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a
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floc
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through
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a
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sedimentation
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tube.
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The
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capture
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velocity
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is
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the
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velocity
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that
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the
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particle
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must
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travel
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to
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fall
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a
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distance
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'x'
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(see
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figure
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above)
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in
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the
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same
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amount
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of
...
time
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that
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a
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particle
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traveling
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at
...
| Latex |
|---|
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\large\[V_\alpha\] |
...
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travel
| Latex |
|---|
\large\[L + |
...
b\tan (\alpha )\] |
Now, we know that one way to determine the travel time of a particle is to divide the distance travelled by the particle by the particle velocity. Therefore, we can equate the following travel times:
| Latex |
|---|
\large\[\frac{d}{{V_c \cos (\alpha )}} = \frac{{L + d\tan(\alpha )}}{{V_\alpha }} = \frac{{L\sin (\alpha ) + \frac{b}{{\cos (\alpha )}}}}{{V_{up} }}\] |
Solving for the capture velocity by equating the first and third expressions, we find that:
| Latex |
|---|
\large\[V_c = \frac{{dV_{up} }}{{L_{tube} \sin (\alpha )\cos(\alpha ) + d}}\] |
Where L is the length of the tube, d is the inner diameter of the tube, Vup is the vertical velocity through one tube, and
| Latex |
|---|
\large\[\alpha \] |
From the capture velocity equation just derived, it is evident that capture velocity is dependent on the diameter, length, and angle of the tube settlers, as well as the flow rate through the settlers.