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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
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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
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| Latex |
|---|
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\large\[V_\alpha\] |
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travel
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| Latex |
|---|
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\large\[L + b\tan (\alpha )\] |
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Now,
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we
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know
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that
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one
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way
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to
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determine
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the
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travel
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time
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of
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a
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particle
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is
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to
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divide
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the
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distance
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travelled
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by
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the
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particle
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by
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the
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particle
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velocity.
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Therefore,
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we
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can
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equate
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the
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following
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travel
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times:
| Latex |
|---|
}\large\[\frac{d}{{V_c \cos (\alpha )}} = \frac{{L + d\tan(\alpha )}}{{V_\alpha }} = \frac{{L\sin (\alpha ) + \frac{b}{{\cos (\alpha )}}}}{{V_{up} }}\]{latex} |
Solving
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for
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the
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capture
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velocity
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by
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equating
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the
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first
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and
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third
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expressions,
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we
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find
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that:
| Latex |
|---|
{latex}\large\[V_c = \frac{{dV_{up} }}{{L_{tube} \sin (\alpha )\cos(\alpha ) + d}}\]{latex} |
Where
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L
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is
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the
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length
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of
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the
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tube,
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d
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is
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the
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inner
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diameter
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of
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the
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tube,
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Vup
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is
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the
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vertical
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velocity
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through
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one
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tube,
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and
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| Latex |
|---|
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\large |
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\[\alpha \] |
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equal
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to
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sixty
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degrees.
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From
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the
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capture
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velocity
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equation
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just
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derived,
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it
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is
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evident
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that
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capture
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velocity
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is
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dependent
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on
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the
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diameter,
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length,
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and
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angle
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of
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the
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tube
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settlers,
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as
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well
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as
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the
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flow
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rate
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through
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the
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settlers.
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