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Sludge
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Drain
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Design
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Program
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This
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program
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designs
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the
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channel
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that
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will
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be
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used
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for
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the
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sedimentation
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tank
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sludge
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drainage.
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The
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sludge
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drain
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runs
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along
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the
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bottom
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of
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the
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each
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sedimentation
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tank
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and
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collects
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the
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flocs
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as
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they
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fall
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from
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the
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lamella
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and
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slopes.
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Sludge
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Drain
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Design
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Algorithm
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Algorithm
The number of sludge drains is determined by the number of sloped pairs in the sedimentation tanks. This is defined as N.SedSludge,
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and
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uses
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the
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number
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of
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slope
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pairs
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calculated
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in
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the
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...
...
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program.
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The
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orifice
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spacing
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of
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the
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sludge
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drain
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is
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set
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so
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that
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there
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are
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two
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orifices
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per
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slope
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plate.
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So
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orifice
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spacing
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is
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calculated
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as
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W.SedSlopePlate/2.
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The
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width
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of
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the
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sed
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slope
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plates
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is
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a
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basic
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user
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input.
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Next,
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the
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number
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of
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orifices
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in
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the
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pipe
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can
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be
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calculated
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given
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the
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orifice
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spacing
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and
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the
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length
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of
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the
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sedimentation
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tank
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from
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the
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program.
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| Include Page | ||||
|---|---|---|---|---|
|
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The
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dimensions
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of
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the
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sludge
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drain
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channel
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and
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the
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sludge
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valve
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are
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determined
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based
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on
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the
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maximum
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acceptable
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head
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loss
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through
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the
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drain.
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Here
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it
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is
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assumed
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that
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we
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are
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willing
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to
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use
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80%
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of
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the
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available
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head
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to
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get
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the
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flow
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through
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the
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valve.
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So
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HL.Valve
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=
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0.8
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HW.Sed.
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Calculation
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of
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the
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diameter
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of
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the
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valve
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requires
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that
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we
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know
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the
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drain
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rate.
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This
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value
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is
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determined
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by
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the
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dimensions
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of
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the
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sed
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tank
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and
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the
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time
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needed
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to
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drain
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the
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tank,
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a
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user
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defined
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value.
| Latex |
|---|
} \large $$ Q_{SedSludgeDrain} = {{W_{SedBay} L_{Sed} HW_{SedSedEst} } \over {0.5Ti_{SludgeDrain} }} $$ {latex} |
This
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initial
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drain
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rate
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is
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then
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used
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to
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calculate
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the
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diameter
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of
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the
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valve
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needed
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via
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the
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D.pipeschedule
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funcion
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of
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the
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...
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program.
| Latex |
|---|
} \large $$ ND_{SedSludgeValve} = D_{pipeschedule} (Q_{SedSludgeDrain} ,EN_{PipeSpec} ,HL_{Valve} ,T_{PlantWall} ,Nu_{Water} ,EpE_{vcPvc} ,K_{GateValve} + K_{PipeExit} ) $$ {latex} |
The
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actual
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head
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loss
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across
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the
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valve
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is
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then
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calculated
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from
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the
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head
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loss
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function
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found
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in
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| Latex |
|---|
Functions|Fluids Functions Design Program] {latex} \large $$ HL_{Valve} = h_e (Q_{SedSludgeDrain} ,innerdiameter(ND_{SedSludgeValve} ,EN_{PipeSpec} ),K_{GateValve} + K_{PipeExit} ) $$ {latex} |
Using
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this
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result
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we
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can
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find
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the
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desired
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head
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loss
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across
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the
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sludge
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drain
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and
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then
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the
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required
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size
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of
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the
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drain
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channel.
| Latex |
|---|
} \large $$ HL_{SludgeDrain} = HW_{Sed} - HL_{Valve} $$ {latex} The size of the channel is first |
The diameter of the sludge drain pipe is estimated through an iterative process, using the ID.Manifold equation found in the Fluids Functions program.
| Include Page | ||||
|---|---|---|---|---|
|
Because the sludge drain is no longer a pipe but now a rectangular channel, this diameter is then used to calculate the required cross-sectional area of the drain. Based on manifold theory, the total area of the sludge orifices is equal to the cross sectional area of the manifold.
| Latex |
|---|
\large $$ A_{SedSludgecalculated as a diameter using the manifold equation from the [Fluids Functions|Fluids Functions Design Program] program {latex} \large $$ HL_{SludgeDrain} = HW_{Sed} - HL_{Valve} $$ {latex} The diameter of the sludge drain pipe is estimated through an iterative process, using the ND.Manifold equation found in the [Fluids Functions|Fluids Functions Design Program] program. {include:ND.SedSludge} Because the sludge drain is no longer a pipe but now a rectangular channel, this diameter is then used to calculate the required cross-sectional area of the drain. Based on manifold theory, the total area of the sludge orifices is equal to the cross sectional area of the manifold. {latex} \large $$ TotalArea_{SludgeOrifices} = {\pi \over 4}NDID_{SedSludge} ^2 $$ |
In order to reduce the total depth of the sed tanks we assume that the sludge drain is twice as wide as it is high.
| Latex |
|---|
\large
$$
W_{SedSludge} = \sqrt {2A_{SedSludge} }
$$
|
| Latex |
|---|
{latex} Given the required area for uniform flow, and the depth of the drain, H.SedSludge (set to be 5 cm in [Design Assumptions|Design Assumptions Design Program]), the width of the drain is calculated. {latex} \large $$ WH_{SedSludge} = {{TotalAreaA_{SludgeOrificesSedSludge} } \over {HW_{SedSludge} }} $$ {latex} |
Once
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the
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total
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area
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of
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the
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orifices
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and
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the
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number
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of
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orifices
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have
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been
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calculated
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the
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diameter
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of
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each
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orifice
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is
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found
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by
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rounding
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the
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required
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diameter
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up
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to
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the
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next
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available
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drill
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diameter.
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The
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initial
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flow
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rate
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through
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the
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sludge
...
drain
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is
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calculated
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using
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the
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Q.Orifice
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equation
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found
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in
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| Latex |
|---|
|Fluids Functions Design Program]: {latex} \large $$ Q_{SludgeDrainInitial} = Pi_{VenaContractaOrifice} A_{SedSludgeOrifice} \sqrt {2gHW_{Sed} } $$ {latex |
The thickness and width of the drain cover are determined using geometry.
| Latex |
|---|
\large
$$
T_{SedSludge} = T_{SedInletSlope} (1 + \sin (AN_{SedTopInlet} ))
$$
|
Determination of W.SedDrainCover:
| Latex |
|---|
} The initial flow rate is then used to calculate the total time needed to empty the sludge drain: {latex} \large $$ TimeW_{SludgeDrainSedDrainCover} = {{2LW_{SedSedSludgeFlat} {{W + 2_{SedWSedSludgeSF} } \over+ 2{N_{SlopePairs} }}HW{T_{SedSedInletSlope} } \over {Q_{SludgeDrainInitial} N\sin (AN_{SedSludgeOrificesSedTopInlet} )}} $$ {latex |
| Wiki Markup |
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{float:left|border=2px solid black}
[!bottomsedtank.png!|^bottomsedtank.png]|width=800px!
{float} |