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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 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.
Sludge Drain Design Algorithm
Sludge Drain AutoCAD Drawing Program
Algorithm
The number of sludge drains is determined by the number of sloped pairs in the sedimentation tanks. This is defined as N.SedSludge, and uses the number of slope pairs calculated in the Sedimentation Inlet Slopes program.
The orifice spacing of the sludge drain is set so that there are two orifices per slope plate. So orifice spacing is calculated as W.SedSlopePlate/2. The width of the sed slope plates is a basic user input.
Next, the number of orifices in the pipe can be calculated given the orifice spacing and the length of the sedimentation tank from the Sedimentation program.
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The dimensions of the sludge drain channel and the sludge valve are determined based on the maximum acceptable head loss through the drain. Here it is assumed that we are willing to use 80% of the available head to get the flow through the valve. So HL.Valve = 0.8 HW.Sed.
Calculation of the diameter of the valve requires that we know the drain rate. This value is determined by the dimensions of the sed tank and the time needed to drain the tank, a user defined value.
| Latex |
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\large
$$
Q_{SedSludgeDrain} = {{W_{SedBay} L_{Sed} HW_{SedEst} } \over {0.5Ti_{SludgeDrain} }}
$$
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This initial drain rate is then used to calculate the diameter of the valve needed via the D.pipeschedule funcion of the Fluids Functions program.
| Latex |
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\large
$$
ND_{SedSludgeValve} = D_{pipeschedule} (Q_{SedSludgeDrain} ,EN_{PipeSpec} ,HL_{Valve} ,T_{PlantWall} ,Nu_{Water} ,E_{Pvc} ,K_{GateValve} + K_{PipeExit} )
$$
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The actual head loss across the valve is then calculated from the head loss function found in Fluids Functions
| Latex |
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\large
$$
HL_{Valve} = h_e (Q_{SedSludgeDrain} ,innerdiameter(ND_{SedSludgeValve} ,EN_{PipeSpec} ),K_{GateValve} + K_{PipeExit} )
$$
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Using this result we can find the desired head loss across the sludge drain and then the required size of the drain channel.
| Latex |
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\large
$$
HL_{SludgeDrain} = HW_{Sed} - HL_{Valve}
$$
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The diameter of the sludge drain pipe is estimated through an iterative process, using the ID.Manifold equation found in the Fluids Functions program.
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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 |
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\large $$ A_{SedSludge h2. Sludge Drain Design Algorithm [Sludge Drain Inputs|Sludge Drain Design Program Inputs] [Sludge Drain Outputs|Sludge Drain Design Program Outputs] [Sludge Drain AutoCAD Drawing Program|AutoCAD Sludge Pipe Program] h3. Algorithm The number of sludge drains is determined by the number of sloped pairs in the sedimentation tanks. This is defined as N.SedSludge, and uses the number of slope pairs calculated in the [Sedimentation Inlet Slopes|Sedimentation Inlet Slopes Design Program] program. Next, the number of orifices in the pipe can be calculated given the orifice spacing from the [Design Assumptions|Design Assumptions Design Program], and the given length of the sedimentation tank from the [Sedimentation|Sedimentation Design Program] program. {include:N.SedSludgeOrifices} The diameter of the sludge drain pipe is estimated through an iterative process, using the ND.Manifold equation found in the [Fluids Functions|Fluids Functions Design Program] program. {include:ND.SedSludge} Because the sludge drain is no longer a pipe but now a rectangular channel, this nominal diameter is then used to calculate the required cross-sectional area of the drain. Based on manifold theory, the total area of the sludge orifices is equal to the cross sectional area of the manifold. {latex} \large $$ TotalArea_{SludgeOrifices} = {\pi \over 4}NDID_{SedSludge} ^2 $$ {latex} Given the required area for uniform flow, and the depth of the drain, H.SedSludge (set to be 5 cm in Design Assumptions), the width of the drain is calculated. |
In order to reduce the total depth of the sed tanks we assume that the sludge drain is twice as wide as it is high.
| Latex |
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\large
$$
W_{SedSludge} = \sqrt {2A_{SedSludge} }
$$
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| Latex |
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{latex} \large $$ 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
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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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...
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:
| Latex |
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} \large $$ Q_{SludgeDrainInitial} = Pi_{VenaContractaOrifice} A_{SedSludgeOrifice} \sqrt {2gHW_{Sed} } $$ {latex} The |
The thickness and width of the drain cover are determined using geometry.
| Latex |
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\large
$$
T_{SedSludge} = T_{SedInletSlope} (1 + \sin (AN_{SedTopInlet} ))
$$
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Determination of W.SedDrainCover:
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initial flow rate is then used to calculate the total time needed to empty the sludge drain: {latex} \large $$ TimeW_{SludgeDrainSedDrainCover} = {{2LW_{SedSedSludgeFlat} {{W + 2_{SedWSedSludgeSF} } \over+ 2{N_{SlopePairs} }}HW{T_{SedSedInletSlope} } \over {Q_{SludgeDrainInitial} N\sin (AN_{SedSludgeOrificesSedTopInlet} )}} $$ {latex |
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{float:left|border=2px solid black}
[!bottomsedtank.png!|^bottomsedtank.png]|width=800px!
{float} |