Sludge Drain Design Program
This program designs the pipe channel that will be used for the sedimentation tank sludge drainage. The sludge drain runs along the bottom of the each sedimentation tank and collects the flocs as they fall from the lamella and slopes.
Sludge Drain Design Algorithm
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Sludge Drain AutoCAD Drawing Program
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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 from the Design Assumptions, and the given length of the sedimentation tank from the Sedimentation program.
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The initial flow rate through the sludge drain is calculated using values found in the Sedimentation program, and the drainage time for the sedimentation found in the Design Assumptions program.
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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.
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$$
Q_{SedSludgeDrain} = {{W_{SedBay} L_{Sed} HW_{SedEst} } \over {0.5Ti_{SludgeDrain} }}
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This initial drain rate is then used to calculate the diameter of the valve needed via the D.pipeschedule funcion of the Fluids Functions program.
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$$
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
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$$
HL_{Valve} = h_e (Q_{SedSludgeDrain} ,innerdiameter(ND_{SedSludgeValve} ,EN_{PipeSpec} ),K_{GateValve} + K_{PipeExit} )
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Using this result we can find the desired head loss across the sludge drain and then the required size of the drain channel.
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$$
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 NDID.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 nominal diameter is then used to calculate the required cross-sectional area of the drain. 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.
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The head loss in the sludge drain is also determined using the HL.Manifold function, also found in the Fluids Functions program.
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Using this head loss, the diameter of each orifice is calculated using the D.orifice equation from the Fluids Functions program. This uses a Q.orifice, which is equivalent to the flow rate through the sedimentation tank divided by the number of slope pairs.
Based on manifold theory, the total area of the sludge orifices is equal to the cross sectional area of the manifold.
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$$
A_{SedSludge} = {\pi \over 4}ID_{SedSludge} ^2
$$
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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.
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$$
W_{SedSludge} = \sqrt {2A_{SedSludge} }
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$$
H_{SedSludge} = {{A_{SedSludge} } \over {W_{SedSludge} }}
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Once the total area of the orifices and the number of orifices have been calculated the diameter of each orifice is found by rounding the required diameter up to the next available drill diameter.
The initial flow rate through the sludge drain is calculated using the Q.Orifice equation found in Fluids Functions:
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$$
Q_{SludgeDrainInitial} = Pi_{VenaContractaOrifice} A_{SedSludgeOrifice} \sqrt {2gHW_{Sed} }
$$
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The thickness and width of the drain cover are determined using geometry.
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$$
T_{SedSludge} = T_{SedInletSlope} (1 + \sin (AN_{SedTopInlet} ))
$$
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Determination of W.SedDrainCover:
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$$
W_{SedDrainCover} = W_{SedSludgeFlat} + 2_{WSedSludgeSF} + 2{{T_{SedInletSlope} } \over {\sin (AN_{SedTopInlet} )}}
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