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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}
\large
$$
Q_{SedSludgeDrain}  = {{W_{SedBay} L_{Sed} HW_{SedEst} } \over {0.5Ti_{SludgeDrain} }}
$$
{latex}

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}
\large
$$
ND_{SedSludgeValve}  = D_{pipeschedule} (Q_{SedSludgeDrain} ,EN_{PipeSpec} ,HL_{Valve} ,T_{PlantWall} ,Nu_{Water} ,E_{Pvc} ,K_{GateValve}  + K_{PipeExit} )
$$
{latex}

The actual head loss across the valve is then calculated from the head loss function found in Fluids Functions

{latex}
\large
$$
HL_{Valve}  = h_e (Q_{SedSludgeDrain} ,innerdiameter(ND_{SedSludgeValve} ,EN_{PipeSpec} ),K_{GateValve}  + K_{PipeExit} )
$$
{latex}

Using this result we can find the desired head loss across the sludge drain and then the required size of the drain channel.

{latex}
\large
$$
HL_{SludgeDrain}  = HW_{Sed}  - HL_{Valve}
$$
{latex}

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}
\large
$$
A_{SedSludge}  = {\pi  \over 4}ID_{SedSludge} ^2
$$
{latex}

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}
\large
$$
H_{SedSludge}  = {{A_{SedSludge} } \over {W_{SedSludge} }}
$$
{latex}

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:

{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
$$
T_{SedSludge}  = T_{SedInletSlope} (1 + \sin (AN_{SedTopInlet} ))
$$
{latex}

Determination of W.SedDrainCover:

{latex}
\large
$$
W_{SedDrainCover}  = W_{SedSludgeFlat}  + 2_{WSedSludgeSF}  + 2{{T_{SedInletSlope} } \over {\sin (AN_{SedTopInlet} )}}
$$
{latex}

{float:left|border=2px solid black}
[!bottomsedtank.png!|^bottomsedtank.png]|width=800px!
{float}

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