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The first step is to determine the width of the inlet. The width is found by using the width of each bay (set by the user), as well as the width between the plates, thickness of the inlet slopes, and angle of the slopes.

{latex}
\large
$$
W_{SedInlet} = {{W_{SedBay} } \over 2} - {{W_{SedSludgeFlat} } \over 2} - T_{SedInletSlope} \cdot \sin \left( {AN_{SedTopInlet} } \right)
$$
{latex}

The height of the slope manifold is calculated based on the width of the inlet and the angles of the slopes.

{latex}
\large
$$
H_{SedSlopeManifold}  = \tan (AN_{SedTopInlet} ) - (\tan (AN_{SedBottomInlet} )) \cdot W_{SedInlet}
$$
{latex}

The water will then flow out of ports that run along the sedimentation tank. The flow rate is designed to be equal through each port. The flow rate involves an iterative process that compares the calculated flow to the desired manifold flow based on the hydraulic grade line.

{latex}
\large
$$
Q_{SedSlopePort} = V_{SedUpBod} \cdot W_{Bay} \over2 \cdot W_{SedSlopePlate}
$$
{latex}

The next step is to determine the necessary width of the port introducing water to the sedimentation tank. This port has to be designed to not breakup the flocs created in the flocculator, thus the energy dissipation of the port has to be less than that of the end of the flocculator.

{latex}
\large
$$
B_{SedPort} = \sqrt {A_{Port} \left( {Pi_{FlocDissipation} ,K_{PipeEnt} ,Q_{SedSlopePort} ,ED_{SedInlet} ,Pi_{VenaContractaOrifice} } \right)} = {1 \over {Pi_{VenaContractaOrifice} }}\left( {{{K_{PipeEnt} Q_{SedSlopePort} ^3 } \over {2Pi_{FlocDissipation} ED_{SedInlet} }}} \right)^{{3 \over 7}}
$$
{latex}

The number of bays in each sedimentation tank is determined based on the number of sedimentation tanks (defined by the user) and the plant flow rate. It makes sure that the length of the sedimentation tank meets the requirements for V.SedUpBod. The length of the sedimentation tank is then recalculated based on both the number of bays and the velocity.

{latex}
\large
$$
L_{Sed} = {{Q_{Sed} } \over {W_{SedBay} N_{SedBays} V_{SedUpBod} }}
$$
{latex}

The width of the inlet slopes are then redefined to incorporate the loss from adding the dividing walls between the adjacent slope pairs.

{latex}
\large
$$
W_{SedInlet} = {{W_{SedBay} } \over 2} - {{W_{SedSludgeFlat} } \over 2} - T_{SedInletSlope} \cdot \sin \left( {AN_{SedTopInlet} } \right) - {{T_{ChannelWall} \left( {N_{SedBays} - 1} \right)} \over {2N_{SedBays} }}
$$
{latex}

The length of the slope plate is then calculated based on this width.

{latex}
\large
$$
L_{SedSlopeManifold} = {{W_{SedInlet} } \over {\cos \left( {AN_{SedTopInlet} } \right)}}
$$
{latex}

The width of the the bay is then recalculated taking into account the width of the bay dividers

{latex}
\large
$$
{\rm{W}}_{{\rm{SedBayActual}}} = {{W_{Sed} - \left( {N_{SedBays} - 1} \right) \cdot T_{ChannelWall} } \over {N_{SedBays} }}
$$
{latex}

The inlet manifold is formed by laying concrete plates next to each other. The width of each slope plate is defined by the user. If the length of the sedimentation tank is not equally divided by the width of the plate, there is a leftover space that needs to be filled by a fraction of a plate. This is used for construction purposes. The equation used to determine the leftover length can be found in the lamella program