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h2. Sedimentation Tank Inlet Slopes Design Program Algorithm

[Sedimentation Tank Inlet Slopes

 Inputs|Sedimentation Tank Inlet Slopes Design Program Inputs]
[Sedimentation Tank Inlet Slopes Outputs|Sedimentation Tank Inlet Slopes Design Program Outputs]

h2. Design Algorithm

The sedimentation inlet slopes program begins by designing the rough dimensions of the sedimentation tank and then moves on to design the trapezoidal shaped channel located at the bottom of the tank. This channel uniformly distributes water to the entire bottom of the sedimentation tank creating a uniform flow of water out of the slopes and up through the sedimentation tank. 

There are several major concerns with this design. One concern is ensuring that water flows uniformly out of the slopes. Achieving this goal requires that the water velocity within the slope be significantly lower than the water flowing out of the slope.

Another concern is that flocs will settle out of the water flowing in the slopes. If flocs start to build up in the slopes then they decrease the area of the exit, which in turn could cause floc breakup. Another concern is with regard to floc breakup in general. The specific parameters surrounding floc breakup are generally unknown, and it is a concern that flocs will be broken in transit from the floc tank to the sedimentation tank. The main point of concern for breakup is the exit ports into the sedimentation tank. 

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|User Inputs Design Algorithm], 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_{SedInlet}  = W_{SedInlet}  \cdot \left( {\tan \left( {AN_{SedTopInlet} } \right) - \tan \left( {AN_{SedBottomInlet} } \right)} \right)
$$
{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
$$
$$
$$
Q_{SedSlopePort}  = V_{SedUpBod}  \cdot W_{SedInlet}  \cdot W_{SedSlopePlate} 
$$
$$
{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. 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 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.

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