\large
$$
L.Inactive = L.SedPlate \cdot \cos (AN.SedPlate) + W.InletChannel + W.ExitChannel + 2 \cdot T.ChannelWall
$$

\large
$$
V.SedUpActiveBelow = {{Q.Sed} \over {W.Sed \cdot \left( {L.Sed - L.SedInactive} \right)}}
$$

\large
$$
L.SedPlateEst = {{B.SedPlateMin \cdot \left( {{{V.SedUpActiveBelow} \over {V.SedCBod}} - 1} \right) + T.SedPlate} \over {\sin \left( {AN.SedPlate} \right) \cdot \cos \left( {AN.SedPlate} \right)}}
$$

\large
$$
L.SedPlate = {{L.SedPlateSheet} \over {floor\left( {{{L.SedPlateSheet} \over {L.SedPlateEst}}} \right)}}
$$

\large
$$
B.SedPlate = {{L.SedPlate \cdot \sin \left( {AN.SedPlate} \right) \cdot \cos \left( {AN.SedPlate} \right) - T.SedPlate} \over {{{V.SedUpActiveBelow} \over {V.SedCBod}} - 1}}
$$

\large
$$
B.SedPlateHorizontal = {{B.SedPlate} \over {\sin \left( {AN.SedPlate} \right)}}
$$

\large
$$
N.SedPlates = ceil\left( {{{L.SedActiveMax} \over {B.SedPlateHorizontal}}} \right)
$$

\large
$$
H.SedPlate = L.SedPlate \cdot \cos \left( {AN.SedPlate} \right)
$$

\large
$$
HW.Sed = \max \left( {\left( {Z.SedSlopes + H.SedFrameWall + H.SedBetween + 2 \cdot outerdiameter(ND.SedPlateFrame) + H.SedPlate + H.SedAbove} \right),\left( {H.SedManifoldPort + H.SedBetween + T.ChannelWall + H.InletChannel} \right)} \right)
$$

\large
$$
H.SedBayDivider = Z.SedSlopes + H.SedFrameWall
$$

 efficiently. 
!lamella front view.png!

h2. Lamella Design Program Inputs and Outputs
[Lamella Program Inputs|Lamella Design Program Inputs]
[Lamella Program Outputs|Lamella Design Program Outputs]

h2. Lamella Design Program Algorithm


The Lamella Design Program uses four constraints to determine design values, the critical velocity of 10 m/day, the upward velocity at the bottom of the tank, the minimum space between the lamella and the predetermined length of the sedimentation tank. All of these constraints come together to determine the length of the lamella. The minimum spacing between the lamella was determine via laboratory experiments, at spacing closer than 2 cm failure occured.  The length of the sedimentation tank is set by the [Sedimentation Program|Sedimentation Design program]. The critical velocity is the rate at which a particle must fall to ensure that it settles out within the plate settlers. If the critical velocity is too large, flocs will not settle out, and will remain in the water sent through the distribution system. However, a small critical velocity comes at the expense of a large cross sectional tank area (so it is not practical to have an unnecessarily small critical velocity). The upward velocity at the bottom of the tank is important for sludge blanket formation, too high and the blanket will form too thin and will not capture particles, too slow and the blanket will either settle out instead of remaining suspended or the shear value in the blanket will be so high that flocs will get broken up in the blanket. Either of these issues would result in the sludge blanket being detrimental to the sedimentation process. 

The program starts by determining the height needed for the launders above the lamella. This height needed for the launders is same as the depth of water needed above the lamella. This value is simply a function of leaving enough available headloss through the exit launder about the lamella to keep it properly submerged.

{include:H.SedAbove}

To determine what the how long the lamella need to be, firs the active length of the tank and the upward velocity under the lamella must be determined, but both of these values are dependent upon the length of the lamella. Therefore, an iterative loop of the following three equations was created to determine length of the lamella. 


The length found in the above loop is an estimated length, The actual lamella length is dependent on length of the plastic sheeting material that is available. 


From this number the actual upward velocity under the lamella and the actual space needed  between the lamella are recalculated. 


Using the available active length in the sedimentation tank and the known length of the lamella the number of lamella that can fit in the tank can be calculated as follows.
The Number of Lamella:
{include:N.SedPlate}


The thickness of the lamella contributes a small but significant dead zone to the tank. Now that the exact number of lamella has been calculated, more accurate values of active tank length, upward velocity, and critical velocity can be found. Calculations for these values are shown below.


Vertical height taken up by the lamella:
{include:H.SedPlate}



Horizontal Distance Center to Center between Lamella:
{include:B.SedPlateHorizontal}

Open Space between Lamella:
{include:S.SedPlate}




Active Length of the Tank:
{include:L.SedActive}

The Actual Upward Velocity at the Bottom of the Tank:
{include:V.SedUp}

The Critical Velocity Up through the Lamella:
{include:V.SedC}

The height of the water in the sedimentation tank can now be determined as the max height taken up by the inlet manifold and the channels, or the inlet manifold, lamella, lamella frame, and launder. 

For tanks where there are more than one bay per tank, a wall is constructed to separate bays. This wall has height that comes up to the top of ledge that supports the lamella frame. This was done so that the wall can lend support to the center section of the lamella. The equation used is as follows. 



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
$$
{\rm{W}}_{{\rm{SedSlopePlateRemaining}}}  = L_{Sed}  - N_{SedPorts}  \cdot W_{SedSlopePlate} 
$$
{latex}