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

 Program

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 three constraints to determine design values, the critical velocity of 10 m/day, the upward velocity at the bottom of the tank of 70 m/day and the predetermined length of the sedimentation tank. All of these constraints come together to determine the spacing of the lamella which is the most important value in terms of functionality. 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 for drinking. 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 velocity). The upward velocity at the bottom of the tank is important for sludge blanket formation, too high and the blanket will form to 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 available for the lamella. After the available height is determined the length of the lamella can be found given an assumed angle of 60deg. 
In order to find the vertical height available for the lamella, first the height of the water needed above the lamella is found. 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}

The distance below the lamella, H.SedBelowSlope, was found in the sedimentation program and based off of the tank fraction given by the user. The vertical height available for the lamella is simply the remainder of the water depth in the sedimentation tank after the bottom slopes and the space needed above the lamella has been accounted for. 

{include:H.SedPlate}

The lenght of the lamella:
{include:L.SedPlate}

The next step is to determine the space between the lamella needed to satisfy the critical velocity, the active upward velocity and active tank length. The active length of the tank is the length in which water will be able to flow up through the lamella. The 60ddeg angle and the channels create an inactive area in the tank through which water does not flow. The inactive length is found below.
{include:L.SedInactive}

The actvie upward velocity is the flow through the sedimentation tank divided by the cross sectional area of the active portion of the sedimentation tank.
Upward Velocity under the Active Area below the Lamella:
{include:V.SedUpActiveBelow}

Now the critical spacing between the lamella can be found.The equation below determines the perpendicular distance center to center between lamella. Typically the lamella spacing should be around 5cm apart. Closer distances are thought to possibly lead to improper floc settling and possible clogging. 
Distance from Center to Center between Lamella:
{include:B.SedPlate}


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

The open space between the lamella is the area for water to flow up through the lamella. This spacing is the center to center spacing between the lamella (B.SedPlate) minus the thickness of the lamella material. 
Open Space between Lamella:
{include:S.SedPlate}

The number of lamella placed in the tank is determined by the maximum number of lamella that can fit in the tank. This number is function of the geometry of the space available and the following equation is used.
The Number of Lamella:
{include:N.SedPlate}

Without knowing the exact number of lamella that will be placed in the tank it is not possible to calculate the exact parameters of 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.

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 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}