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

\large
$$
{\rm{W}}_{{\rm{SedSlopePlateRemaining}}}  = L_{Sed}  - N_{SedPorts}  \cdot W_{SedSlopePlate}
$$
 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 the triple constraints of the a critical velocity of 10 m/day, an upward velocity at the bottom of the tank of 70 m/day to calculate the space needed between the lamella and the length of the tank set by the [Sedimentation Program|Sedimentation Design Algorithm]. The critical velocity is the rate at which a particle must fall to ensure that it settles out in the plate settlers. If the critical velocity is too large, flocs will not settle out. However a small critical velocity comes at the expense of 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. If the velocity is too low the blanket will either settle out or the shear value in the blanket will be so high that floc will get broken up in the blanket and thus the sludge blanket could be detrimental to the sedimentation process. 
The program starts by determining the height available for the lamella. After the height available is determined the length of the lamella can be found given an assumed angle of 60deg. Inorder to find the vertical height avaiable for the lamella, first the height of the water needed above the lamella is found.

{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 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 given the tank length found previously. In order to determine the space between the lamella the inactive length of the tank and the upward velocity under the lamella  must be found first. The inactive length of the tank consists of the space occupided by the inlet and exit channels. 
{include:L.SedInactive}

Upward Velocity under the Active Area below the Lamella:
{include:V.SedUpActiveBelow}

Distance from Center to Center between Lamella:
{include:B.SedPlate}

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

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

The Number of Lamella:
{include:N.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}


Critical velocity is the rate at which a particle must fall to ensure that it settles out in the plate settlers. If the critical velocity is too large, flocs will not settle out. However a small critical velocity comes at the expense of area (so it is not practical to have an unnecessarily small velocity). 
 We are designing our tanks to have an upward velocity of 100 m/day. We've found that this is the velocity allows for the formation of a sludge blanket in the bottom of the tank. -Since a portion of the tank's length is rendered unusable due to the sloping of the lamella, the actual length of the tank is greater than the active length.- {color:red}Explain the dual constraints of critical velocity and upflow velocity and detail how both constraints could be met simultaneously or how they could both be set as maximum values. {color}


Sedimentation is a basic step of most traditional water treatment processes. In our plant it comes between flocculation and chlorination. It uses gravity to separate water from the particles - particles settle to the bottom of the tank while the clean water rises to the top. Any particle settling faster than the critical velocity of the tank should settle out. Critical velcoty is a function of the flow rate and setting area of the tank. A particle's settling velcotiy depends on its size and density. Larger particles settle faster and therefore are thereby easier to separate from the clean water. Our design employs plate settlers which lessen the distance a particle must fall in order to settle out. This increases the tanks efficiency.