h1. Energy Dissipation Flocculation Design Program
This flocculator program determines the size of the flocculator channels and number and spacing of baffles based on a setan energy dissipation rate determined for each 180 degree turn around a baffle. This program also outputs arrays of the location of each baffle in the tank; these arrays are used by the AutoCAD scripts to draw the baffles.
!floc tank top view.PNG!
!floctank front view.PNG!
h2. Flocculator Program Inputs and Outputs
[Flocculation Tank Program Inputs|Flocculation Tank Design Program Inputs]
[Flocculation Tank Program Outputs|Flocculation Tank Design Program Outputs]
[Flocculation Tank AutoCAD Drawing Program|AutoCAD Flocculation Tank Program]
h3. Flocculation Design Algorithm
The first step in the flocculator program is to assume that the headloss of the water traveling from the end of the flocculator to the sedimentation tank is negligible, with this assumption it was determined that the height of the water at the end of the flocculator is the same and water height in the sedimentation tank. The largest baffle spacing was set to be one half of the height of water at the end of the flocculator.
The width of the flocculator channels are calaculated to give the final spacing of the flocculator section a set energy dissipation rate. The equation used can be seen below.
{latex}
\large
$${W_{FlocChannel}} = {{2{Q_{Plant}}} \over {H{W_{FlocEnd}}}}{\left( {{{{K_{FlocBaffle180}}} \over {2P{i_{Epsilon}} \cdot H{W_{FlocEnd}} \cdot E{D_{FlocFinal}}}}} \right)^{1/3}}$$
{latex}
If this calulated width is smaller than 45 cm then the width of the flocculator channel will default to 45 cm. This minimum value was set to ensure that a person can fit into the channel for construction purposes.
The flocculator was divided into spacing sections. Each section was set to have a different and decreasing energy dissipation rate, and thus a different baffle spacgng. The spacing for each section was determined by the following equation using the three different values of energy dissipation set in the design assumptions.
{latex}
\large
$${S_{FlocBaffle}} = {{{Q_{Plant}}} \over {{W_{FlocChannel}}}}{\left( {{{{K_{FlocBaffle180}}} \over {2P{i_{Epsilon}} \cdot H{W_{FlocEnd}} \cdot E{D_{Floc}}}}} \right)^{1/3}}$$
{latex}
The center to center distance between baffles includes the thickness of the baffles. This thickness is added to the spacing calculated above.
The next step is to calculate the number of baffles in each spacing section. The number of baffles per spacing section is found to be a ratio of energy dissipation ratios for the entire section over the energy dissipation ratio for a single baffle.
{latex}
\large
$${N_{FlocBaffleSection}} = ceil\left( {{{P{i_{FlocCP}}} \over {length\left( {E{D_{Floc}}} \right)P{i_{FlocBaffleCP}}}}} \right)$$
{latex}
The length of the flocculator taken up by the the baffles is determined by summing the product of the number of baffles in each section by the spacing for each section.
{latex}
\large
$${L_{FlocSections}} = \sum {{B_{FlocBaffle}}{N_{FlocBaffleSection}}} $$
{latex}
The number of channels in the flocculator is determined by taking the estimated length of the flocculator needed to fit all of the baffles and dividing by the length of the sedimentation tank. Each of the flocculator channels is set to be same length as the sedimentation tank. The resulting fractional number of channels is rounded up.
{latex}
\large
$${N_{FlocChannels}} = ceil\left( {{{{L_{FlocTankEst}}} \over {{L_{Sed}}}}} \right)$$
{latex}
The total exact length of the flocculator is recalculated by multiplying the number of channels by the length of one floc channel.
{latex}
\large
$${L_{FlocTank}} = {N_{FlocChannels}} \cdot {L_{Sed}}$$
{latex}
The residence time of the flocculator is calculated with the equation below. From the floc model created by Monroe Weber-Shirk, the ideal residence time was found to be around 20 minutes.
{latex}
\large
$${\theta _{Floc}} = {{H{W_{FlocEnd}} \cdot {L_{FlocTank}} \cdot {W_{FlocChannel}}} \over {{Q_{Plant}}}}$$
{latex}
The height of the flocculator channel is determined by adding the head loss through the flocculator to the water level at the end of the flocculator. The head loss is determined per baffle using the hl.erect function in the [fluids function program|Fluids Functions Design Program]. An additional 10 cm of freeboard space was added to the water level found at the beginning of the flocculator.
Water flows between channels in the flocculator through ports cut in the concrete. The area of these ports is determined to ensure flocs will not be broken up.This is done by setting the port to have an energy dissipation rate no greater than that of the final section.
The width of this port is set to be the same as the baffle spacing in the final section. The height of the port is determined by the dividing the total port area by the set width.
The placement of the baffles in the flocculator is determined by an algorithm that creates a matrix of baffle displacements from the end of the flocculator. Water flows back and forth with flow direction alternating in each successive channel.
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