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The length of the exit channel is found first. The channel is defined to span perpendicular to the sedimentation tanks, and thus its length must always be the total width occupied by all sedimentation tanks.

{latex}
\large
$$
L_{ExitChannel} = (N_{SedTanks} )(W_{Sed} ) + (N_{SedTanks} + 1)(T_{PlantWall} )
$$
{latex}

The width of the exit channel is designed based weir orientation and the constraint that the head loss in the open channel must be very small compared with the head loss in the launder orifices to ensure that the flow is uniformly distributed between sedimentation tank bays. To ensure this the head loss in the channel was chosen to be twenty times smaller than the head loss in the launder. Using the head loss equation this ratio was converted to use as an input the ratio of flow between the sedimentation tank with shortest route to the exit channel and the tank with the longest route to the channel.

{latex}
\large
$$
h_L  = C_{p_1 } {{Q_1 ^2 } \over {2gA^2 }}
$$
$$
C_{p_1 } Q_1 ^2  = C_{p_2 } Q_2 ^2
$$
{latex}

The variable Π _loss was assigned a value of 1/20, representing the ratio of head loss between the channel and the orifice. The flow ratio was then solved as a function of the loss ratio.

{latex}
\large
$$
h_{L_{shortpath} }  = {1 \over {\Pi _{loss} }}
$$
$$
h_{L_{longpath} }  = {1 \over {\Pi _{loss} }} + 1
$$
$$
\Pi _{QSedTanks}  = \sqrt {{{{1 \over {\Pi _{loss} }}} \over {{1 \over {\Pi _{loss} }} + 1}}}
$$
$$
\Pi _{loss}  = {{1 - \Pi _{QSedTanks} ^2 } \over {\Pi _{QSedTanks} ^2 }}
$$
{latex}

For simplicity the channel is assumed to be square (w=b). The code starts with the width equal to the inlet channel width, then iterates to find the smallest width that fulfills the head loss requirement. The larger of either a W _{ExitChannelMin} or the returned value from the iteration is returned. W _{ExitChannelMin} is needed to ensure that the tank is large enough for a person to put their hand in the channel to cap the launders. This value is approximately equal to 1.5*(ND.launder), where ND.launder is the diameter of the launder pipe.

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The exit weir controls the flow of water leaving the plant and regulates the water heights throughout the plant. The width of the exit weir is designed based on the following equation:

{latex}
\large
$$
W = {3 \over 2}{Q \over {K_{VC} \sqrt {2g} H^{{3 \over 2}} }}
$$
{latex}

Where W is the width of the weir and H is the head loss over the weir. There are two possible orientations for the weir: perpendicular to the length of the channel, or parallel.

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