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Exit Channel Design Program Algorithm

Exit Channel Program Inputs
Exit Channel Program Outputs
Exit Channel AutoCAD Drawing Program

Algorithm

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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.

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

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The width of the exit channel is defined to be the same as the width of the inlet channel. This was done for ease of construction. 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.

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

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.

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

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.

The depth of the water in the exit channel is lower than the depth of water in the sedimentation tank by the head loss in the effluent launder. That value is set to approximately 5 cm. The channel walls are as high as the walls in the sed tank and thus the freeboard for the channel is the freeboard in the rest of the plant (10 cm) plus the head loss in the launder (5 cm)The depth of the exit channel is the depth of water in the exit channel plus the plant free board. The height of water is dependent on the head loss through the sedimentation tank launders, which has not yet been determined. The depth of the exit channel is thus found at the end of this algorithm.

Exit Weir Specifications

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 a large diameter pvc pipe that functions as a free-fall overflow weir. The equation used to determine the pipe size necessary is a derivative of the fluid dynamics sharp crested weir equation. The length of the weir, over which water flows, is assumed to be the circumference of the pipe used. The necessary diameter of pipe is then determined to minimize the water lip height over the weir, while still being a reasonably common pipe size.

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designed based on the following equation:

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

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.

Parallel Weir

The parallel weir design has the weir placed parallel to the length of the channel and attached to the inner half of the channel. Water flows in from the launders into the inner box created by the weir, and then overflows into the outer channel and into the distribution tank. The channel with the parallel weir is designed so that the outer channel that flows to the distribution tank satisfies the condition that the head loss in the open channel be far less than the head loss in the launder orifices.

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Perpendicular Weir

The weir will be placed in the exit channel such that the head loss in the open channel is very small compared with the head loss in the launder orifices so that the flow between sedimentation tank bays is uniformly distributed. The weir must also be designed so that a constant water level is obtained throughout the entire plant.

Image Added

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This calculated diameter is rounded up to next available pipe size.

In order to calculated the height of the weir needed the actual lip height of the water over the edge of the weir has be found.

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The height of the weir is then found by subtracting this water lip height from the water level in the exit channel. The height of the water in the exit channel depends on the about of head loss in the sedimentation launders, and thus is also calculated at the end of the program.

Sedimentation Tank Exit Launders

Water that leaves the sedimentation tank exits at the top of the tank through holes drilled in pvc pipes that run the length of the tank. The holes drilled in the sides of the pipe ensure uniform flow of water up through the tank. The water exits into the exit channel. The launder parameters to be determined are the launder length, pipe size and orifice size.
The first step to designing the sedimentation launders is to determine the length of the launders. The launders are defined to run the entire length of the sedimentation tank, minus the widths of both the inlet and exit channels.

The size of the launder pipe is dependent on the length of the pipe, the flow through the pipe, an estimated head loss available, and the given acceptable ratio of the flow in the last orifice to the flow through the first orifice. This ratio is assumed to be 0.8 for this program. As a reference, a ratio of 1 indicates that the flow is exactly the same in the first and last holes. Less than 1 indicates some discrepancy. This function (ND.Manifold) is defined in the fluids functions program and returns the nominal diameter for the sedimentation launder (ND.SedLaunder).

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The launder should be placed at a height that is as close to the top of the sedimentation tank as possible, but still always under water. The height of launder is placed below the water level in the sedimentation tank by the total head loss through the launder.

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The height of the water in the exit channel can now be determined and is defined to be the height of water in the sedimentation tank less the head loss through the sedimentation tank launder. The depth of the exit channel is depth of the water in the exit channel plus the plant free board of 10cm.

The height of the plant weir is the height of the water in the exit channel less the height of the lip of water over the weir.

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{float}

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