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The flow rate (Q) through the tube settlers is calculated based on a desired upflow velocity (Vup) of 100 m/day through the tube settlers. We note here that the tube settlers are angled at the standard sixty-degrees from the horizon in order to reduce plate length. We also note that flow through the tubes is assumed to be laminar, resulting in a parabolic velocity profile with the maximum velocity (Va) occurring at the center of the tubes. The desired upflow velocity is dependent primarily on the critical velocity (Vc) necessary to allow flocs to settle out of the water: 
Below is the calculation of the flow rate, regulated by a pump, through the tube settlers.
Where Ased is the cross-sectional area of one tube and Qsed is the flow rate through one tube settler.
As seen above, the flow rate is also based on the inner diameter of the tube settlers. The inner diameter of the tubes is analogous to the spacing between lamella in parallel plate sedimentation. The determination of the optimal diameter is multi-faceted.
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Since substituting our parameters into this equation yields an unreasonably small minimum diameter of 20 µm, shear stress is not the limiting factor for tube settler diameter. Therefore, the diameters tested in this experiment are based on floc size, the length/diameter ratio of twenty-four mentioned above, and material availability. The minimum diameter was set to be at least twice the diameter of a floc (estimated at 2 mm), and the length of the tubes was set to be .304 m. The table below lists the parameters of the tube settler apparatus for this experiment.
Results and Discussion
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