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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 optimize floc settling and accessibility for cleaning. 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:
Where b is the tube diameter.
Below are the equations used to calculate 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. Additionally, the critical velocity (Vc) is dependent on the inner diameter of the tube settlers (see equation below). The critical velocity is the velocity of the flow that facilitates particle settling.
Where b is the tube diameter.
Evidently, analysis of the inner diameter of the tube settlers is important to understand how to optimize other parameters of the system such as flow rate and critical velocity. 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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