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When this ratio is greater than one (ie the settling velocity is greater than the velocity experienced by the floc particles in the tube), the flocs will fall back into floc blanket and fail to travel to the effluent. When this ratio is equal to one, the particles will remain stationary in the tube settler. And when the ratio is less than one, the velocity of the particles will exceed the settling velocity and the floc particles will roll up into the effluent, creating a highter turbidity.
Figure 1: The ratio of Sedimentation Velocity to Fluid Velocity vs. Floc Diameter
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Assuming an upward flow velocity of 100 m/day, the diameter of floc that will roll-up was determined by using a root finding algorithm, and the plate settling or tube diameter was plotted versus the minimum floc diameter.
Figure 2: Plate Spacing or Tube Diameter vs. Minimum Floc Diameter
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insert S equations and explanations?
Figure 3: Floc Diameter vs. Spacing
Figure 3 shows how the linearized equations provide an excellent solution with only tiny divergence for big flocs in small tubes.
Figure 4: Floc Spacing vs. Floc Diameter
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insert S eqtn for plate settlers
Figure 5: Minimum spacing vs. Floc Sedimentation
Figure 6: Minimum Plate Settler Spacing vs. Capture Velocity
The Reynold's Number was checked to ensure that the flow in the settler tube is in fact laminar. Next, the entrance region was checked to ensure that the parabolic velocity profile was fully established.
Figure 7: Ratio of Entrance Length to Plate Length vs. Plate Spacing
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