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Since flow through the tube settlers is laminar, the shear stress is greatest at the tube surface. Below is a calculation of the minimum diameter based on the shear stress at the tube surface. We assume that floc integrity begins to suffer under shear stresses of 1 Pa.
The velocity gradient equation:
yields the equation for maximum shear stress:
Substituting the head loss equation:
into the maximum shear stress equation yields:
Since this calculation 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 twelve inches. Table 2 below lists the parameters of the tube settlers for this experiment.
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