Page History

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Observation of the tube settlers yielded interest in floc buildup and floc flow in tubes. As the flocs began to build up, some started to roll up the tubes and flow out into the effluent instead of falling back into the floc blanket. It was determined that a drag force was possibly preventing the flocs from settling out. The question remained, however, as to why smaller tubes at higher flow rates experienced the rolling flocs but not the larger tubes.
It was determined that velocity gradients vary with the tube diameter, and that the drag force was related to the velocity gradient at the tube wall. As the diameter decreased at the same

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The Reynolds number and entrance region length were calculated to determine whether the flow through the tubes was transient or laminar. With Reynolds numbers below 100 the length of the entrance region was determined by the following equation:

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$l_e  = 0.06{\mathop{\rm Re}\nolimits}  \cdot d$
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It was then determined that the flow though the tubes became fully developed very quickly.

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The next calculation involved the Navier Stokes equation for laminar flow through a cylindrical tube, as seen below.

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$\frac{{\partial v}}{{\partial r}} = \frac{1}{\mu }\left( {\frac{{\partial p}}{{\partial z}}} \right)R + c_1 $
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Final equation:

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$\frac{{\partial v}}{{\partial r}} = \frac{{4 \cdot V}}{R}$

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This equation was evaluated at R, the radius of the tube, to find the maximum velocity gradient at the tube walls. Table 1 lists the velocity gradient values for each tube at the test critical velocities.

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In order to determine a minimum plate spacing for the tanks in AguaClara plants, a Navier Stokes equation for laminar flow between two flat plates was used.

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$\frac{{\partial u}}{{\partial y}} = \frac{1}{\mu }\left( {\frac{{\partial p}}{{\partial x}}} \right)y + c_1 $
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Final equation:

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$\frac{{\partial u}}{{\partial y}} = \frac{{3V}}{{2h}}$

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The minimum spacing for plate settlers can be determined using the above equations.

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