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These values were found using the following equations:

Velocity Gradient

$$
G_s  = {{8Q} \over {3\pi r^3 }}
$$

The velocity gradient in a curved tube is given by (Mishra & Gupta 1979)

$$
G_c  = G_s \left( {1 + 0.033\log \left( {De} \right)^4 } \right)^{{\raise0.7ex\hbox{$1$} \!\mathord{\left/
 {\vphantom {1 2}}\right.\kern-\nulldelimiterspace}
\!\lower0.7ex\hbox{$2$}}} 
$$ 

Where De is the nondimensional Dean Number and characterizes the effect of curvature on fluid flow:

$$
De = \sqrt {{r \over {R_c }}} {\mathop{\rm Re}\nolimits} _d 
$$

Residence Time

Several flocculator designs were used in the trial runs of the experiment. The initial flocculator was oriented horizontally across the work bench. This orientation led to a numerous small bubbles trapped throughout the system. It also made the flocculator difficult to fill. The first change therefore, was to use a vertical flocculator orientation. This allowed bubbles in the flocculator to flow upwards towards the top where a tee and vertical tube open to the atmosphere released any bubbles in the flocculator.

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