Secondary clarifiers used with trickling filters and RBCs provide effluent clarification by removing large, sloughed solids. Therefore, the design criteria are based on particle size and density.
Environmental engineers can formulate the gravitational force (FG) and the frictional drag force (FD) acting on a spherical particle settling through a liquid using the classic laws of Newton and Stokes, respectively, as follows:
ps = particle density p = liquid density g = gravitational acceleration Vs = particle volume CD = drag coefficient
As = projected area of the particle perpendicular to the direction of settling v = particle settling velocity
The particle settling velocity v becomes the terminal settling velocity vc when FG = FD. Therefore, the following equation applies vc = [4gd(ps — p)/3pCd]05 7.29(3)
where d = particle diameter (1.5V./AJ.
Under laminar flow conditions, Equation 7.29(3) can be modified as follows:
where / = liquid viscosity.
For the design of continuous-flow secondary clarifiers, vc is designated as the surface overflow rate as follows:
Q = influent wastewater flow rate Qr = recirculation flow rate A = surface area of the secondary clarifier D = depth of the secondary clarifier 03c = LRT in the secondary clarifier
The total fraction of biological solids removed F is calculated as follows:
where (1 — Xs) = fraction of particles with settling velocities >vc, and the second term at the right side of Equation 7.29(6) indicates the fraction of particles removed with settling velocities vs < vc.
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