Empirical equations for the limiting solids flux of final clarifiers

Using the solids flux theory, two quantities (i.e., the dimensionless limiting solids flux [G = kGL/v(o)] and the dimensionless underflow velocity [U = FR/(Av(o))] are introduced for a final clarifier based on the Vesilind equation of sludge zone-settling velocity (v = v(o) exp[-kX], where X is the suspended solids concentration, v(o) and k are empirical coefficients, and GL, FR, and A are the limiting solids flux, recycle flowrate, and surface area of the settling tank, respectively). In this paper, the dimensionless limiting solids flux is shown to be a function of the dimensionless underflow velocity only and is accurately represented by empirical equations. The limiting solids flux can, thus, be easily calculated by using the empirical equations without resorting to tedious numerical procedures. Furthermore, using the dimensionless quantities (G and U), two final clarifier equations that express the relationship among suspended solids concentration, surface area of the clarifier, recycle flowrate, and wastewater flowrate are derived. Their applications to final clarifier analysis and to determining required surface area of final clarifier are illustrated.