Primary treatment is designed to remove readily settleable organic solids and floating debris from municipal wastewater, reducing the organic load on subsequent secondary biological treatment units. Following screening and grit removal, primary sedimentation tanks (PSTs) utilize plain gravity settling to clarify sewage, removing approximately 50% to 70% of total suspended solids (TSS) and 30% to 40% of five-day biochemical oxygen demand ($\text{BOD}_5$). The performance of a ideal continuous-flow primary settling basin is governed by the Surface Overflow Rate (SOR) , defined as the volume of wastewater applied per unit surface area of the tank per day ($v_0$): $$v_0 = \frac{Q}{A_s} = \frac{Q}{W \cdot L}$$ Where $Q$ is the influent flow rate, $A_s$ is the top surface area, $W$ is tank width, and $L$ is tank length. Mathematically, any discrete particle with a terminal settling velocity $v_s \ge v_0$ will be 100% removed. For discrete particles with $v_s $$X_r = \frac{v_s}{v_0}...