Surface overflow concept: For a sedimentation basin of length L and width B treating a discharge Q, the settling (terminal) velocity required for a particle to be fully removed in ideal plug flow is

Introduction / Context:
Clarifier sizing often uses the concept of surface overflow rate (SOR), also called overflow velocity. Under ideal plug-flow assumptions, removal of a particle requires its settling velocity to be at least equal to the upward (overflow) velocity across the plan area.

Given Data / Assumptions:

• Basin plan dimensions: length L and width B; depth D does not affect ideal SOR.
• Flow rate: Q (steady, uniform distribution).
• Ideal settling without short-circuiting or turbulence.

Concept / Approach:
The theoretical criterion is v_s ≥ Q / A_plan, where A_plan = L * B. This means a particle whose settling velocity equals or exceeds Q / (L * B) will reach the sludge zone before escaping with the effluent.

Step-by-Step Solution:
Compute plan surface area: A_plan = L * B.Overflow (upward) velocity: v_o = Q / A_plan.Removal criterion: v_s ≥ v_o = Q / (L * B).

Verification / Alternative check:
Depth D mainly affects detention time and sludge storage but not the ideal surface loading criterion; hence it is absent from the ideal v_s expression.

Why Other Options Are Wrong:
Formulas involving D (depth) contradict the surface loading logic.Expressions multiplying L/B or using LBD do not represent plan overflow.

Common Pitfalls:

• Including depth in the ideal SOR calculation.
• Ignoring short-circuiting; real designs often apply safety factors.

Final Answer:
v_s = Q / (L * B)