Detention period in sedimentation (settling) tanks:\r Which description best represents the detention period used in design and analysis of settling basins?

Introduction / Context:
Detention period (also called theoretical residence time) is a fundamental parameter in the design of sedimentation tanks. It directly relates tank volume to flow rate and indicates the time available for particles to settle under quiescent conditions.

Given Data / Assumptions:

• Tank volume V is known; influent flow Q is approximately steady.
• Plug flow is assumed for theoretical definition, knowing that real flow deviates.
• Multiple equivalent descriptions are presented.

Concept / Approach:
The detention period t_d is defined by t_d = V / Q. This equals the theoretical time to fill the tank at flow Q, the average retention time, and the ratio of volume to discharge. These statements are equivalent ways to express the same definition used in preliminary design.

Step-by-Step Solution:
Start with t_d = V / Q.Interpretation 1: theoretical passage time for a parcel of water through the tank.Interpretation 2: time to fill from empty at constant flow Q.Interpretation 3: average time water is retained in the basin.All are consistent, so “All of the above” is correct.

Verification / Alternative check:
Tracer tests in real tanks show mean residence time near V / Q but effective flow through period may be less due to short-circuiting; however, the definition of detention period remains V / Q.

Why Other Options Are Wrong:

• Each individual statement is true but incomplete; the comprehensive option captures the equivalence explicitly.

Common Pitfalls:

• Confusing theoretical detention with effective flow through period; the latter is lower because of non-ideal hydraulics.
• Assuming detention period alone guarantees settling performance without considering particle characteristics and overflow rates.

Final Answer:
All of the above