Detention time definition: In the context of a settling (sedimentation) tank, the detention time t is best defined as the time required for which of the following?

Introduction / Context:
Detention time is a fundamental hydraulic design parameter for sedimentation basins. It relates plant flow to tank volume and serves as a first-cut indicator of whether a basin will provide sufficient quiescent time for settling before short-circuiting occurs.

Given Data / Assumptions:

• Steady average flow rate through the tank.
• Completely mixed inflow distribution is not assumed; definition remains V/Q regardless.
• No reaction or flocculation kinetics included in the definition.

Concept / Approach:
By definition, detention time t = V / Q, where V is the tank volume and Q is the flow rate. Physically, it is the time the flow would take to fill the tank once, not the time a specific particle takes to settle or traverse the basin (which depends on velocity fields and particle properties).

Step-by-Step Solution:
Start from t = V / Q.Interpretation: time to displace a volume equal to the tank volume at the prevailing flow.Hence, the correct qualitative description is the time required for the flow to fill the tank once.

Verification / Alternative check:
Detention time is also called hydraulic retention time (HRT) in many unit processes and is universally defined as V/Q, confirming the selection.

Why Other Options Are Wrong:
Particle travel times (options a, b, e) refer to settling velocity and trajectory, not the hydraulic definition of detention time.None of these: incorrect because option (c) precisely states the definition.

Common Pitfalls:

• Equating detention time with settling time of a specific particle class.
• Ignoring that short-circuiting reduces effective detention time compared to theoretical t = V/Q.

Final Answer:
The incoming sewage flow to fill the tank volume once