Detention Time Calculator
An average, not a uniform time — short-circuiting and dead zones are why tracer studies exist.
The formula
retention time = volume / flow rate
The simplest useful number in process design
Divide the working volume of a tank by the rate liquid flows through it and you get the average time a parcel of water spends inside. Every biological treatment process is designed around it: the bacteria need long enough to do their work, and a tank that empties too fast washes them out faster than they can reproduce.
Average is not uniform
The figure is a mean, and real tanks do not behave like the ideal that assumes. Short-circuiting sends some flow from inlet to outlet in a fraction of the nominal time while dead zones hold other water far longer. Tracer studies exist precisely because the calculated retention time and the actual distribution of residence times can differ substantially.
Where these models stop
Michaelis-Menten assumes a single substrate and a steady state; Langmuir assumes one layer on identical sites with no interaction between them; Stokes-Einstein assumes a hard sphere much larger than the solvent molecules around it. Each is an idealisation that happens to describe real systems well over a useful range, and each fails predictably outside it. Knowing which assumption a number rests on is usually more valuable than the number.