Every unit process in a plant is a promise about time. Settling needs time. Floc formation needs time. Chlorine needs contact time or it has not disinfected anything. The number that measures all of it is the hydraulic detention time, $t = \dfrac{V}{Q}$ — read aloud t equals V over Q.

Name the letters before they work. $t$ is the detention time, the average time a drop of water spends inside the tank — hours for a clarifier, minutes for a rapid mixer. $V$ is the working volume, the water the tank actually holds below the weir, in cubic metres, and not the volume out to the top of the concrete. $Q$ is the flow passing through, in cubic metres per hour or per day. You solve for $t$ when the tank exists and you want to know what it gives; for $V$ when you are sizing one to a specification; and for $Q$ when a regulator has fixed the time and you need the flow ceiling that keeps it.

The argument is a bathtub. A 600 litre tub filling at 200 litres a minute takes three minutes to fill — and if you then run it steadily, plug out and tap on, three minutes is how long the average litre stays. Nothing more sophisticated is happening in a clarifier.

Units are the whole examination. $V$ in m³ over $Q$ in m³/h leaves hours. The same volume over m³/d leaves days, and a primary clarifier quoted in days is the classic sign that nobody checked. Figures worth carrying: rapid mix 1 to 3 minutes, flocculation 20 to 30 minutes, primary clarifier 1.5 to 3 hours, secondary clarifier 2 to 4 hours, chlorine contact 30 minutes at peak flow.

One honest caveat. This is the theoretical detention time, and a real tank never achieves it — short-circuiting sends some water straight from inlet to weir while dead corners hold the rest for hours. A tracer study measures the truth; $V/Q$ sets the ceiling the tank can never beat.