A rapid gravity filter is measured by three numbers, and they are all the same arithmetic wearing different hats.

The filtration rate is $v_f = \dfrac{Q}{A}$, where $v_f$ is the approach velocity in metres per hour, $Q$ is the filtered flow in m³/h and $A$ is the plan area of the media in m². It is the same shape as a clarifier's overflow rate and it means something similar: the speed the water would descend if the sand were not in the way. Conventional rapid sand runs 5 to 12 m/h; a slow sand filter runs 0.1 to 0.3, which is why it needs a hundred times the land.

The backwash volume is $V_{bw} = v_b\,A\,t$ — V-b-w equals v-b, A, t. $v_b$ is the backwash rise rate in m/h, high enough to fluidise the bed and lift the trapped floc out — typically 30 to 50 m/h, several times the forward rate. $A$ is the same bed area, and $t$ is the duration of the wash, usually 8 to 15 minutes. The watchpoint is in plain sight: the rate is per hour and the wash is quoted in minutes. One of them has to move before they multiply.

The housekeeping ratio closes the loop: $\%BW = \dfrac{V_{bw}}{V_f} \times 100$, where $V_f$ is the water the filter produced during the run — the filtration rate, times the area, times the hours it ran. Note carefully what the comparison is against: production, not raw water in. A healthy plant spends 2 to 4% of its own output washing its filters.

Here is the operational nugget. That percentage is a diagnosis, not a cost line. If it climbs past 5%, the filter is usually not the problem — the coagulation is. Poor floc blinds the top of the bed, head loss builds early, runs shorten, and each wash costs the same volume regardless. Chasing it by shortening the washes only leaves dirty media, and dirty media shortens the next run. The fix is upstream, every time.