Half an hour, a litre of mixed liquor and a graduated cylinder will tell you more about a secondary plant than a day of paperwork. The number it produces is the sludge volume index: $\text{SVI} = \dfrac{SV_{30}}{X}$ — S-V-I equals S-V-thirty over X.

$SV_{30}$ is the settled sludge volume after thirty minutes, read straight off the cylinder in millilitres per litre. $X$ is the MLSS of the same sample in mg/L. $\text{SVI}$ is the volume one gram of those solids occupies once settled, in mL/g. In working form, because the units are not friendly: $\text{SVI} = \dfrac{SV_{30}\ [\mathrm{mL/L}] \times 1000}{X\ [\mathrm{mg/L}]}$. That thousand is the milligram-to-gram bridge and it is the one thing this calculation gets wrong.

Read the scale like a thermometer. Around 100 mL/g is a healthy, well-settling sludge and it is the number to anchor on. Below about 70 the sludge is dense and often old — it settles fast, but it can shear into pin floc that never settles at all and leaves a hazy effluent. Above about 150 the sludge is bulking: filaments have taken over, the flocs cannot pack down, and the blanket climbs toward the weir.

Notice why the division matters. A high settled volume on its own means nothing — thick mixed liquor should fill more of the cylinder. Only volume per gram is a judgement, and that is precisely why the index exists.

The return line is the answer to what the index reveals. $Q_r = \dfrac{Q\,X}{X_r - X}$, where $Q_r$ is the return activated sludge flow in m³/d, $Q$ is the influent flow, $X$ is the target MLSS in the basin and $X_r$ is the return sludge concentration off the clarifier floor — subscript r is the return line, always the thicker of the two. It is nothing but a solids balance: what the return carries in must equal what the mixed liquor carries out.

Read the denominator and the operating life of a secondary plant falls out of it. The driver is the difference $X_r - X$, not $X_r$ itself. When the sludge bulks, it will not thicken, $X_r$ falls toward $X$, the difference shrinks — and the return flow needed to hold the same MLSS climbs steeply. That is the spiral: bulking forces more return, more return loads the clarifier harder, and the blanket rises faster still. The pump can hold the line for a while. Only fixing the sludge ends it.