1) It represents the concentration of the sludge in the system which helps in controlling rate of return of sludge.

2) In order to maintain the desired MLSS concentration corresponding to a particular $\frac{R}{M}$ ratio to achieve the required degree of treatment.

$$ SV_1 \rightarrow X_U \rightarrow Q_R \rightarrow X \rightarrow \frac{F}{M} \rightarrow n(\%)$$

3) Sludge Volume Index is defined as the volume occupied in ml by 1 gram of solid in mixed liquor when allowed to settle for 30 minute.

$$ SV_1 (ml/gm) \lt----\gt X_U (mg/l) (conc) $$

$\frac{10^6}{SV_1}=X_U$

$SV_1=\frac{10^6}{X_4}$

$\frac{Q_R}{Q}=\frac{X}{X_4-X}=\frac{X}{\frac{10^6}{SV_1}-X}$

4) For municipal sewage, sludge volume index is 80-150 ml/gram.

5) Sludge volume index is determined by collecting 1 gram of the mixed liquor from the discharge end of the aeration tank in the calibrated container and is allowed to settle for 30 minutes and the volume of solids settled in it are noted.

6) After remixing the solid in the sample it is further being tested for MLSS present in it performing the standard test to determine suspended solid in the given sample.

$SV_1=\frac{V_0b(ml/l)}{X_0b(mg/l)}(ml/gm)$

$SV_1=\frac{V_0b*10^3}{X_0b}$(ml/g)