Water operator math tutorial
Sludge Volume Index (SVI)
Relate 30-minute settled volume to MLSS to judge how well sludge settles.
SVI is the volume in mL occupied by one gram of activated sludge after 30 minutes of settling. A lower SVI means sludge that settles and compacts well.
It is a quick health check on the biology, and operators trend it alongside the F/M ratio and MCRT.
The formula
SVI (mL/g) = [settled sludge volume (mL/L) × 1,000] ÷ MLSS (mg/L)
| Variable | Unit |
|---|---|
| 30-minute settled volume | mL/L |
| MLSS | mg/L |
| Result: SVI | mL/g |
Conversion factors used: 1,000 mg per gram.
Applies to: Wastewater Treatment.
Common exam tip: Use the 30-minute reading, not the 60-minute one. SVI is defined at 30 minutes.
Calculator
SVI
100 mL/g
- 1. (250 × 1,000) ÷ 2,500 = 100 mL/g
For instructional use. Results assume the standard conversion factors shown on this page. Actual field calculations may need chemical strength, density, temperature, and other adjustments, so check your plant’s procedures.
Worked examples
Example 1
A 30-minute settleometer reads 250 mL/L at 2,500 mg/L MLSS.
- (250 × 1,000) ÷ 2,500 = 100 mL/g
Answer: 100 mL/g
Example 2
300 mL/L settles from 3,200 mg/L MLSS.
- (300 × 1,000) ÷ 3,200 = 93.8 mL/g
Answer: 93.8 mL/g
Common mistakes
Wrong result: 0.1 mL/g
leaving out the 1,000 multiplier
Wrong result: 10,000 mL/g
dividing MLSS by the settled volume (upside down)
Practice questions
1. Settled volume 180 mL/L, MLSS 2,000 mg/L. SVI?
- A0.1 mL/g
- B11,111.1 mL/g
- C90 mL/g
- D900 mL/g
Show answer and explanation
Correct answer: C. (180 × 1,000) ÷ 2,000 = 90 mL/g Answer: 90 mL/g. A common slip is leaving out the 1,000 multiplier, which gives 0.1 mL/g.
2. Settled volume 400 mL/L, MLSS 2,800 mg/L. SVI?
- A0.1 mL/g
- B7,000 mL/g
- C1,429 mL/g
- D142.9 mL/g
Show answer and explanation
Correct answer: D. (400 × 1,000) ÷ 2,800 = 142.9 mL/g Answer: 142.9 mL/g. A common slip is leaving out the 1,000 multiplier, which gives 0.1 mL/g.
3. Settled volume 220 mL/L, MLSS 3,500 mg/L. SVI?
- A62.9 mL/g
- B0.1 mL/g
- C15,909.1 mL/g
- D629 mL/g
Show answer and explanation
Correct answer: A. (220 × 1,000) ÷ 3,500 = 62.9 mL/g Answer: 62.9 mL/g. A common slip is leaving out the 1,000 multiplier, which gives 0.1 mL/g.
Where this formula applies
This calculation can appear in the disciplines below. Exact exam coverage depends on your state, certification level, and official exam outline.
Wastewater Treatment
Study guides
Keep going with the full guide
Water Operator Math Made Simple walks through operator math step by step and includes printable references plus a full practice exam.
Water Operator Math Made Simple
A Step-by-Step Guide to the Math Every Water Operator Needs to Know