One litre of sewage gives sludge volume of 40 cm³ after 30 minutes settling. If dry solids = 4.0 g, the sludge volume index (SVI) is
- A40
- B10Correct
- C30
- D81
Solution
Concept
Sludge Volume Index definition and calculation
Formula
SVI = (Settled Sludge Volume in mL/L) / (MLSS in g/L)
Step-by-step solution
1. Settled sludge volume V30 = 40 cm³ = 40 mL. 2. Dry suspended solids mass X = 4.0 g in 1 L. 3. SVI = V30 / X = 40 mL / 4.0 g = 10 mL/g. 4. Therefore, the sludge volume index is 10. Answer: B
Explanation
Sludge Volume Index (SVI) is defined as the volume in milliliters occupied by 1 gram of activated sludge after 30 minutes of settling in a 1-liter graduated cylinder. Given settled sludge volume = 40 cm³ = 40 mL and suspended solids dry mass = 4.0 g in 1 L, SVI = (40 mL) / (4.0 g) = 10 mL/g.
Why the other options are wrong
A) 40 takes only the volume without dividing by dry solids mass. C) 30 confuses settling time (30 minutes) with index value. D) 81 is an erroneous calculation.
Shortcut
SVI = mL of settled sludge / g of dry solids = 40 / 4 = 10.
Common mistake
Inverting the ratio or using incorrect unit conversions between cm³ and mL.
Correct answer: B) 10