MathSVI calculation from settleometer and MLSS

SVI Calculation from Settleometer and MLSS

Calculate the Sludge Volume Index from a 30-minute settleometer test. Covers the SVI formula, unit conversion trap (mL vs L), and interpretation.

An activated sludge plant runs a 30-minute settleometer test using a 1-L graduated cylinder. After 30 minutes, the settled sludge volume (SV30) reads 280 mL. The lab reports MLSS = 2,400 mg/L from the aeration basin sample. Extraneous data: RAS flow = 850 gpm and SRT = 10 days. Using SVI = (settled volume in mL/L × 1000) ÷ MLSS (mg/L), what is the Sludge Volume Index (SVI) in mL/g? (Note: a 1-L cylinder reading in mL is numerically equal to mL/L.)

Answer Choices

A) 117 mL/g Correct

Correct. SV30 = 280 mL/L (because the test used a 1-L cylinder). SVI = (280 mL/L × 1000) ÷ (2400 mg/L) = 116.7 mL/g ≈ 117 mL/g. Sanity check: 117 mL/g is a typical, reasonable SVI value for activated sludge.

B) 8.6 mL/g

This comes from inverting the relationship or forgetting the ×1000 conversion to mL/g: 2400 ÷ 280 = 8.6. SVI is based on settled volume per mass of solids, so the settled volume goes in the numerator and the 1000 factor is needed to convert mg to g.

C) 0.12 mL/g

This results from converting 280 mL to 0.28 L and then still treating it as if the formula used mL/L: (0.28 × 1000) ÷ 2400 = 0.117. The formula requires settled volume in mL/L, so use 280 mL/L, not 0.28 L/L.

D) 672 mL/g

This comes from multiplying MLSS and settled volume instead of dividing and/or putting 1000 in the wrong place: (280 × 2400) ÷ 1000 = 672. SVI should decrease as MLSS increases (for the same settled volume), so division by MLSS is required.

Step-by-Step Solution

  1. Given SV30 = 280 mL in a 1-L cylinder ⇒ 280 mL/L
  2. Given MLSS = 2,400 mg/L
  3. SVI = (SV30 mL/L × 1000 mg/g) ÷ (MLSS mg/L)
  4. SVI = (280 mL/L × 1000 mg/g) ÷ (2,400 mg/L)
  5. SVI = (280,000 mL·mg/(L·g)) ÷ (2,400 mg/L) = 116.7 mL/g
  6. Rounded SVI ≈ 117 mL/g

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