Solved Problems

Applying sedimentation principles to basin design
Problem 1: Sedimentation Basin Sizing
A water treatment plant treats a flow (QQ) of 10,000 m³/day. The design surface overflow rate (v0v_0) is 20 m³/m²·day. The basin depth (HH) is 3 m.

Procedure

  1. Calculate the required surface area of the basin.
  2. Calculate the hydraulic retention time (HRT) in hours.

Example

Sedimentation Basin Sizing

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Problem 2: F/M Ratio Calculation
An aeration tank has a volume (VV) of 2,000 m³ and operates with a Mixed Liquor Volatile Suspended Solids (MLVSS, XX) concentration of 2,500 mg/L. The influent flow rate (Q0Q_0) is 5,000 m³/day and the influent BOD (S0S_0) is 200 mg/L.

Procedure

  1. Calculate the total mass of microorganisms (MLVSS) in the tank (kg).
  2. Calculate the daily BOD load entering the tank (kg/day).
  3. Calculate the F/M ratio (day⁻¹).

Example

F/M Ratio Calculation

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Disinfection Kinetics (Chick's Law)

Calculating pathogen reduction over time

A water treatment plant uses chlorine for disinfection. The initial concentration of coliform bacteria is N0=10,000 organisms/100 mLN_0 = 10,000 \text{ organisms/100 mL}. The decay constant kk is 0.5 min−10.5 \text{ min}^{-1}. Calculate the contact time tt required to achieve a 99.9%99.9\% reduction (3-log removal) of coliforms.

Example

Chick's Law Calculation

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Sludge Volume Index (SVI)

Evaluating sludge settleability

In a mixed liquor sample, the suspended solids concentration (MLSS) is 3,000 mg/L3,000 \text{ mg/L}. After 30 minutes of settling in a 1,000 mL1,000 \text{ mL} graduated cylinder, the settled sludge volume is 240 mL240 \text{ mL}. Calculate the Sludge Volume Index (SVI) and evaluate the sludge settleability.

Example

Calculate SVI

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