Question

The Streeter-Phelp's oxygen sag equation for a river is based on a few assumptions. The correct assumption(s) is/are

• A. At any instant the deoxygenation rate is directly proportional to the amount of oxidizable organic material present.
• B. At any instant the deoxygenation rate is inversely proportional to the amount of oxidizable organic material present.
• C. The reoxygenation rate is directly proportional to the dissolved oxygen deficit.
• D. The reoxygenation rate and deoxygenation rate are directly proportional to the saturation concentration of dissolved oxygen.

Answer 1

The Correct Option is A, C

Step 1: Key principles of the Streeter–Phelps oxygen sag equation. The Streeter–Phelps model describes the change in dissolved oxygen (DO) in a river due to two main processes: 

1. Deoxygenation: Oxygen is consumed by the breakdown of organic matter. 
2. Reoxygenation: Oxygen is replenished from the atmosphere. 

Step 2: Assumptions of the model. 1. The deoxygenation rate is proportional to the amount of oxidizable organic matter present in the water. This is mathematically represented as: \[ r_{\text{deoxygenation}} = k_d L \] where \( k_d \) is the deoxygenation rate constant, and \( L \) is the concentration of oxidizable organic matter. 2. The reoxygenation rate is proportional to the oxygen deficit (\( D \)), which is the difference between the saturation DO and the actual DO: \[ r_{\text{reoxygenation}} = k_r D \] where \( k_r \) is the reoxygenation rate constant, and \( D \) is the oxygen deficit. 

Step 3: Analyze each statement. 
(1) At any instant the deoxygenation rate is directly proportional to the amount of oxidizable organic material present: 
This is correct, as the deoxygenation rate depends on the organic matter available for breakdown. 
(2) At any instant the deoxygenation rate is inversely proportional to the amount of oxidizable organic material present: 
This is incorrect, as the deoxygenation rate is directly proportional, not inversely proportional, to the organic matter concentration. 
(3) The reoxygenation rate is directly proportional to the dissolved oxygen deficit: 
This is correct, as the oxygen deficit drives the reoxygenation process. 
(4) The reoxygenation rate and deoxygenation rate are directly proportional to the saturation concentration of dissolved oxygen: 
This is incorrect, as the reoxygenation rate is proportional to the deficit, not directly to the saturation DO concentration.