Critical Time Given Self Purification Constant With Critical Oxygen Deficit Calculator

Formula Used:

\[ t_c = \frac{\log_{10}\left(\frac{D_c \times f}{L_t}\right)}{K_D} \]

Critical Oxygen Deficit (Dc):

Self-Purification Constant (f):

Oxygen Equivalent (Lt):

kg/m³

Deoxygenation Constant (KD):

1/s

Critical Time (tc):

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1. What is Critical Time?

Critical Time refers to the minimum dissolved oxygen concentration occurs, found by differentiating the dissolved oxygen equation with respect to time. It represents the point where the deoxygenation rate exceeds the reoxygenation rate in water bodies.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ t_c = \frac{\log_{10}\left(\frac{D_c \times f}{L_t}\right)}{K_D} \]

Where:

\( t_c \) — Critical Time (seconds)
\( D_c \) — Critical Oxygen Deficit
\( f \) — Self-Purification Constant (ratio of reoxygenation constant to deoxygenation constant)
\( L_t \) — Oxygen Equivalent (kg/m³, oxidizable organic matter present in sewage)
\( K_D \) — Deoxygenation Constant (1/s, value obtained after decomposing of oxygen in sewage)

Explanation: The formula calculates the time when oxygen deficit reaches its maximum value in a water body undergoing organic pollution.

3. Importance of Critical Time Calculation

Details: Calculating critical time is essential for water quality management, predicting oxygen sag curves in rivers and streams, and designing wastewater treatment systems to prevent anaerobic conditions.

4. Using the Calculator

Tips: Enter all required parameters with appropriate units. Ensure all values are positive and the expression (Dc * f / Lt) results in a positive number for valid logarithm calculation.

5. Frequently Asked Questions (FAQ)

Q1: What is Critical Oxygen Deficit?
A: Critical Oxygen Deficit refers to the condition where the deoxygenation rate exceeds the reoxygenation rate in a water body.

Q2: What does Self-Purification Constant represent?
A: Self-Purification Constant is the ratio of reoxygenation constant to deoxygenation constant, indicating the natural cleansing capacity of a water body.

Q3: How is Oxygen Equivalent measured?
A: Oxygen Equivalent represents the oxidizable organic matter present in sewage, typically measured in kg/m³ through biochemical oxygen demand tests.

Q4: What factors affect Deoxygenation Constant?
A: Deoxygenation Constant depends on temperature, nature of organic matter, and microbial activity in the water body.

Q5: When is this calculation most applicable?
A: This calculation is particularly useful for predicting oxygen levels in rivers and streams receiving organic waste discharges.