Critical Time Given Self Purification Factor Calculator

Critical Time Formula:

\[ t_c = -\frac{\log_{10}\left(1 - \frac{(f - 1) \cdot D_c \cdot f}{L_t}\right)}{K_D \cdot (f - 1)} \]

Self-Purification Constant (f):

(unitless)

Critical Oxygen Deficit (Dc):

(unitless)

Oxygen Equivalent (Lt):

kg/m³

Deoxygenation Constant (KD):

1/s

Critical Time (tc):

Unit Converter ▲

Unit Converter ▼

From:	To:

1. What is Critical Time?

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

2. How Does the Calculator Work?

The calculator uses the Critical Time formula:

\[ t_c = -\frac{\log_{10}\left(1 - \frac{(f - 1) \cdot D_c \cdot f}{L_t}\right)}{K_D \cdot (f - 1)} \]

Where:

\( t_c \) — Critical Time (seconds)
\( f \) — Self-Purification Constant (unitless)
\( D_c \) — Critical Oxygen Deficit (unitless)
\( L_t \) — Oxygen Equivalent (kg/m³)
\( K_D \) — Deoxygenation Constant (1/s)

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

3. Importance of Critical Time Calculation

Details: Calculating critical time is essential for water quality management, wastewater treatment planning, and environmental impact assessment of organic pollution in water bodies.

4. Using the Calculator

Tips: Enter all required parameters with appropriate units. Ensure values are positive and Self-Purification Constant is greater than 1 to avoid mathematical errors.

5. Frequently Asked Questions (FAQ)

Q1: What is Self-Purification Constant?
A: Self-Purification Constant is the ratio of reoxygenation constant to deoxygenation constant, representing the natural cleansing capacity of a water body.

Q2: What does Critical Oxygen Deficit represent?
A: Critical Oxygen Deficit represents the condition where the deoxygenation rate exceeds the reoxygenation rate in a water body.

Q3: How is Oxygen Equivalent defined?
A: Oxygen Equivalent refers to the oxidizable organic matter present in sewage, measured in kg/m³.

Q4: What is Deoxygenation Constant?
A: Deoxygenation Constant is the value obtained after decomposition of oxygen in sewage, measured in 1/s.

Q5: When is this calculation most relevant?
A: This calculation is most relevant for environmental engineers and water quality specialists assessing the impact of organic pollution on dissolved oxygen levels in natural water bodies.