Oxygen Deficit Given Critical Time In Self Purification Factor Calculator

Formula Used:

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

Oxygen Equivalent (Lt):

kg/m³

Self-Purification Constant (f):

Critical Time (tc):

seconds

Deoxygenation Constant (KD):

1/s

Critical Oxygen Deficit (Dc):

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1. What is Critical Oxygen Deficit?

Critical Oxygen Deficit refers to the condition where the deoxygenation rate exceeds the reoxygenation rate in water bodies. It represents the maximum oxygen deficit that occurs during the self-purification process of wastewater.

2. How Does the Calculator Work?

The calculator uses the oxygen deficit formula:

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

Where:

\( D_c \) — Critical Oxygen Deficit (kg/m³)
\( L_t \) — Oxygen Equivalent - oxidizable organic matter (kg/m³)
\( f \) — Self-Purification Constant (ratio of reoxygenation to deoxygenation constants)
\( t_c \) — Critical Time - when minimum dissolved oxygen occurs (seconds)
\( K_D \) — Deoxygenation Constant (1/s)

Explanation: The equation calculates the maximum oxygen deficit that occurs during the self-purification process, considering the balance between oxygen consumption and reaeration.

3. Importance of Critical Oxygen Deficit Calculation

Details: Calculating critical oxygen deficit is crucial for assessing the impact of wastewater discharge on receiving water bodies, designing wastewater treatment systems, and predicting oxygen sag curves in rivers and streams.

4. Using the Calculator

Tips: Enter Oxygen Equivalent in kg/m³, Self-Purification Constant (must not equal 1), Critical Time in seconds, and Deoxygenation Constant in 1/s. All values must be positive numbers.

5. Frequently Asked Questions (FAQ)

Q1: What is the significance of Critical Oxygen Deficit?
A: It helps determine the maximum oxygen depletion in water bodies, which is critical for maintaining aquatic life and assessing the assimilative capacity of receiving waters.

Q2: Why must the Self-Purification Constant not equal 1?
A: When f=1, the denominator becomes zero, making the equation undefined. This represents a special case where reoxygenation and deoxygenation rates are equal.

Q3: What are typical values for Deoxygenation Constant?
A: KD typically ranges from 0.1 to 0.4 per day (0.00000116 to 0.00000463 per second) for domestic sewage, depending on temperature and wastewater characteristics.

Q4: How is Critical Time determined?
A: Critical Time is found by differentiating the dissolved oxygen equation with respect to time and setting the derivative equal to zero to find the minimum point.

Q5: What factors affect the Self-Purification Constant?
A: The Self-Purification Constant depends on water temperature, flow velocity, depth, and atmospheric conditions that affect oxygen transfer rates.