DO Deficit Using Streeter-Phelps Equation Calculator

Streeter-Phelps Equation:

\[ D = \frac{K_D \cdot L}{K_R - K_D} \cdot (10^{-K_D \cdot t} - 10^{-K_R \cdot t}) + D_o \cdot 10^{-K_R \cdot t} \]

Deoxygenation Constant (K_D):

1/s

Organic Matter at Start (L):

kg/m³

Reoxygenation Coefficient (K_R):

1/s

Time in Days (t):

days

Initial Oxygen Deficit (D_o):

kg/m³

Oxygen Deficit (D):

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1. What is the Streeter-Phelps Equation?

The Streeter-Phelps equation is a fundamental model in water quality engineering that describes the dissolved oxygen (DO) deficit in rivers and streams. It accounts for both the deoxygenation caused by organic matter decomposition and the reoxygenation from atmospheric exchange.

2. How Does the Calculator Work?

The calculator uses the Streeter-Phelps equation:

\[ D = \frac{K_D \cdot L}{K_R - K_D} \cdot (10^{-K_D \cdot t} - 10^{-K_R \cdot t}) + D_o \cdot 10^{-K_R \cdot t} \]

Where:

\( D \) — Oxygen Deficit (kg/m³)
\( K_D \) — Deoxygenation Constant (1/s)
\( L \) — Organic Matter at Start (kg/m³)
\( K_R \) — Reoxygenation Coefficient (1/s)
\( t \) — Time in Days
\( D_o \) — Initial Oxygen Deficit (kg/m³)

Explanation: The equation models the balance between oxygen consumption by organic matter decomposition and oxygen replenishment from atmospheric reaeration.

3. Importance of DO Deficit Calculation

Details: Accurate DO deficit calculation is crucial for assessing water quality, predicting oxygen sag curves in rivers, and designing wastewater treatment systems to maintain healthy aquatic ecosystems.

4. Using the Calculator

Tips: Enter all parameters in consistent units. Deoxygenation and reoxygenation coefficients should be in 1/s, organic matter and oxygen deficit in kg/m³, and time in days. Ensure K_R ≠ K_D for valid calculation.

5. Frequently Asked Questions (FAQ)

Q1: What is oxygen deficit in water quality modeling?
A: Oxygen deficit refers to the difference between the saturated dissolved oxygen concentration and the actual dissolved oxygen concentration in water.

Q2: How are K_D and K_R determined?
A: K_D is typically determined from BOD tests, while K_R is estimated from empirical relationships based on stream velocity, depth, and temperature.

Q3: What is the significance of the oxygen sag curve?
A: The oxygen sag curve shows the spatial or temporal variation of dissolved oxygen downstream from a pollution discharge point, helping identify critical deficit points.

Q4: What are typical values for K_D and K_R?
A: K_D typically ranges from 0.1-0.5 day⁻¹ (1.16×10⁻⁶ to 5.79×10⁻⁶ s⁻¹), while K_R ranges from 0.2-2.0 day⁻¹ (2.31×10⁻⁶ to 2.31×10⁻⁵ s⁻¹) for most rivers.

Q5: What are the limitations of the Streeter-Phelps model?
A: The model assumes constant parameters, ignores photosynthesis/respiration, and doesn't account for multiple waste discharges or non-point sources.