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DO Deficit using Streeter-Phelps Equation Formula

GoOxygen Deficit Formula

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Oxygen Deficit is referred as the sum of the minute differences between the measured oxygen uptake and the oxygen uptake occurring during steady-state work at that same rate. Check FAQs

D = (K D \cdot \frac{L}{K R - K D}) \cdot (10^{- K D \cdot t} - 10^{- K R \cdot t} + D o \cdot 10^{- K R \cdot t})

D - Oxygen Deficit?K_D - Deoxygenation Constant?L - Organic Matter at Start?K_R - Reoxygenation Coefficient?t - Time in Days?D_o - Initial Oxygen Deficit?

DO Deficit using Streeter-Phelps Equation Example

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Here is how the DO Deficit using Streeter-Phelps Equation equation looks like with Values.

Here is how the DO Deficit using Streeter-Phelps Equation equation looks like with Units.

Here is how the DO Deficit using Streeter-Phelps Equation equation looks like.

5.3649 = (0.23 \cdot \frac{40}{0.22 - 0.23}) \cdot (10^{- 0.23 \cdot 6} - 10^{- 0.22 \cdot 6} + 7.2 \cdot 10^{- 0.22 \cdot 6})

5.3649mg/L = (0.23d⁻¹ \cdot \frac{40mg/L}{0.22d⁻¹ - 0.23d⁻¹}) \cdot (10^{- 0.23d⁻¹ \cdot 6d} - 10^{- 0.22d⁻¹ \cdot 6d} + 7.2mg/L \cdot 10^{- 0.22d⁻¹ \cdot 6d})

5.3649 = (0.23 \cdot \frac{40}{0.22 - 0.23}) \cdot (10^{- 0.23 \cdot 6} - 10^{- 0.22 \cdot 6} + 7.2 \cdot 10^{- 0.22 \cdot 6})

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DO Deficit using Streeter-Phelps Equation Solution

Follow our step by step solution on how to calculate DO Deficit using Streeter-Phelps Equation?

FIRST Step Consider the formula

D = (K D \cdot \frac{L}{K R - K D}) \cdot (10^{- K D \cdot t} - 10^{- K R \cdot t} + D o \cdot 10^{- K R \cdot t})

Next Step Substitute values of Variables

∴

D = (0.23d⁻¹ \cdot \frac{40mg/L}{0.22d⁻¹ - 0.23d⁻¹}) \cdot (10^{- 0.23d⁻¹ \cdot 6d} - 10^{- 0.22d⁻¹ \cdot 6d} + 7.2mg/L \cdot 10^{- 0.22d⁻¹ \cdot 6d})

Next Step Convert Units

∴

D = (2.7E-6s⁻¹ \cdot \frac{0.04kg/m³}{2.5E-6s⁻¹ - 2.7E-6s⁻¹}) \cdot (10^{- 2.7E-6s⁻¹ \cdot 518400s} - 10^{- 2.5E-6s⁻¹ \cdot 518400s} + 0.0072kg/m³ \cdot 10^{- 2.5E-6s⁻¹ \cdot 518400s})

Next Step Prepare to Evaluate

∴

D = (2.7E-6 \cdot \frac{0.04}{2.5E-6 - 2.7E-6}) \cdot (10^{- 2.7E-6 \cdot 518400} - 10^{- 2.5E-6 \cdot 518400} + 0.0072 \cdot 10^{- 2.5E-6 \cdot 518400})

Next Step Evaluate

∴

D = 0.00536494064125733kg/m³

Next Step Convert to Output's Unit

∴

D = 5.36494064125733mg/L

LAST Step Rounding Answer

∴

D = 5.3649mg/L

DO Deficit using Streeter-Phelps Equation Formula Elements

Variables

Oxygen Deficit

Oxygen Deficit is referred as the sum of the minute differences between the measured oxygen uptake and the oxygen uptake occurring during steady-state work at that same rate.

Symbol: D

Measurement: DensityUnit: mg/L

Note: Value should be greater than 0.

Formulas to find Oxygen Deficit

Deoxygenation Constant

Deoxygenation Constant is referred as the value obtained after decomposing of oxygen in sewage.

Symbol: K_D

Measurement: First Order Reaction Rate ConstantUnit: d⁻¹

Note: Value should be greater than 0.

Formulas to find Deoxygenation Constant

Organic Matter at Start

Organic Matter at Start is referred as the total organic matter present in the sewage at the start of the BOD reaction.

Symbol: L

Measurement: DensityUnit: mg/L

Note: Value should be greater than 0.

Formulas to find Organic Matter at Start

Reoxygenation Coefficient

Reoxygenation Coefficient is referred as the parameter used in water quality modeling to describe the rate at which oxygen is transferred from the atmosphere to the water body.

Symbol: K_R

Measurement: First Order Reaction Rate ConstantUnit: d⁻¹

Note: Value should be greater than 0.

Formulas to find Reoxygenation Coefficient

Time in Days

Time in Days is referred as the critical factor in various calculations and models related to sewage treatment, water quality, and environmental engineering.

Symbol: t

Measurement: TimeUnit: d

Note: Value should be greater than 0.

Formulas to find Time in Days

Initial Oxygen Deficit

Initial Oxygen Deficit is referred as the amount of oxygen required at initial levels.

Symbol: D_o

Measurement: DensityUnit: mg/L

Note: Value should be greater than 0.

Formulas to find Initial Oxygen Deficit

Other Formulas to find Oxygen Deficit

Go Oxygen Deficit

D = S DO - A DO

Other formulas in Oxygen Deficit category

Go Log value of Critical Oxygen Deficit

D c = 10^{\log 10 (\frac{L t}{f}) - (K D \cdot t c)}

Go Oxygen Deficit given Critical Time in Self Purification Factor

D c = (\frac{L t}{f - 1}) \cdot (1 - (\frac{10^{t c \cdot K D \cdot (f - 1)}}{f}))

How to Evaluate DO Deficit using Streeter-Phelps Equation?

DO Deficit using Streeter-Phelps Equation evaluator uses Oxygen Deficit = (Deoxygenation Constant*Organic Matter at Start/(Reoxygenation Coefficient-Deoxygenation Constant))*(10^(-Deoxygenation Constant*Time in Days)-10^(-Reoxygenation Coefficient*Time in Days)+Initial Oxygen Deficit*10^(-Reoxygenation Coefficient*Time in Days)) to evaluate the Oxygen Deficit, The DO Deficit using Streeter-Phelps Equation formula is defined as the sum of the minute differences between the measured oxygen uptake and the oxygen uptake occurring during steady state work at that same rate. Oxygen Deficit is denoted by D symbol.

How to evaluate DO Deficit using Streeter-Phelps Equation using this online evaluator? To use this online evaluator for DO Deficit using Streeter-Phelps Equation, enter Deoxygenation Constant (K_D), Organic Matter at Start (L), Reoxygenation Coefficient (K_R), Time in Days (t) & Initial Oxygen Deficit (D_o) and hit the calculate button.

FAQs on DO Deficit using Streeter-Phelps Equation

What is the formula to find DO Deficit using Streeter-Phelps Equation?

The formula of DO Deficit using Streeter-Phelps Equation is expressed as Oxygen Deficit = (Deoxygenation Constant*Organic Matter at Start/(Reoxygenation Coefficient-Deoxygenation Constant))*(10^(-Deoxygenation Constant*Time in Days)-10^(-Reoxygenation Coefficient*Time in Days)+Initial Oxygen Deficit*10^(-Reoxygenation Coefficient*Time in Days)). Here is an example- 1152.09 = (2.66203703703704E-06*0.04/(2.5462962962963E-06-2.66203703703704E-06))*(10^(-2.66203703703704E-06*518400)-10^(-2.5462962962963E-06*518400)+0.0072*10^(-2.5462962962963E-06*518400)).

How to calculate DO Deficit using Streeter-Phelps Equation?

With Deoxygenation Constant (K_D), Organic Matter at Start (L), Reoxygenation Coefficient (K_R), Time in Days (t) & Initial Oxygen Deficit (D_o) we can find DO Deficit using Streeter-Phelps Equation using the formula - Oxygen Deficit = (Deoxygenation Constant*Organic Matter at Start/(Reoxygenation Coefficient-Deoxygenation Constant))*(10^(-Deoxygenation Constant*Time in Days)-10^(-Reoxygenation Coefficient*Time in Days)+Initial Oxygen Deficit*10^(-Reoxygenation Coefficient*Time in Days)).

What are the other ways to Calculate Oxygen Deficit?

Here are the different ways to Calculate Oxygen Deficit-

Oxygen Deficit=Saturated Dissolved Oxygen-Actual Dissolved Oxygen

Can the DO Deficit using Streeter-Phelps Equation be negative?

No, the DO Deficit using Streeter-Phelps Equation, measured in Density cannot be negative.

Which unit is used to measure DO Deficit using Streeter-Phelps Equation?

DO Deficit using Streeter-Phelps Equation is usually measured using the Milligram per Liter[mg/L] for Density. Kilogram per Cubic Meter[mg/L], Kilogram per Cubic Centimeter[mg/L], Gram per Cubic Meter[mg/L] are the few other units in which DO Deficit using Streeter-Phelps Equation can be measured.

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DO Deficit using Streeter-Phelps Equation Formula

​GoOxygen Deficit Formula

DO Deficit using Streeter-Phelps Equation Example

DO Deficit using Streeter-Phelps Equation Solution

DO Deficit using Streeter-Phelps Equation Formula Elements

Other Formulas to find Oxygen Deficit

Other formulas in Oxygen Deficit category

How to Evaluate DO Deficit using Streeter-Phelps Equation?

FAQs on DO Deficit using Streeter-Phelps Equation

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GoOxygen Deficit Formula