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Critical Time when we have Critical Oxygen Deficit Formula

GoCritical Time Formula

GoCritical Time given Self Purification Constant with Critical Oxygen Deficit Formula

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Critical Time refers to the minimum dissolved oxygen concentration occurs, found by differentiating the dissolved oxygen equation with respect to time. Check FAQs

t c = \log 10 \frac{\frac{D c \cdot K R}{K D \cdot L t}}{K D}

t_c - Critical Time?D_c - Critical Oxygen Deficit?K_R - Reoxygenation Coefficient?K_D - Deoxygenation Constant?L_t - Oxygen Equivalent?

Critical Time when we have Critical Oxygen Deficit Example

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Here is how the Critical Time when we have Critical Oxygen Deficit equation looks like with Values.

Here is how the Critical Time when we have Critical Oxygen Deficit equation looks like with Units.

Here is how the Critical Time when we have Critical Oxygen Deficit equation looks like.

0.5896 = \log 10 \frac{\frac{0.0003 \cdot 0.22}{0.23 \cdot 0.21}}{0.23}

0.5896d = \log 10 \frac{\frac{0.0003 \cdot 0.22d⁻¹}{0.23d⁻¹ \cdot 0.21mg/L}}{0.23d⁻¹}

0.5896 = \log 10 \frac{\frac{0.0003 \cdot 0.22}{0.23 \cdot 0.21}}{0.23}

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Critical Time when we have Critical Oxygen Deficit Solution

Follow our step by step solution on how to calculate Critical Time when we have Critical Oxygen Deficit?

FIRST Step Consider the formula

t c = \log 10 \frac{\frac{D c \cdot K R}{K D \cdot L t}}{K D}

Next Step Substitute values of Variables

∴

t c = \log 10 \frac{\frac{0.0003 \cdot 0.22d⁻¹}{0.23d⁻¹ \cdot 0.21mg/L}}{0.23d⁻¹}

Next Step Convert Units

∴

t c = \log 10 \frac{\frac{0.0003 \cdot 2.5E-6s⁻¹}{2.7E-6s⁻¹ \cdot 0.0002kg/m³}}{2.7E-6s⁻¹}

Next Step Prepare to Evaluate

∴

t c = \log 10 \frac{\frac{0.0003 \cdot 2.5E-6}{2.7E-6 \cdot 0.0002}}{2.7E-6}

Next Step Evaluate

∴

t c = 50937.23449516s

Next Step Convert to Output's Unit

∴

t c = 0.589551325175463d

LAST Step Rounding Answer

∴

t c = 0.5896d

Critical Time when we have Critical Oxygen Deficit Formula Elements

Variables

Functions

Critical Time

Critical Time refers to the minimum dissolved oxygen concentration occurs, found by differentiating the dissolved oxygen equation with respect to time.

Symbol: t_c

Measurement: TimeUnit: d

Note: Value should be greater than 0.

Formulas to find Critical Time

Critical Oxygen Deficit

Critical Oxygen Deficit is referred as the condition where the deoxygenation rate exceeds the reoxygenation rate.

Symbol: D_c

Measurement: NAUnit: Unitless

Note: Value should be greater than 0.

Formulas to find Critical Oxygen Deficit

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

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

Oxygen Equivalent

The Oxygen Equivalent is referred as the oxidizable organic matter present in sewage.

Symbol: L_t

Measurement: DensityUnit: mg/L

Note: Value should be greater than 0.

Formulas to find Oxygen Equivalent

log10

The common logarithm, also known as the base-10 logarithm or the decimal logarithm, is a mathematical function that is the inverse of the exponential function.

Syntax: log10(Number)

Other Formulas to find Critical Time

Go Critical Time

t c = (\frac{1}{K R - K D}) \cdot \log 10 ((\frac{K D \cdot L t - K R \cdot D o + K D \cdot D o}{K D} \cdot L t) \cdot (\frac{K R}{K D}))

Go Critical Time given Self Purification Constant with Critical Oxygen Deficit

t c = \log 10 \frac{D c \cdot \frac{f}{L t}}{K D}

Go Critical Time given Self Purification Factor

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

How to Evaluate Critical Time when we have Critical Oxygen Deficit?

Critical Time when we have Critical Oxygen Deficit evaluator uses Critical Time = log10((Critical Oxygen Deficit*Reoxygenation Coefficient)/(Deoxygenation Constant*Oxygen Equivalent))/Deoxygenation Constant to evaluate the Critical Time, The Critical Time when we have Critical Oxygen Deficit formula is defined as the crucial time period in which certain tasks must be completed to avoid project delays. Critical Time is denoted by t_c symbol.

How to evaluate Critical Time when we have Critical Oxygen Deficit using this online evaluator? To use this online evaluator for Critical Time when we have Critical Oxygen Deficit, enter Critical Oxygen Deficit (D_c), Reoxygenation Coefficient (K_R), Deoxygenation Constant (K_D) & Oxygen Equivalent (L_t) and hit the calculate button.

FAQs on Critical Time when we have Critical Oxygen Deficit

What is the formula to find Critical Time when we have Critical Oxygen Deficit?

The formula of Critical Time when we have Critical Oxygen Deficit is expressed as Critical Time = log10((Critical Oxygen Deficit*Reoxygenation Coefficient)/(Deoxygenation Constant*Oxygen Equivalent))/Deoxygenation Constant. Here is an example- 4.7E-6 = log10((0.0003*2.5462962962963E-06)/(2.66203703703704E-06*0.00021))/2.66203703703704E-06.

How to calculate Critical Time when we have Critical Oxygen Deficit?

With Critical Oxygen Deficit (D_c), Reoxygenation Coefficient (K_R), Deoxygenation Constant (K_D) & Oxygen Equivalent (L_t) we can find Critical Time when we have Critical Oxygen Deficit using the formula - Critical Time = log10((Critical Oxygen Deficit*Reoxygenation Coefficient)/(Deoxygenation Constant*Oxygen Equivalent))/Deoxygenation Constant. This formula also uses Common Logarithm (log10) function(s).

What are the other ways to Calculate Critical Time?

Here are the different ways to Calculate Critical Time-

Critical Time=(1/(Reoxygenation Coefficient-Deoxygenation Constant))*log10(((Deoxygenation Constant*Oxygen Equivalent-Reoxygenation Coefficient*Initial Oxygen Deficit+Deoxygenation Constant*Initial Oxygen Deficit)/Deoxygenation Constant*Oxygen Equivalent)*(Reoxygenation Coefficient/Deoxygenation Constant))
Critical Time=log10(Critical Oxygen Deficit*Self-Purification Constant/Oxygen Equivalent)/Deoxygenation Constant
Critical Time=-(log10(1-(Self-Purification Constant-1)*(Critical Oxygen Deficit/Oxygen Equivalent)*Self-Purification Constant)/(Deoxygenation Constant*(Self-Purification Constant-1)))

Can the Critical Time when we have Critical Oxygen Deficit be negative?

No, the Critical Time when we have Critical Oxygen Deficit, measured in Time cannot be negative.

Which unit is used to measure Critical Time when we have Critical Oxygen Deficit?

Critical Time when we have Critical Oxygen Deficit is usually measured using the Day[d] for Time. Second[d], Millisecond[d], Microsecond[d] are the few other units in which Critical Time when we have Critical Oxygen Deficit can be measured.

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Critical Time when we have Critical Oxygen Deficit Formula

​GoCritical Time Formula

​GoCritical Time given Self Purification Constant with Critical Oxygen Deficit Formula

Critical Time when we have Critical Oxygen Deficit Example

Critical Time when we have Critical Oxygen Deficit Solution

Critical Time when we have Critical Oxygen Deficit Formula Elements

Other Formulas to find Critical Time

How to Evaluate Critical Time when we have Critical Oxygen Deficit?

FAQs on Critical Time when we have Critical Oxygen Deficit

Variable Name

GoCritical Time Formula

GoCritical Time given Self Purification Constant with Critical Oxygen Deficit Formula