✖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.ⓘ Reoxygenation Coefficient [K_R]			+10% -10%
✖Deoxygenation Constant is referred as the value obtained after decomposing of oxygen in sewage.ⓘ Deoxygenation Constant [K_D]			+10% -10%
✖The Oxygen Equivalent is referred as the oxidizable organic matter present in sewage.ⓘ Oxygen Equivalent [L_t]			+10% -10%
✖Initial Oxygen Deficit is referred as the amount of oxygen required at initial levels.ⓘ Initial Oxygen Deficit [D_o]			+10% -10%

✖Critical Time refers to the minimum dissolved oxygen concentration occurs, found by differentiating the dissolved oxygen equation with respect to time.ⓘ Critical Time [t_c]

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Formula

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Critical Time

Formula

`"t"_{"c"} = (1/("K"_{"R"}-"K"_{"D"}))*log10((("K"_{"D"}*"L"_{"t"}-"K"_{"R"}*"D"_{"o"}+"K"_{"D"}*"D"_{"o"})/"K"_{"D"}*"L"_{"t"})*("K"_{"R"}/"K"_{"D"}))`

Example

`"697.8548d"=(1/("0.22d⁻¹"-"0.23d⁻¹"))*log10((("0.23d⁻¹"*"0.21mg/L"-"0.22d⁻¹"*"7.2mg/L"+"0.23d⁻¹"*"7.2mg/L")/"0.23d⁻¹"*"0.21mg/L")*("0.22d⁻¹"/"0.23d⁻¹"))`

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Critical Time Solution

STEP 0: Pre-Calculation Summary

Formula Used

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))
t_c = (1/(K_R-K_D))*log10(((K_D*L_t-K_R*D_o+K_D*D_o)/K_D*L_t)*(K_R/K_D))
This formula uses 1 Functions, 5 Variables

Functions Used

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., log10(Number)

Variables Used

Critical Time - (Measured in Second) - Critical Time refers to the minimum dissolved oxygen concentration occurs, found by differentiating the dissolved oxygen equation with respect to time.
Reoxygenation Coefficient - (Measured in 1 Per Second) - 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.
Deoxygenation Constant - (Measured in 1 Per Second) - Deoxygenation Constant is referred as the value obtained after decomposing of oxygen in sewage.
Oxygen Equivalent - (Measured in Kilogram per Cubic Meter) - The Oxygen Equivalent is referred as the oxidizable organic matter present in sewage.
Initial Oxygen Deficit - (Measured in Kilogram per Cubic Meter) - Initial Oxygen Deficit is referred as the amount of oxygen required at initial levels.

STEP 1: Convert Input(s) to Base Unit

Reoxygenation Coefficient: 0.22 1 Per Day --> 2.5462962962963E-06 1 Per Second (Check conversion here)
Deoxygenation Constant: 0.23 1 Per Day --> 2.66203703703704E-06 1 Per Second (Check conversion here)
Oxygen Equivalent: 0.21 Milligram per Liter --> 0.00021 Kilogram per Cubic Meter (Check conversion here)
Initial Oxygen Deficit: 7.2 Milligram per Liter --> 0.0072 Kilogram per Cubic Meter (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

t_c = (1/(K_R-K_D))*log10(((K_D*L_t-K_R*D_o+K_D*D_o)/K_D*L_t)*(K_R/K_D)) --> (1/(2.5462962962963E-06-2.66203703703704E-06))*log10(((2.66203703703704E-06*0.00021-2.5462962962963E-06*0.0072+2.66203703703704E-06*0.0072)/2.66203703703704E-06*0.00021)*(2.5462962962963E-06/2.66203703703704E-06))

Evaluating ... ...

t_c = 60294655.3173632

STEP 3: Convert Result to Output's Unit

60294655.3173632 Second -->697.854806913926 Day (Check conversion here)

FINAL ANSWER

697.854806913926 ≈ 697.8548 Day <-- Critical Time

(Calculation completed in 00.004 seconds)

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< 4 Critical Time Calculators

Critical Time

Go 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 given Self Purification Factor

Go Critical Time = -(log10(1-(Self-Purification Constant-1)*(Critical Oxygen Deficit/Oxygen Equivalent)*Self-Purification Constant)/(Deoxygenation Constant*(Self-Purification Constant-1)))

Critical Time when we have Critical Oxygen Deficit

Go Critical Time = log10((Critical Oxygen Deficit*Reoxygenation Coefficient)/(Deoxygenation Constant*Oxygen Equivalent))/Deoxygenation Constant

Critical Time given Self Purification Constant with Critical Oxygen Deficit

Go Critical Time = log10(Critical Oxygen Deficit*Self-Purification Constant/Oxygen Equivalent)/Deoxygenation Constant

Critical Time Formula

What is Dissolved Oxygen?

Dissolved Oxygen is the amount of gaseous oxygen (O2) dissolved in the water. Oxygen enters the water by direct absorption from the atmosphere, by rapid movement, or as a waste product of plant photosynthesis.

How to Calculate Critical Time?

Critical Time calculator uses 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)) to calculate the Critical Time, The Critical Time formula is defined as the crucial time period in which certain tasks must be completed to avoid project delays. It often relates to the critical path method (CPM) where the longest stretch of dependent activities determines the shortest possible duration to complete a project. Critical Time is denoted by t_c symbol.

How to calculate Critical Time using this online calculator? To use this online calculator for Critical Time, enter Reoxygenation Coefficient (K_R), Deoxygenation Constant (K_D), Oxygen Equivalent (L_t) & Initial Oxygen Deficit (D_o) and hit the calculate button. Here is how the Critical Time calculation can be explained with given input values -> 0.002576 = (1/(2.5462962962963E-06-2.66203703703704E-06))*log10(((2.66203703703704E-06*0.00021-2.5462962962963E-06*0.0072+2.66203703703704E-06*0.0072)/2.66203703703704E-06*0.00021)*(2.5462962962963E-06/2.66203703703704E-06)).

FAQ

What is Critical Time?

The Critical Time formula is defined as the crucial time period in which certain tasks must be completed to avoid project delays. It often relates to the critical path method (CPM) where the longest stretch of dependent activities determines the shortest possible duration to complete a project and is represented as t_c = (1/(K_R-K_D))*log10(((K_D*L_t-K_R*D_o+K_D*D_o)/K_D*L_t)*(K_R/K_D)) or 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)). 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, Deoxygenation Constant is referred as the value obtained after decomposing of oxygen in sewage, The Oxygen Equivalent is referred as the oxidizable organic matter present in sewage & Initial Oxygen Deficit is referred as the amount of oxygen required at initial levels.

How to calculate Critical Time?

The Critical Time formula is defined as the crucial time period in which certain tasks must be completed to avoid project delays. It often relates to the critical path method (CPM) where the longest stretch of dependent activities determines the shortest possible duration to complete a project is calculated using 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)). To calculate Critical Time, you need Reoxygenation Coefficient (K_R), Deoxygenation Constant (K_D), Oxygen Equivalent (L_t) & Initial Oxygen Deficit (D_o). With our tool, you need to enter the respective value for Reoxygenation Coefficient, Deoxygenation Constant, Oxygen Equivalent & Initial Oxygen Deficit and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

How many ways are there to calculate Critical Time?

In this formula, Critical Time uses Reoxygenation Coefficient, Deoxygenation Constant, Oxygen Equivalent & Initial Oxygen Deficit. We can use 3 other way(s) to calculate the same, which is/are as follows -

Critical Time = log10((Critical Oxygen Deficit*Reoxygenation Coefficient)/(Deoxygenation Constant*Oxygen Equivalent))/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)))

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