Critical Time Calculator

✖Reoxygenation coefficient implies the higher the flow velocity, the higher the re-oxygenation coefficient.ⓘ Reoxygenation coefficient [K_R]			+10% -10%
✖Deoxygenation Constant is the value obtained after decomposing of oxygen in sewage.ⓘ Deoxygenation Constant [K_D]			+10% -10%
✖Oxygen Equivalent is the oxidisable organic matter present in sewage.ⓘ Oxygen Equivalent [L_t]			+10% -10%
✖Initial oxygen deficit is the amount of oxygen required at initial levels.ⓘ Initial oxygen deficit [D_o]			+10% -10%

✖Critical time is the time after which the minimum dissolved oxygen occurs can be found by differentiating the equation.ⓘ 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

`"49.29315d"=(1/("0.1d⁻¹"-"0.23d⁻¹"))*log10((("0.23d⁻¹"*"0.21mg/L"-"0.1d⁻¹"*"7.2mg/L"+"0.23d⁻¹"*"7.2mg/L")/"0.23d⁻¹"*"0.21mg/L")*("0.1d⁻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 is the time after which the minimum dissolved oxygen occurs can be found by differentiating the equation.
Reoxygenation coefficient - (Measured in 1 Per Second) - Reoxygenation coefficient implies the higher the flow velocity, the higher the re-oxygenation coefficient.
Deoxygenation Constant - (Measured in 1 Per Second) - Deoxygenation Constant is the value obtained after decomposing of oxygen in sewage.
Oxygen Equivalent - (Measured in Kilogram per Cubic Meter) - Oxygen Equivalent is the oxidisable organic matter present in sewage.
Initial oxygen deficit - (Measured in Kilogram per Cubic Meter) - Initial oxygen deficit is the amount of oxygen required at initial levels.

STEP 1: Convert Input(s) to Base Unit

Reoxygenation coefficient: 0.1 1 Per Day --> 1.15740740740741E-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/(1.15740740740741E-06-2.66203703703704E-06))*log10(((2.66203703703704E-06*0.00021-1.15740740740741E-06*0.0072+2.66203703703704E-06*0.0072)/2.66203703703704E-06*0.00021)*(1.15740740740741E-06/2.66203703703704E-06))

Evaluating ... ...

t_c = 4258927.75604381

STEP 3: Convert Result to Output's Unit

4258927.75604381 Second -->49.2931453245812 Day (Check conversion here)

FINAL ANSWER

49.2931453245812 ≈ 49.29315 Day <-- Critical time

(Calculation completed in 00.020 seconds)

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Created by Ishita Goyal

Meerut Institute of Engineering and Technology (MIET), Meerut

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Verified by Suraj Kumar

Birsa Institute of Technology (BIT), Sindri

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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 is the time after which the minimum dissolved oxygen occurs can be found by differentiating the equation. 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 -> 0.000571 = (1/(1.15740740740741E-06-2.66203703703704E-06))*log10(((2.66203703703704E-06*0.00021-1.15740740740741E-06*0.0072+2.66203703703704E-06*0.0072)/2.66203703703704E-06*0.00021)*(1.15740740740741E-06/2.66203703703704E-06)).

FAQ

What is Critical Time?

The Critical Time is the time after which the minimum dissolved oxygen occurs can be found by differentiating the equation 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 implies the higher the flow velocity, the higher the re-oxygenation coefficient, Deoxygenation Constant is the value obtained after decomposing of oxygen in sewage, Oxygen Equivalent is the oxidisable organic matter present in sewage & Initial oxygen deficit is the amount of oxygen required at initial levels.

How to calculate Critical Time?

The Critical Time is the time after which the minimum dissolved oxygen occurs can be found by differentiating the equation 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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