Critical Time given Self Purification Factor Solution

STEP 0: Pre-Calculation Summary
Formula Used
Critical time = -(log10(1-(Self purification constant-1)*(Critical oxygen deficit/Oxygen Equivalent)*Self purification constant)/(Deoxygenation Constant*(Self purification constant-1)))
tc = -(log10(1-(f-1)*(Dc/Lt)*f)/(KD*(f-1)))
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.
Self purification constant - Self purification constant is the ratio of reoxygenation constant to deoxygenation constant.
Critical oxygen deficit - Critical oxygen deficit is the condition where the deoxygenation rate exceeds the reoxygenation rate.
Oxygen Equivalent - (Measured in Kilogram per Cubic Meter) - Oxygen Equivalent is the oxidisable organic matter present in sewage.
Deoxygenation Constant - (Measured in 1 Per Second) - Deoxygenation Constant is the value obtained after decomposing of oxygen in sewage.
STEP 1: Convert Input(s) to Base Unit
Self purification constant: 0.6 --> No Conversion Required
Critical oxygen deficit: 6 --> No Conversion Required
Oxygen Equivalent: 0.21 Milligram per Liter --> 0.00021 Kilogram per Cubic Meter (Check conversion here)
Deoxygenation Constant: 0.23 1 Per Day --> 2.66203703703704E-06 1 Per Second (Check conversion here)
STEP 2: Evaluate Formula
Substituting Input Values in Formula
tc = -(log10(1-(f-1)*(Dc/Lt)*f)/(KD*(f-1))) --> -(log10(1-(0.6-1)*(6/0.00021)*0.6)/(2.66203703703704E-06*(0.6-1)))
Evaluating ... ...
tc = 3602698.30395132
STEP 3: Convert Result to Output's Unit
3602698.30395132 Second -->41.6978970364736 Day (Check conversion here)
FINAL ANSWER
41.6978970364736 41.6979 Day <-- Critical time
(Calculation completed in 00.004 seconds)

Credits

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 given Self Purification Factor Formula

Critical time = -(log10(1-(Self purification constant-1)*(Critical oxygen deficit/Oxygen Equivalent)*Self purification constant)/(Deoxygenation Constant*(Self purification constant-1)))
tc = -(log10(1-(f-1)*(Dc/Lt)*f)/(KD*(f-1)))

What is self purification factor?

The ratio of reoxygenation constant to deoxygenation constant (or R'/K') is called the self purification constant f and it is equal to 0.50 to 5.0.

How to Calculate Critical Time given Self Purification Factor?

Critical Time given Self Purification Factor calculator uses Critical time = -(log10(1-(Self purification constant-1)*(Critical oxygen deficit/Oxygen Equivalent)*Self purification constant)/(Deoxygenation Constant*(Self purification constant-1))) to calculate the Critical time, The Critical Time given Self Purification Factor is the total time required to complete the reaction. Critical time is denoted by tc symbol.

How to calculate Critical Time given Self Purification Factor using this online calculator? To use this online calculator for Critical Time given Self Purification Factor, enter Self purification constant (f), Critical oxygen deficit (Dc), Oxygen Equivalent (Lt) & Deoxygenation Constant (KD) and hit the calculate button. Here is how the Critical Time given Self Purification Factor calculation can be explained with given input values -> 0.000483 = -(log10(1-(0.6-1)*(6/0.00021)*0.6)/(2.66203703703704E-06*(0.6-1))).

FAQ

What is Critical Time given Self Purification Factor?
The Critical Time given Self Purification Factor is the total time required to complete the reaction and is represented as tc = -(log10(1-(f-1)*(Dc/Lt)*f)/(KD*(f-1))) or Critical time = -(log10(1-(Self purification constant-1)*(Critical oxygen deficit/Oxygen Equivalent)*Self purification constant)/(Deoxygenation Constant*(Self purification constant-1))). Self purification constant is the ratio of reoxygenation constant to deoxygenation constant, Critical oxygen deficit is the condition where the deoxygenation rate exceeds the reoxygenation rate, Oxygen Equivalent is the oxidisable organic matter present in sewage & Deoxygenation Constant is the value obtained after decomposing of oxygen in sewage.
How to calculate Critical Time given Self Purification Factor?
The Critical Time given Self Purification Factor is the total time required to complete the reaction is calculated using Critical time = -(log10(1-(Self purification constant-1)*(Critical oxygen deficit/Oxygen Equivalent)*Self purification constant)/(Deoxygenation Constant*(Self purification constant-1))). To calculate Critical Time given Self Purification Factor, you need Self purification constant (f), Critical oxygen deficit (Dc), Oxygen Equivalent (Lt) & Deoxygenation Constant (KD). With our tool, you need to enter the respective value for Self purification constant, Critical oxygen deficit, Oxygen Equivalent & Deoxygenation Constant 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 Self purification constant, Critical oxygen deficit, Oxygen Equivalent & Deoxygenation Constant. We can use 3 other way(s) to calculate the same, which is/are as follows -
  • 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*Reoxygenation coefficient)/(Deoxygenation Constant*Oxygen Equivalent))/Deoxygenation Constant
  • Critical time = log10(Critical oxygen deficit*Self purification constant/Oxygen Equivalent)/Deoxygenation Constant
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