Oxygen Deficit given Critical Time in Self Purification Factor Solution

STEP 0: Pre-Calculation Summary
Formula Used
Critical oxygen deficit = (Oxygen Equivalent/(Self purification constant-1))*(1-((10^(Critical time*Deoxygenation Constant*(Self purification constant-1)))/Self purification constant))
Dc = (Lt/(f-1))*(1-((10^(tc*KD*(f-1)))/f))
This formula uses 5 Variables
Variables Used
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.
Self purification constant - Self purification constant is the ratio of reoxygenation constant to deoxygenation constant.
Critical time - (Measured in Second) - Critical time is the time after which the minimum dissolved oxygen occurs can be found by differentiating the equation.
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
Oxygen Equivalent: 0.21 Milligram per Liter --> 0.00021 Kilogram per Cubic Meter (Check conversion here)
Self purification constant: 0.6 --> No Conversion Required
Critical time: 0.5 Day --> 43200 Second (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
Dc = (Lt/(f-1))*(1-((10^(tc*KD*(f-1)))/f)) --> (0.00021/(0.6-1))*(1-((10^(43200*2.66203703703704E-06*(0.6-1)))/0.6))
Evaluating ... ...
Dc = 0.000262060383838781
STEP 3: Convert Result to Output's Unit
0.000262060383838781 --> No Conversion Required
FINAL ANSWER
0.000262060383838781 0.000262 <-- Critical oxygen deficit
(Calculation completed in 00.020 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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5 Oxygen Deficit Calculators

DO Deficit using Streeter-Phelps Equation
Go 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))
Initial Oxygen Deficit in First Stage Equation
Go Initial oxygen deficit = 1-(((1/Critical oxygen deficit)^(Self purification constant-1))*((Oxygen Equivalent/Self purification constant)^Self purification constant)/(Self purification constant-1))
Oxygen Deficit given Critical Time in Self Purification Factor
Go Critical oxygen deficit = (Oxygen Equivalent/(Self purification constant-1))*(1-((10^(Critical time*Deoxygenation Constant*(Self purification constant-1)))/Self purification constant))
Log value of Critical Oxygen Deficit
Go Critical oxygen deficit = 10^(log10(Oxygen Equivalent/Self purification constant)-(Deoxygenation Constant*Critical time))
Oxygen Deficit
Go Oxygen Deficit = Saturated Dissolved Oxygen-Actual Dissolved Oxygen

Oxygen Deficit given Critical Time in Self Purification Factor Formula

Critical oxygen deficit = (Oxygen Equivalent/(Self purification constant-1))*(1-((10^(Critical time*Deoxygenation Constant*(Self purification constant-1)))/Self purification constant))
Dc = (Lt/(f-1))*(1-((10^(tc*KD*(f-1)))/f))

What is self purification constant?

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 Oxygen Deficit given Critical Time in Self Purification Factor?

Oxygen Deficit given Critical Time in Self Purification Factor calculator uses Critical oxygen deficit = (Oxygen Equivalent/(Self purification constant-1))*(1-((10^(Critical time*Deoxygenation Constant*(Self purification constant-1)))/Self purification constant)) to calculate the Critical oxygen deficit, The Oxygen Deficit given Critical Time in Self Purification Factor is the sum of the minute differences between the measured oxygen uptake and the oxygen uptake occurring during steady state work at that same rate. Critical oxygen deficit is denoted by Dc symbol.

How to calculate Oxygen Deficit given Critical Time in Self Purification Factor using this online calculator? To use this online calculator for Oxygen Deficit given Critical Time in Self Purification Factor, enter Oxygen Equivalent (Lt), Self purification constant (f), Critical time (tc) & Deoxygenation Constant (KD) and hit the calculate button. Here is how the Oxygen Deficit given Critical Time in Self Purification Factor calculation can be explained with given input values -> 0.000262 = (0.00021/(0.6-1))*(1-((10^(43200*2.66203703703704E-06*(0.6-1)))/0.6)).

FAQ

What is Oxygen Deficit given Critical Time in Self Purification Factor?
The Oxygen Deficit given Critical Time in Self Purification Factor is the sum of the minute differences between the measured oxygen uptake and the oxygen uptake occurring during steady state work at that same rate and is represented as Dc = (Lt/(f-1))*(1-((10^(tc*KD*(f-1)))/f)) or Critical oxygen deficit = (Oxygen Equivalent/(Self purification constant-1))*(1-((10^(Critical time*Deoxygenation Constant*(Self purification constant-1)))/Self purification constant)). Oxygen Equivalent is the oxidisable organic matter present in sewage, Self purification constant is the ratio of reoxygenation constant to deoxygenation constant, Critical time is the time after which the minimum dissolved oxygen occurs can be found by differentiating the equation & Deoxygenation Constant is the value obtained after decomposing of oxygen in sewage.
How to calculate Oxygen Deficit given Critical Time in Self Purification Factor?
The Oxygen Deficit given Critical Time in Self Purification Factor is the sum of the minute differences between the measured oxygen uptake and the oxygen uptake occurring during steady state work at that same rate is calculated using Critical oxygen deficit = (Oxygen Equivalent/(Self purification constant-1))*(1-((10^(Critical time*Deoxygenation Constant*(Self purification constant-1)))/Self purification constant)). To calculate Oxygen Deficit given Critical Time in Self Purification Factor, you need Oxygen Equivalent (Lt), Self purification constant (f), Critical time (tc) & Deoxygenation Constant (KD). With our tool, you need to enter the respective value for Oxygen Equivalent, Self purification constant, Critical time & 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 oxygen deficit?
In this formula, Critical oxygen deficit uses Oxygen Equivalent, Self purification constant, Critical time & Deoxygenation Constant. We can use 1 other way(s) to calculate the same, which is/are as follows -
  • Critical oxygen deficit = 10^(log10(Oxygen Equivalent/Self purification constant)-(Deoxygenation Constant*Critical time))
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