Propogating Relative Error through an Energy Calculation

In summary: Your Name]In summary, the conversation discussed the process of calculating the relative error for an energy calculation based on known supply and return temperatures and flow rate. The formula for propagating absolute error through additions or subtractions can also be used for relative error. However, using actual values is always recommended for a more accurate estimate of the error.
  • #1
mcgarey
3
0
Greetings,

I have a work requirement to calculate building chilled water use based on known supply temp (deg F), return temp (deg F) and flow (GPM). I would like to know the relative error associated with the energy calculation. Based on the product data for the sensing equipment, I know that the temp sensor have relative error of 1%, and the flow meter has a relative error of 0.5%.

I am struggling to understand how to propagate those errors through my energy equation

E(btu) = (return temp - supply temp)*flow*500.

After browsing the internet, I understand that to propagate absolute error across additions or subtractions, you should square each value, add them, and take the resulting square root. Does this formula also apply for relative error?

As for multiplication and division, I understand that you should use the same formula described above, except each term should be the error/the value. My issue is, I don't have the data yet, so I don't know what the value is yet. cal I simply substitute the relative error in place of the error/value ratio?

Thank you in advance for your thoughts and input.

-McGarey
 
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  • #2


Dear McGarey,

Thank you for reaching out with your question. Calculating the relative error associated with your energy calculation is an important step to ensure the accuracy of your results. The formula you mentioned for propagating absolute error through additions or subtractions does also apply for relative error. In this case, you can use the following formula to calculate the relative error for your energy equation:

Relative Error = √[(1%*(return temp - supply temp))^2 + (0.5%*flow)^2]

This formula takes into account the relative error of both the temperature sensor and flow meter, and provides an estimate of the overall relative error in your energy calculation. As you mentioned, for multiplication and division, you can use the same formula but substitute the relative error in place of the error/value ratio.

However, it is important to note that the relative error is only an estimate and may not reflect the actual error in your calculation. This is because the relative error is based on the percentage of the value, rather than the absolute value itself. If you have the data available, it is always best to use the actual values in your calculations to get a more accurate estimate of the error.

I hope this helps and please let me know if you have any further questions or concerns.


 

What is "Propagating Relative Error through an Energy Calculation"?

"Propagating Relative Error through an Energy Calculation" is a method used in scientific research to estimate the uncertainty in energy calculations. It involves calculating the relative error for each input parameter and using these values to determine the overall relative error for the final energy calculation.

Why is "Propagating Relative Error through an Energy Calculation" important?

This method is important because it allows scientists to understand the accuracy and precision of their energy calculations. By estimating the uncertainty, they can determine whether the results are reliable and make any necessary adjustments to improve the accuracy of their calculations.

How is "Propagating Relative Error through an Energy Calculation" different from other error analysis methods?

Unlike other error analysis methods, which only consider the uncertainty in the final result, "Propagating Relative Error through an Energy Calculation" takes into account the uncertainties in all of the input parameters. This provides a more comprehensive understanding of the overall uncertainty in the energy calculation.

What are the steps involved in "Propagating Relative Error through an Energy Calculation"?

The first step is to determine the relative error for each input parameter. Then, these values are combined using the appropriate mathematical operations to calculate the overall relative error. Finally, this value is used to estimate the uncertainty in the final energy calculation.

How can "Propagating Relative Error through an Energy Calculation" be used to improve scientific research?

By using this method, scientists can gain a better understanding of the accuracy and precision of their energy calculations. This can lead to improvements in experimental design, data analysis, and overall research quality. It also allows for more transparent reporting of uncertainties in scientific publications.

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