Propogating Relative Error through an Energy Calculation

In summary, the conversation discusses calculating the relative error associated with an energy calculation using known supply and return temperatures and flow rate. The formula for propagating absolute error is discussed, as well as the need for the actual values in determining the relative 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
Welcome to PF, mcgarey! :smile:

You have it right.
But you will need the values of return temp and supply temp to calculate first the absolute error of their difference, and then convert that to a relative error, which is relative to the difference.
 
  • #3
What if I don't have that information yet? Can I calculate the error of the difference in temperature using the relative error given on the sensor product information?

Thanks, McGarey
 
  • #4
Yes, if you have an estimate of the temperature, that suffices to calculate the error in the difference of the temperatures.

However, when you want to propagate this to the product, you need to determine the relative error of the difference.
For this you need the actual difference.
This is important, because the difference could be close to zero, in which case the relative error skyrockets.
 
  • #5


Hello McGarey,

Thank you for your question. I can certainly help you understand how to propagate relative error through an energy calculation. First, let's define relative error - it is the ratio of the absolute error to the true value of the measurement. Relative error is typically expressed as a percentage and can also be referred to as percent error.

In your case, you have two sources of relative error - the temperature sensor with a relative error of 1% and the flow meter with a relative error of 0.5%. To propagate these errors through your energy equation, you can follow the same steps as you would for absolute error - square each value, add them, and take the resulting square root. However, instead of using the error value, you will use the relative error value (e.g. 0.01 for 1% and 0.005 for 0.5%). This will give you the total relative error for your energy calculation.

For multiplication and division, you can use the same formula, but you will need to substitute the relative error in place of the error/value ratio. So for your energy equation, it would look like this:

Relative error for energy = square root of ((0.01*(return temp - supply temp))^2 + (0.005*flow)^2)

As you mentioned, you do not have the data yet, so you can use the relative error values provided for the sensors as a placeholder. Once you have the actual data, you can substitute it into the equation to get a more accurate relative error for your energy calculation.

I hope this helps you understand how to propagate relative error through an energy calculation. If you have any further questions, please do not hesitate to ask. Good luck with your work!

Sincerely,
 

What is relative error?

Relative error is a way to measure the accuracy of a calculation by comparing the difference between the calculated value and the actual value.

Why is propagating relative error important in energy calculations?

Propagating relative error is important in energy calculations because it allows us to understand how small errors in our measurements or calculations can affect the final result. This can help us make more accurate and precise predictions and decisions.

How do you propagate relative error through an energy calculation?

To propagate relative error through an energy calculation, we use the chain rule from calculus. This involves taking the derivative of the equation used to calculate energy with respect to each variable, multiplying it by the relative error of that variable, and then adding all of these contributions together to get the total relative error for the energy calculation.

What factors can contribute to relative error in energy calculations?

There are many factors that can contribute to relative error in energy calculations, such as human error in taking measurements, rounding errors in calculations, and uncertainties in the values of constants used in the calculation. It is important to consider and account for all of these potential sources of error to get a more accurate result.

How can we minimize relative error in energy calculations?

To minimize relative error in energy calculations, we can take multiple measurements and average them, use more precise instruments, and carefully consider and reduce any sources of uncertainty. We can also use more accurate equations and values for constants in our calculations.

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