# Propogating Relative Error through an Energy Calculation

• mcgarey

#### mcgarey

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?

-McGarey

Welcome to PF, mcgarey! 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.

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

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.