How to calculate BTU output from exhaust temperature and flue diameter

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I have a gas water heater that has an exhaust of 475 degrees Fahrenheit. I would like to know, what formula can I use to determine the amount of BTU's that the water heater produces (or wastes) per hour of use. I only have the temperature of the exhaust (475 Deg. F) and the diameter of the flue which is 3". I would appreciate any help or guidance. Thank you.
 
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You can't calculate it from the exhaust temp. But You can read your gas meter a couple of times when it us running. Or read it off the nameplate...
 
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You could do an experiment . A BTU is the amount of heat needed to raise one pound of water one degree F . You could place a glass jug of water near the exhaust and measure the temp increase . And of course measure the amount of water . Or you could
do it in calories , then convert to joules and then divide by the amount of time it took so this will give you power .
At least this would give a crude approximation .
 
@ cragar: it is a great method to estimate the heater's power within three orders of magnitude.

@attitudeworks: it is impossible to tell using only this information. Can't you contact the company?