Uncertainty Analysis of Determining a Building Height using a Barometer

In the analysis of the previous page we determined that the height of the column of air was given by the the following formula:

Our first task is to determine to what accuracy can we infer the pressure difference ΔP from the mercury barometer difference in height. Note that the error can be either negative or positive, thus we develop the analysis in terms of a Root Mean Square error in order to remove the sign from possibly cancelling the total error.

A very important lesson learned: Whenever a result is dependent upon the difference between two large values, evaluate it very carefully, since the absolute value of the error does not change. We now continue to evaluate the error in the height, which is a function of ΔP, the air density ρ_air, and the acceleration due to gravity g. We noticed above that the error in g has a minimal effect and can be neglected.

The problem here is that the nominal value of ρ_air = 1.18 [kg/m³] refers to a very pleasant day of 25°C. Unfortunately the possible variation in temperature (0°C - 40°C) has a significant effect on the air density.

At this stage we combine both errors (ΔP and ρ_air) to determine the final error in height:

Niels Bohr, we salute you! (recall the Legend of Niels Bohr from the Virtual Teacher).

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Engineering Thermodynamics by Israel Urieli is licensed under a Creative Commons Attribution-Noncommercial-Share Alike 3.0 United States License