14.7 psi is the ambient pressure all around us, right? psi gauge inserted into a tire is measuring the *difference in pressure* between in the tire and outside the tire. I think you were sort of guessing that yourself in your question. It seemed like you were thinking along the right lines.
If the tire was so empty that it was less pressure than outside, you could imagine a negative reading on the gauge even though there’s some pressure exerted by the air lingering in the tire.
What you are observing is called gauge pressure. Its common in things like tires or other pressure systems, where the gauge measures how far above or below atmospheric pressure something is.
It does that because the way gauges measure pressure is by having the gas in the container push against the surroundings of the gauge (usually on a spring).
So it just tells you what the pressure is vs the surroundings, where that is air, water, air on top of a mountain or whatever.
Gauges are showing relative pressure. They are showing you the differential between the outside pressure vs. the pressure that is measured by whatever is providing resistance in the gauge. Since we are always assumed to be at 1atm, pressure measurements for most purposes are given relative to that value.
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