Gauge pressure

Gauge pressure is the amount by which the pressure at a point exceeds the surrounding atmospheric pressure. Absolute pressure is gauge pressure plus atmospheric pressure, so the two are never interchangeable.

A pressure gauge reads zero in open air, so what it reports is not the whole pressure but the excess over its surroundings. Essential knowledge 8.2.B.2 puts it as a sum: the absolute pressure at a point equals a reference pressure $P_0$ , typically the atmospheric pressure $P_{\text{atm}}$ , plus the gauge pressure.

For a vertical column of fluid, EK 8.2.B.3 gives the gauge pressure directly, and the AP Physics 1 sheet prints both lines:

P_{\text{gauge}} = \rho g h \qquad P = P_0 + \rho g h

Use $g = 9.8\ \text{m/s}^2$ from the AP table of information. Here $h$ is the depth below the free surface, not the height of the container and not the length of a slanted tube.

Where the exam catches people is the swap. A tyre gauge reading $220\ \text{kPa}$ describes air at an absolute $320\ \text{kPa}$ . A question that asks for the force on a submerged hatch, or feeds a pressure into Bernoulli's equation, wants absolute pressure. A question about how far a gauge needle moves wants the gauge value. Gauge pressure can also be negative, which is all that a partial vacuum means.

Depth problems worked end to end are in Fluids in AP Physics 1.

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