This is a simple one that I acquired from McMaster Carr, but the concept is essentially the same across most mechanical boost gauges:

behind the face of the boost gauge lies a simple balloon device made of brass or other expanding metal; the concept is essentially like a birthday party horn that is coiled up, the coil isn't tightly wound up like a party ballon, and is more crescent in shape, but much like a party horn coil, when air is blown into it, the coil begins to straighten.

Lever, gear, and guts.

The coil pressure rating is calibrated to whatever fits the corresponding gauge interval that it's designed for. When air pressure fills up the coil, it begins to straighten (not too much), and that straightening action is converted to rotational movement with the help of lever that then propels a shaft attached to a gauge needle; simple really..
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