Guage pressure is the pressure in excess of the atmospheric pressure, which is around 15 psi. Absoute pressure is the pressure relative to a vacuum. Guage pressure can be negative if you are measuring pressure in a container which has been evacuated. Absolute pressure is always positive. The different systems came about because guage pressure is easier to measure, and is often the relevant property for the task at hand anyway. As an example, consider a car tire. When measured with a common tire guage, which reads guage pressure because it is balancing forces with the atmosphere on one side, the pressure in the tire is 35 psi. Put the car in orbit in space, and the guage would be reading absolute pressure. It would read 50 psi.
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The 'g' added on to bar means 'gauge', as opposed to bara, meaning 'absolute'. The 'zero' of a normal gauge is normally set at atmospheric pressure (things like tire pressure gauges, water gauges etc.) These gauges will read as "10 bar" but really mean that the absolute pressure is 10 bar + atmospheric pressure (~1.01325 bar). Some gauges however are absolute gauges. These might include weather gauges, or gauges on closed processes. bara = barg + atmospheric pressure
A Bourdon Tube or a Bellows gauge
A bourdon tube is a type of curved tube where the inside radius is smaller than the outside radius. As Force = Pressure x Area this means that when a pressure is applied internally to the tube the greater surface area on the outside causes the tube to straighten out. This is connected via a mechanical linkage to dial on the front of the gauge. Your typical industrial pressure gauge is the Bourdon Tube tyep.
A Bourdon gauge consists of a C-shaped pipe with one end closed and the other end attached to a chamber whose pressure is being measured. When there is a pressure difference between the inside of the pipe and the outside, there will be a net force acting on the C-shaped pipe which will either try to curl the pipe into a tighter C shape (if the pressure in the pipe is less than the ambient air pressure), or the force will tend to straighten out the pipe (if the pressure is higher inside). This force can be measured, and from the measurement of this force, the gauge pressure within the pipe can be calculated.
The Pirani gauge is a robust thermal conductivity gauge used for the measurement of the pressures in vacuum systems. This gauge is used to measure the pressure between 0.5 torr to 10-4 torr.