No, cylinder = 130 - 10 psi drop across valve = 120 gauge.
the actual pressure drop if probably a psi or two on the special schraders, vs. 10 to 30 on the tire valves. But lets keep using 10 psi spring as the example, it is much easier to visualize. Off topic, the spring force is probably fractions of an ounce, but the area of the valve seat is so small it takes the 10 psi to lift the valve slightly off its seat.
If the cylinder would be 130, it loses 10 psi across the cracking of the valve, and gauge would read 120.
If the cyl. was 110,you can’t get an increase to 120 on the gauge.
Think of it as a spring loaded loaded check valve (which it is), in a hole in the wall of a tank (the combustion chamber of the cylinder). At just over 10 psi, it will crack and relieve some flow out of the tank. However, it doesn’t just open up and stay open like you are visualizing.
The sum of the forces trying to open the valve are the pressure in the tank, the 130 psi used in this example, times the seat area of the valve. Tiny little hole.
The sum of the forces trying to close the valve are the outside pressure (the gauge side) times the valve seat area plus the spring force on that valve area, which we say equates to 10 psi.
So 130 is trying to open, and x + 10 is trying to close. The valve will leak some air into the gauge until x is 120 and the valve is seated closed again. But that 10 psi diffefential is always there.
Another bunny trail, most of you will ignore this, but the opening (cracking) area of the poppet or valve is NOT truly the same as the effective area once it slightly opens. There are fluid forces on a larger area, so the pressure has to reduce slightly below the set point before the valve closes. Example: a direct acting relief valve set to crack open at 1500 psi, will rise slightly with flow across it to 1500-1600-1700 psi etc., but then if flow is reduced, it has to drop down below 1500, maybe 1450 or 1475 before it closes fully. This is hysterisis. Doesn’’t matter on a log splitter, but the rising pressure with flow, and the hysterisis for reset can matter a lot in some circuits (like oil cooler control, filter bypass, or hydrostatic charge pressure control). The flow rise is handled by using a ‘pilot operated’ relief valve where a tiny pilot orifice controls a larger spool for the actual main flow. It also reduces the hysterisis.
The real cheap and simple relief valves are just a spring pushing a ball against a seat. Cheap, rugged, tolerate dirt, but a lot of pressure rise and hysterisis.
Next step up is a poppet style valve and spring, and the better valve is the pilot operated spool valve. the pilot is built into the inside of the spool as part of a cartridge valve usually.