Gauge pressure is an essential concept when dealing with fluids, such as the oil and water in our barrel. Unlike absolute pressure, which includes atmospheric pressure, gauge pressure only considers the pressure relative to atmospheric pressure.
This is why when you measure gauge pressure, it can show as zero if the pressure is the same as the atmospheric pressure, and rise above zero when higher.
To calculate gauge pressure in any fluid at a specific point, we use the formula for hydrostatic pressure:
Here, \( P \) represents the pressure we want to find; \( \rho \) is the density of the fluid; \( g \) is the gravitational acceleration (9.81 m/s\(^2\)); and \( h \) is the height of the fluid above that point.
When we calculated for the oil-water interface, we found \( 705.6 \) pascals.
For the bottom of the barrel, it was \( 3158.1 \) pascals, showing how pressure accumulates from the top down.