The basic principle involves applying the hydrostatic pressure formula, which states that the pressure at a given depth in a fluid is equal to the atmospheric pressure plus the product of the fluid's density, gravitational acceleration, and the depth of the fluid column above the point of measurement.
To account for atmospheric pressure, you add it to the pressure exerted by the water column. The total pressure on the air pocket is the sum of the atmospheric pressure and the pressure due to the water column, calculated using the hydrostatic pressure formula.
The density of water is a crucial factor because it directly affects the hydrostatic pressure. The pressure exerted by the water column is proportional to the water's density. Higher density results in greater pressure at a given depth.
The depth of the water column is directly proportional to the pressure exerted by the water. As the depth increases, the pressure increases linearly. This is because the weight of the water column above the air pocket increases with depth, thus increasing the pressure.
The formula to calculate the pressure of an air pocket in a pressurized water column is: \( P = P_{\text{atm}} + \rho \cdot g \cdot h \), where \( P \) is the total pressure, \( P_{\text{atm}} \) is the atmospheric pressure, \( \rho \) is the density of water, \( g \) is the acceleration due to gravity, and \( h \) is the depth of the water column.