Pressure measurement is fundamental across fields like atmospheric science and engineering, but units vary significantly. Weather reports often use inches of mercury (\(\text{in Hg}\)), while industrial applications rely on pounds per square inch (\(\text{psi}\)). Converting a reading like \(28 \text{ in Hg}\) into pounds per square inch absolute (\(\text{psia}\)) requires understanding the different reference points and physical principles defining each unit.
Understanding Absolute vs. Manometric Pressure Units
The unit inches of mercury (\(\text{in Hg}\)) is a manometric measurement based on the height of a liquid column in a barometer. It is defined by the hydrostatic pressure exerted by a one-inch column of mercury under specific standard conditions. Historically, \(\text{in Hg}\) was the standard for barometric pressure readings used in meteorology and aviation.
The pressure value depends on the density of the mercury and the local force of gravity. For standardization, the density of mercury is set at its value at \(0^\circ \text{C}\) (\(32^\circ \text{F}\)), and the acceleration due to gravity is set at a standard value of \(9.80665 \text{ m/s}^2\).
In contrast, pounds per square inch absolute (\(\text{psia}\)) is a direct measurement of force per unit area, referenced against a perfect vacuum. Absolute pressure is a true measure of the total force exerted by a gas or liquid on a surface. This is distinct from pounds per square inch gauge (\(\text{psig}\)), which only measures pressure relative to the surrounding atmospheric pressure. \(\text{Psia}\) provides the most complete measure of pressure for engineering calculations.
The Direct Conversion Result
To convert a barometric pressure reading of \(28 \text{ in Hg}\) into \(\text{psia}\), a standard conversion factor is applied. This factor is derived from the established physical relationship between the pressure exerted by a column of mercury and the force it generates. The conversion factor is approximately \(1 \text{ in Hg} = 0.49115 \text{ psia}\).
Applying this factor directly, \(28 \text{ in Hg}\) is converted to \(\text{psia}\) by multiplying \(28\) by \(0.49115\). This calculation results in a pressure of approximately \(13.75 \text{ psia}\). This value represents the absolute force per unit area exerted when a mercury barometer indicates a height of \(28\) inches.
Step-by-Step Conversion Methodology
The conversion factor of \(0.49115 \text{ psia}\) per inch of mercury is derived from the fundamental hydrostatic equation, which defines pressure (\(P\)) as the product of fluid density (\(\rho\)), acceleration due to gravity (\(g\)), and the height of the fluid column (\(h\)). This relationship is expressed as \(P = \rho g h\).
The standard density of mercury at \(0^\circ \text{C}\) is \(13,595.1 \text{ kilograms per cubic meter}\) (\(\text{kg/m}^3\)). Standard gravity is defined as \(9.80665 \text{ meters per second squared}\) (\(\text{m/s}^2\)). To find the pressure generated by a \(1\)-inch column, the height \(h\) must be converted to meters (\(0.0254 \text{ m}\)).
Multiplying these standard values yields the pressure in Pascals (\(\text{Pa}\)), the SI unit for pressure. This calculation shows that \(1 \text{ in Hg}\) is equivalent to about \(3,386.39 \text{ Pa}\).
To arrive at the \(\text{psia}\) value, this Pascal result is converted to the imperial unit of pounds per square inch. Since \(1 \text{ psi}\) is equal to \(6,894.76 \text{ Pa}\), dividing the Pascal value for \(1 \text{ in Hg}\) by this conversion factor confirms the factor of \(0.49115\). This factor is then multiplied by the \(28 \text{ inches}\) to obtain the final \(\text{psia}\) reading of \(13.75 \text{ psia}\).