The density of mercury changes approximately linearly with...

The density of mercury changes approximately linearly with temperature as $\rho_{\mathrm{Hg}}=851.5-0.086$ $T \mathrm{lbm} / \mathrm{ft}^{3}$ ( $T$ in degrees Fahrenheit), so the same pressure difference will result in a manometer reading that is influenced by temperature. If a pressure difference of $14.7 \mathrm{lbf} / \mathrm{in} .{ }^{2}$ is measured in the summer at $95 \mathrm{~F}$ and in the winter at $5 \mathrm{~F}$, what is the difference in column height between the two measurements?

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Key Concepts

Hydrostatic Pressure Principle

This principle states that the pressure exerted by a static fluid is directly proportional to the product of its density, the gravitational acceleration, and the height of the fluid column. It is foundational for understanding manometer readings and relates how changes in fluid density can affect the measured height for a given pressure difference.

Temperature Dependence of Fluid Properties

Many fluid properties, including density, vary with temperature. Recognizing that the density of a fluid can change—often approximated by a simple linear relationship—is important when assessing how variations in temperature alter the behavior of fluids in systems and affect measurements like those in manometry.

Unit Conversion and Consistency

In solving problems involving fluid pressure and density, it is crucial to convert and maintain consistent units. This ensures accurate application of the hydrostatic equation and reliable calculations, as pressure, density, and gravitational acceleration may be given in different units that must be correctly aligned.

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