As shown in Fig. 1.6, a manometer is attached to a tank of...

As shown in Fig. 1.6, a manometer is attached to a tank of gas in which the pressure is $104.0 \mathrm{kPa}$. The manometer liquid is mercury, with a density of $13.59 \mathrm{~g} / \mathrm{cm}^{3}$. If $g=9.81 \mathrm{~m} / \mathrm{s}^{2}$ and the atmospheric pressure is $101.33 \mathrm{kPa}$, calculate (a) the difference in mercury levels in the manometer, in $\mathrm{cm}$. (b) the gage pressure of the gas, in $\mathrm{kPa}$.

As shown in Fig. 1.6, a manometer is attached to a tank of gas in which the pressure is $104.0 \mathrm{kPa}$. The manometer liquid is mercury, with a density of $13.59 \mathrm{~g} / \mathrm{cm}^{3}$. If $g=9.81 \mathrm{~m} / \mathrm{s}^{2}$ and the atmospheric pressure is $101.33 \mathrm{kPa}$, calculate
(a) the difference in mercury levels in the manometer, in $\mathrm{cm}$.
(b) the gage pressure of the gas, in $\mathrm{kPa}$.

Key Concepts

Unit Conversion

Unit conversion is a critical concept when performing calculations in physics to ensure consistency. This includes converting units of density (such as g/cm³ to kg/m³), pressure (from kPa to Pa if necessary), and length (from centimeters to meters). Correct conversion guarantees that the computed values maintain dimensional consistency and accuracy.

Hydrostatic Pressure

Hydrostatic pressure refers to the pressure exerted by a fluid at rest due to the force of gravity. This pressure is directly proportional to the density of the fluid, the gravitational acceleration, and the height of the fluid column. It forms the basis for understanding how differences in fluid column heights can be converted into pressure differences, as seen in manometer applications.

Manometer Principle

A manometer is a device used to measure pressure differences by comparing the heights of a liquid column. The principle relies on the fact that a difference in pressure between two points will produce a difference in the height of the liquid column in the manometer. This measurement can then be used to calculate the absolute or gauge pressure of a system.

Gauge Pressure

Gauge pressure is defined as the pressure relative to the atmospheric pressure, rather than absolute zero. It represents the difference between the measured pressure in a system and the ambient atmospheric pressure. Understanding gauge pressure is important when interpreting manometer readings, as they often provide a direct measure of this pressure difference.

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