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2.4: Convenience Units

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  • Occasionally one finds that certain quantities are represented by terms that do not have the appropriate units. The classic example of this situation is associated with the use of mercury barometers to measure the pressure. It is a straightforward matter to use the laws of hydrostatics to show that the atmospheric pressure measured by the barometer shown in Figure \(\PageIndex{1}\) is given by

    \[p_{o} =\rho_{\mathrm{Hg}} gh + p_{\mathrm{Hg}}^{ o} \label{2-17}\]

    Here \(p_{\mathrm{Hg}}^{ o}\) represents the vapor pressure of mercury and under normal circumstances this pressure is extremely small compared to \(p_{ o}\). This allows us to write Equation as

    \[p_{ o} = \rho_{\mathrm{Hg}} gh \label{18}\]

    Since the density of mercury and the gravitational constant are essentially constant, the atmospheric pressure is often reported in terms of \(h\), i.e. millimeters of mercury. While this is convenient, it can lead to errors if units are not used carefully. The message here should be clear: Beware of convenience units!

    Figure \(\PageIndex{1}\): Mercury barometer

    The pressure over and above the constant ambient pressure is often a convenient quantity to use in engineering calculations. For example, if one is concerned about the possibility that a tank might rupture because of an excessively high pressure, it would be the pressure difference between the inside and outside that one would want to know. The pressure over and above the surrounding ambient pressure is usually known as the gauge pressure and is identified as \(p_{g}\). The gauge pressure is defined by

    \[p_{g} =p - p_{ o} \label{19}\]

    where \(p_{ o}\) is the ambient pressure. One should note that the gauge pressure may be negative if the pressure in the system is less than \(p_{ o}\).

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