# pressure gauges

The simplest pressure gauge is the open-tube manometer (Fig. 12.8a). The U-shaped tube contains a liquid of density r, often mercury or water. The left end of the tube is connected to the container where the pressure p is to be measured, and the right end is open to the atmosphere at pressure p_{0} = p_{atm}. The pressure at the bottom of the tube due to the fluid in the left column is p + rgy_{1}, and the pressure at the bottom due to the fluid in the right column is p_{atm} + rgy_{2}. These pressures are measured at the same level, so they must be equal:

In Eq. (12.8), p is the absolute pressure, and the difference p - p_{atm} between absolute and atmospheric pressure is the gauge pressure. Thus the gauge pressure is proportional to the difference in height h = y_{2} - y_{1} of the liquid columns. Another common pressure gauge is the mercury barometer. It consists of a long glass tube, closed at one end, that has been filled with mercury and then inverted in a dish of mercury (Fig. 12.8b). The space above the mercury column

contains only mercury vapor; its pressure is negligibly small, so the pressure p0 at the top of the mercury column is practically zero. From Eq. (12.6),

So the height h of the mercury column indicates the atmospheric pressure patm. Pressures are often described in terms of the height of the corresponding mercury column, as so many “inches of mercury” or “millimeters of mercury” (abbreviated mm Hg). A pressure of 1 mm Hg is called 1 torr, after Evangelista Torricelli, inventor of the mercury barometer. But these units depend on the density of mercury, which varies with temperature, and on the value of g, which varies with location, so the pascal is the preferred unit of pressure.

Many types of pressure gauges use a flexible sealed tube (Fig. 12.9). A change in the pressure either inside or outside the tube causes a change in its dimensions. This change is detected optically, electrically, or mechanically.

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