Measuring Pressure

The Mercury Barometer

Figure J5-5a shows a very basic mercury barometer, a device used to measure the pressure of the atmosphere. The long glass tube is filled with mercury and inverted with its open end in a dish of mercury, as the figure shows. The space above the mercury column contains only mercury vapor, whose pressure is so small at ordinary temperatures that it can be neglected. We can use Eq. 15-7 to find the atmospheric pressure Po in terms of the height h of the mercury column. We choose level I of Fig. 15-2 to be that of the mercury interface and level 2 to be that of the top of the mercury column, as labeled in Fig. 15-5a. We then substitute.

)’1 = 0, PI = Po and .\’2 = 17, P2 = 0

into Eq. 15-7, finding that

Po = pgh,

where P is the density of the mercury. For a given pressure, the height 17 of the mercury column does not depend on

the cross-sectional area of the vertical tube. The fanciful mercury barometer ofFig. 15-5b gives the same reading as that of Fig. 15-5a; all that counts is the vertical distance” between the mercury levels. Equation 15-9 shows that, for a given pressure, the height of the column of mercury depends on the value of g at the location of the barometer and on the density of mercury, which varies with temperature. The column height (in millimeters) is numerically equal to the pressure (in torr) only if the barometer is at a place where g has its accepted standard value of 9.80665 m/s2 and the temperature of the mercury is O°c. If these conditions do not prevail (and they rarely do), small corrections must be made before the height of the mercury column can be transformed into a pressure.

**The Open-Tube Manometer**

vessel whose gauge pressure we wish to measure and the other end open to the atmosphere. We can use Eq. 15-7 to find the gauge pressure in terms of the height shown in Let us choose levels I and 2 as shown in. We then substitute

Yt = 0, Pt = Po and Y2 = -h, P2 = P

into Eq. 15-7, finding that

= P – Po = pgh,

where p is the density of the liquid in the tube. The gauge pressure PR is directly proportional to h. The gauge pressure can be positive or negative, depending on whether P > Poor P < Po. In inflated tires or the human circulatory system, the (absolute) pressure is greater than atmospheric pressure, so the gauge pressure is a positive quantity, sometimes called the overpressure. If you suck on a straw to pull fluid up the straw, the (absolute) pressure in your lungs is actually less than atmospheric pressure. The gauge pressure in your lungs is then a negative quantity.