11.4

Pressure Gauges

One of the simplest pressure gauges is the mercury barometer used for measuring atmospheric pressure. This device is a tube sealed at one end, filled completely with mercury, and then inverted, so that the open end is under the surface of a pool of mercury (see Figure 11-12). Except for a negligible amount of mercury vapor, the space above the mercury in the tube is empty, and the pressure P1 is nearly zero there. The pressure P2 at point A at the bottom of the mercury column is the same as that at point B—namely, atmospheric pressure—for these two points are at the same level. With and , it follows from Equation 11.4 that . Thus, the atmospheric pressure can be determined from the height h of the mercury in the tube, the density of mercury, and the acceleration due to gravity. Usually weather forecasters report the pressure in terms of the height h, expressing it in millimeters or inches of mercury. For instance, using and for the density of mercury, we find that .* Slight variations from this value occur, depending on weather conditions and altitude.

Figure 11-12 A mercury barometer.

Figure 11-13 shows another kind of pressure gauge, the open-tube manometer. The phrase “open-tube” refers to the fact that one side of the U-tube is open to atmospheric pressure. The tube contains a liquid, often mercury, and its other side is connected to the container whose pressure P2 is to be measured. When the pressure in the container is equal to the atmospheric pressure, the liquid levels in both sides of the U-tube are the same. When the pressure in the container is greater than atmospheric pressure, as in Figure 11-13, the liquid in the tube is pushed downward on the left side and upward on the right side. The relation can be used to determine the container pressure. Atmospheric pressure exists at the top of the right column, so that . The pressure P2 is the same at points A and B, so we find that , or

Figure 11-13 The U-shaped tube is called an open-tube manometer and can be used to measure the pressure P2 in a container.

The height h is proportional to , which is called the gauge pressure. The gauge pressure is the amount by which the container pressure differs from atmospheric pressure. The actual value for P2 is called the absolute pressure.

Problem solving insight When solving problems that deal with pressure, be sure to note the distinction between gauge pressure and absolute pressure.

The sphygmomanometer is a familiar device for measuring blood pressure. As Figure 11-14 illustrates, a squeeze bulb can be used to inflate the cuff with air, which cuts off the flow of blood through the artery below the cuff. When the release valve is opened, the cuff pressure drops. Blood begins to flow again when the pressure created by the heart at the peak of its beating cycle exceeds the cuff pressure. Using a stethoscope to listen for the initial flow, the operator can measure the corresponding cuff gauge pressure with, for example, an open-tube manometer. This cuff gauge pressure is called the systolic pressure. Eventually, there comes a point when even the pressure created by the heart at the low point of its beating cycle is sufficient to cause blood to flow. Identifying this point with the stethoscope, the operator can measure the corresponding cuff gauge pressure, which is referred to as the diastolic pressure. The systolic and diastolic pressures are reported in millimeters of mercury, and values of less than 120 and 80, respectively, are typical of a young, healthy heart.

Figure 11-14 A sphygmomanometer is used to measure blood pressure.

The physics of a sphygmomanometer.

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