第14章流体力学

One of the most important classes of pressure gauges applies the property that pressure due to the weight of a fluid of constant density is given by $p=h\rho g$. The U-shaped tube shown in Figure 14.12 is an example of a manometer; in part (a), both sides of the tube are open to the atmosphere, allowing atmospheric pressure to push down on each side equally so that its effects cancel.

A manometer with only one side open to the atmosphere is an ideal device for measuring gauge pressures. The gauge pressure is $p_{\text{g}}=h\rho g$ and is found by measuring h. For example, suppose one side of the U-tube is connected to some source of pressure $p_{\text{abs}},$ such as the balloon in part (b) of the figure or the vacuum-packed peanut jar shown in part (c). Pressure is transmitted undiminished to the manometer, and the fluid levels are no longer equal. In part (b), $p_{\text{abs}}$ is greater than atmospheric pressure, whereas in part (c), $p_{\text{abs}}$ is less than atmospheric pressure. In both cases, $p_{\text{abs}}$ differs from atmospheric pressure by an amount $h\rho g,$ where $\rho$ is the density of the fluid in the manometer. In part (b), $p_{\text{abs}}$ can support a column of fluid of height h, so it must exert a pressure $h\rho g$ greater than atmospheric pressure (the gauge pressure $p_{\text{g}}$ is positive). In part (c), atmospheric pressure can support a column of fluid of height h, so $p_{\text{abs}}$ is less than atmospheric pressure by an amount $h\rho g$ (the gauge pressure $p_{\text{g}}$ is negative).

Manometers typically use a U-shaped tube of a fluid (often mercury) to measure pressure. A barometer (see Figure 14.13) is a device that typically uses a single column of mercury to measure atmospheric pressure. The barometer, invented by the Italian mathematician and physicist Evangelista Torricelli (1608–1647) in 1643, is constructed from a glass tube closed at one end and filled with mercury. The tube is then inverted and placed in a pool of mercury. This device measures atmospheric pressure, rather than gauge pressure, because there is a nearly pure vacuum above the mercury in the tube. The height of the mercury is such that $h\rho g=p_{\text{atm}}$. When atmospheric pressure varies, the mercury rises or falls.

Weather forecasters closely monitor changes in atmospheric pressure (often reported as barometric pressure), as rising mercury typically signals improving weather and falling mercury indicates deteriorating weather. The barometer can also be used as an altimeter, since average atmospheric pressure varies with altitude. Mercury barometers and manometers are so common that units of mm Hg are often quoted for atmospheric pressure and blood pressures.