14.2 Measuring pressure

Manometers

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 [link] 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).

Barometers

Manometers typically use a U-shaped tube of a fluid (often mercury) to measure pressure. A barometer (see [link] ) 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.