Measuring Pressure : The Mercury barometer and The Open-Tube Manometer

The Mercury Barometer

 

Figure 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 equation

to find the atmospheric pressure p₀ in terms of the height h of the mercury column. We choose level 1 of figure to be that of the air – mercury interface and level 2 to be that of the top of the mercury column , as labeled in figure . We then substitute

Into equation finding that

Where rho is density of mercury

 

For given pressure , the height h of the mercury column does not depend on the cross-sectional area of the vertical tube . The fanciful mercury barometer of figure b gives the same reading as that of figure a; all that counts is the vertical distance h between the mercury levels.

Equation

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 height of the column ( in millimeters ) is numerically equal to the pressure ( in torr ) only if the barometer is at place where g has its accepted standard value of 9.80665 m/s² and the temperature of the mercury is 0⁰C. 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

An open-tube manometer measures the gauge pressure p_g of gas. It consists of a U-tube containing a liquid, with one end of the tube connected to the vessel whose gauge pressure we wish to measure and the other end open to the atmosphere. We can use equation

To find the gauge pressure in terms of the height h shows in figure. Let us choose levels 1 and 2 as shown in figure . We then substitute

Into equation

Finding that

Where rho is the density of the liquid in the tube. The gauge pressure p_g is directly proportional to h.

The gauge pressure can be positive or negative , depending on whether p > p₀ or p <p₀ . 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.

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