# Fluid Mechanics Applications/B21:Barometer

Barometer: The simplest practical application of the hydrostatic formula is the barometer (Figure.1), which measures atmospheric pressure. A tube is filled with mercury and inverted while submerged in a reservoir. This causes a near vacuum in the closed upper end because mercury has an extremely small vapor pressure at room temperatures (0.16Pa at 20 °C). Since atmospheric pressure forces a mercury column to rise a distance hi nto the tube, the upper mercury surface is at zero pressure. A barometer measures local absolute atmospheric pressure: (a) the height of a mercury column is proportional to p atm; (b) a modern portable barometer, with digital readout, uses the resonating silicon element.At sea-level standard, with pa = 101,350 Pa and ρg=133,100 N/m3 , the barometric height is h = 101,350/133,100 = 0.761 m or 761 mm. Mercury is used because it is the heaviest common liquid. A water barometer would be 34 ft high.

## Principle

When a one-meter long, open ended glass tube is filled with mercury and is then turned upside down into a container filled with mercury, part of the mercury flows out of the glass tube into the container. "Torricellian vacuum" is then produced at the top of the glass tube and the mercury level stabilizes at approximately 76 cm from the mercury level in the container (See Figure 2). Torricelli's experiment revealed that such a height indicates the ambient atmospheric pressure.

The principle of mercury barometer is to measure atmospheric pressure from precise measurement of this height.

$-\nabla p+\rho {\overrightarrow {g}}=0(\rho =\rho _{Hg})g=-k{\hat {g}}$ ${\frac {\mathrm {d} }{\mathrm {d} z}}\left(p\right)=-\rho g$ on integration,

$p(h)=p(z=0)-\rho gh$ But, at the same level ${\frac {\mathrm {d} }{\mathrm {d} x}}\left(p\right)={\frac {\mathrm {d} }{\mathrm {d} y}}\left(p\right)=0andp(z=0)=p_{atm}$ Therefore, $p(h)=p_{atm}-\rho gh$ $p(h)$ is nothing but the vapor pressure of Hg in the space over the liquid Hg in the tube. Generally,

$p(h)=P_{y}\sim 0$ (very small at room temperature)

Hence, $p_{atm}=\rho gh$ .

## Advantages of Using Mercury as Fluid

Mercury is more dense. Its relative density is 13.534 times that of water. So, to measure the atmospheric pressure, which is 760 mm of mercury you need a barometer ,with mercury, of length slightly more than 0.76 meter, say one meter to cover the special cases of some higher pressure. If you use water, you have to have the length of barometer of length (or height) 13.534 times the length of mercury barometer, which may be more than 11 meter in length. Further mercury, being a metal has the shining quality which highlight its reading clear. Also mercury, having comparatively lower specific heat and good conductor of heat, could come to the same temperature of the atmosphere more quickly.

## Applications

• Measuring Weather
• Temperature

The density of mercury will change with temperature, so a reading must be adjusted for the temperature of the instrument. For this purpose a mercury thermometer is usually mounted on the instrument. No such compensation is required for an aneroid barometer.

• Altitude Measurements

As the air pressure will be decreased at altitudes above sea level (and increased below sea level) the actual reading of the instrument will be dependent upon its location. This pressure is then converted to an equivalent sea-level pressure for purposes of reporting and for adjusting aircraft altimeters (as aircraft may fly between regions of varying normalized atmospheric pressure owing to the presence of weather systems). Aneroid barometers have a mechanical adjustment for altitude that allows the equivalent sea level pressure to be read directly and without further adjustment if the instrument is not moved to a different altitude.

## Types Of Barometers

Water based barometers

This type of barometer has an enclosed body and is made of a glass. A spout enters the container below the water level, while the other end remains above the water level in contact with the atmosphere.Another name for this instrument is the "Goether Thermometer". As the pressure drops, the water level within the instrument rises, but when pressure is increased the water level decreases.

Mercury barometers

In the mercury barometer, atmospheric pressure balances a column of mercury, the height of which can be precisely measured. To increase their accuracy, mercury barometers are often corrected for ambient temperature and the local value of gravity. Common pressure units include pounds per square inch; dynes per square centimetre; newtons per square metre (the SI unit called the pascal).

Vacuum Pump Oil barometer

Using vacuum pump oil as the working fluid in a barometer has led to the creation of the new "World's Tallest Barometer" in February 2013. The barometer at Portland State University (PSU) uses doubly distilled vacuum pump oil and has a nominal height of ~12.4 m for the oil column height; expected excursions are in the range of ±0.4 m over the course of a year. Vacuum pump oil has very low vapor pressure and it is available in a range of densities; the lowest density vacuum oil was chosen for the PSU barometer to maximize the oil column height.

Aneroid barometers

An aneroid barometer is a container that holds a sealed chamber from which some air has been removed, creating a partial vacuum. An elastic disk covering the chamber is connected to a needle or pointer on the surface of the container by a chain, lever, and springs. As atmospheric pressure increases or decreases, the elastic disk contracts or expands, causing the pointer to move accordingly.

One type of aneroid barometer has a pointer that moves from left to right in a semicircular motion over a dial, reflecting low or high pressure. The simple clocklike aneroid barometer hanging on the wall of many homes operates on this basis. Another type of aneroid barometer has the pointer resting on the side of a rotating cylinder wrapped with graph paper. As the cylinder rotates on its own axis, the pointer makes a tracing on the paper that reflects increases and decreases in pressure. A recording barometer of this design is known as a barograph.