# Pressure Units

# You, at some point in your life, must have heard the expressions: working under pressure, the pressure of modern life, high blood pressure, low blood pressure, depression, among others. How many times do we not read or hear the word “pressure”! These expressions have different meanings, however, the origin of the words is the same.

Pressure is the relationship between the magnitude of a force acting perpendicularly on a surface and the area of that surface. Mathematically, we have that the pressure is given by:

This equation implies that the pressure is inversely proportional to the area and directly proportional to the force applied on a given surface.

The unit of pressure in the international system (SI) is the N/m² (Newton per square meter), which can also be called the pascal, whose symbol is Pa.

There are some practical units of pressure, derived from the hydrostatic pressure _{phidr} , of which the most important derive from Torricelli’s experience.

Torricelli filled a glass tube about 1 meter long with mercury. He capped its open end with his finger and dipped it into a container that also contained mercury. Torricelli verified that the column of the tube descended until it was balanced at a height of 76 cm from the mercury level in the container.

With this experiment he concluded that the pressure exerted by the air, that is, the atmospheric pressure * ^{patm}* , is equivalent to the pressure exerted by a column of mercury 76 cm high at sea level. Hence the habit of saying that atmospheric pressure at sea level is worth one atmosphere (1 atm).

So we can conclude that the pressure units are:

– Atmosphere (atm): pressure exerted at its base by a 76 cm high mercury column, at 0º C and in a place where g = 9.8 m/s2.

– Centimeter of mercury (cmHg): pressure exerted at its base by a column of mercury 1 cm high, at 0 °C and in a place where g = 9.8 m/s².

– Millimeter of mercury (mmHg): pressure exerted at its base by a column of mercury 1 mm high, at 0 °C and in a place where gravity is 9.8 m/s².

Considering for mercury a density equal to 13.6 g/cm³ or 13.6 . 10³ kg/m³ and g = 9.8 m/s², we have that:

1 cmHg = d . g. h = 13.6 . 10³ 9.8. 10-2 → 1 cm Hg = 1.33. 10³ N/m²

1 mmHg = d . g.h = 13.6. 10³ 9.8. 10-3 → 1 mmHg = 1.33. 10² N/m²

1 atm = d. g. h = 13.6 . 10³ 9.8. 76 .10-2 → 1 atm = 1.013 . 105 N/m2

Typically, 1 atm is used as 105 N/m2.