Atmospheric pressure and pressure units
Torricelli’s experiment
Evangelista Torricelli (1608–1647) performed an experiment in 1643 that proved that the atmosphere of the Earth exerts a certain amount of pressure on us. He filled a tube closed at one end with mercury, then inverted it into a dish of mercury. The mercury did not flow out completely, but an approximately 76 cm long column remained in the tube.
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The explanation is that the pressure inside the tube (the hydrostatic pressure of mercury, \(p = \varrho_{\mathsf{Hg}} h g\)) keeps equilibrium with the pressure outside (atmospheric pressure, \(p_0\)). The atmospheric pressure balances a certain height (approximately 76 cm) of mercury and does not let it flow out: \[p_0 = \varrho_{\mathsf{Hg}} h g = 13600\,\frac{\mathrm{kg}}{\mathrm{m}^3} \cdot 0.76\,\mathrm{m} \cdot 9.81\,\frac{\mathrm{m}}{\mathrm{s}^2} = 1.013 \cdot 10^5\,\mathrm{Pa}.\] As the atmospheric pressure changes, so does the height, which means the tube can be calibrated and scaled to measure atmospheric pressure. The device made this way is called a barometer. |
Medical pressure unit: millimetre of mercury (Hgmm)
Torricelli’s experiment shows us that since the hydrostatic pressure of a mercury column is a linear function of fluid height, we can define pressure units on the basis of length units if we specify the fluid. This is how the most common pressure unit in medicine, the millimetre of mercury (mmHg) is interpreted: 1 millimetre of mercury equals the hydrostatic pressure of a mercury column whose height is 1 mm:
\[1\,\mathrm{mmHg} = 13600\,\frac{\mathrm{kg}}{\mathrm{m}^3} \cdot 0.001\,\mathrm{m} \cdot 9.81\,\frac{\mathrm{m}}{\mathrm{s}^2} = 133.3\,\mathrm{Pa}\]