ATMOSPHERIC PRESSURE
In this part, we will discuss about the atmospheric pressure and how it can be very powerful. Let's begin by some historical facts.
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History:
The invention of the barometer
Evangelista Torricelli, born October 15, 1608 in Faenza, in Emilia-Romagna - died October 25, 1647 in Florence (wikipedia)
In 1644 Evangelista Torricelli, Italian physicist and mathematician, able for the first time to measure the value of the atmospheric pressure with the mercury barometer he invented. Atmospheric pressure at sea level is 760 mm Hg or 10.33 m of water. It also has the value: 1.01325 · 10^5 Pa or 1 bar. Atmospheric pressure decreases with altitude because the air density decreases. At sea level, air pressure is the highest because the lower layers support the weight of the air above them, this allows us to say that this pressure is a manifestation of the force of gravity but also more useful, unlike gravity who is always directed towards the center of the earth, the forces of atmospheric pressure can act in all directions
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The Magdeburg hemispheres experience
Otto von Guericke, born 20 November 1602 in Magdeburg and died May 11, 1686 in Hamburg (wikipedia)
The experience of Otto Von Guericke in 1654, known by the Magdeburg hemispheres (very popular at that time), highlighted the strength of the atmospheric pressure in the presence of the vacuum. 12 horses and 24 could not separate the two hemispheres, the calculation gives a force equivalent to a weight of a mass of 2 tons, hemispheres had a diameter about 50 cm (les merveilles de la science L.Figuier)
Power of the atmospheric pressure:
In the present invention, atmospheric pressure will provide energy to run our engine because indeed we use the vacuum to create the pressure differential on the piston, so atmospheric pressure pushes the piston with all its strength. The atmospheric pressure provides the necessary force to operate the engine, it is important to have an idea of this force. The force and pressure are connected by this formula (Pascal Law):
P : pressure in Pa
S : surface in m^2
F : force in N
we can deduce F = P .S = P.π.D² / 4, where S is the surface of the piston and D its diameter,the atmospheric pressure is taken at sea level with the value of 1.01325 · 10^5 Pa, F becomes
Atmospheric pressure is constant (in facts, it slightly fluctuate with the weather), the force depends only on the diameter of the piston squared and therefore it has the form of a function , which means that when I double the diameter of the piston, force is multiplied by 4.
graphical representation of the strength of the atmospheric pressure as a function of the piston diameter:
For reasons of simplicity, we assume that the vacuum is absolute at 0 Pa, The force is expressed in daN, 1 daN corresponds to a force generated by a mass of 1 kg, this gives us a better idea about the forces.
In this figure we notice that the force of atmospheric pressure is 795.8 tons with a diameter of 10 m, but it is 3 183.2 tons with a diameter of 20 m, when you double the diameter of the piston you obtain 4 times more forces.
curve of forces vs diametre
If you want to replace a 10 m diameter cylindre by 10 smaller cylinders in purpose to obtain equivalent surface (so force), the small cylinders must have a diametre of 3.1622 m each, atmospheric pressure is weak by comparison to the high pressure steam, that's why big piston is needed to compensate this weakness, but we are lucky because of formula discussed before, the forces rise quickly when the diameter increase slowly.
Experiment from Mythbusters:
If you like MYTHBUSTERS experiments like i do, you can see in this video the atmospheric pressure acting as a giant and invisible hand crushing a car tank with half inch of thickness