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People usually talk about pressure acting on such and such points like the pressure on a point at height h in a water tank or the air pressure on a point on the Earth's surface. But the definition of pressure is about a force acted upon an "area", not a point. Do people usually mean a differential area located somewhere in space and oriented in a certain way when they talk about a point or is there something I don't know?

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  • $\begingroup$ Does this answer your question? Adding pressure $\endgroup$ Jun 16, 2022 at 18:20
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    $\begingroup$ The ratio of force to area is taken as the limit for an infinitesimal area. $\endgroup$ Jun 16, 2022 at 18:20
  • $\begingroup$ @Chemomechanics My question is mainly about if "pressure on a point" is a thing. $\endgroup$ Jun 16, 2022 at 18:28

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The pressure is the one third the negative trace ($P=-\frac{\sigma_{11}+\sigma_{22}+\sigma_{33}}{3}$) of the stress tensor. Now, stress is defined as a force per unit area, and stress and pressure measurements must be conducted over a finite area. When we talk about the pressure (or stress) at a point, we're idealizing this area as infinitesimal; that is, we're taking the limit of the force-to-area ratio as the area is reduced toward zero.

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