Section 11.3 Pressure Applied Over Areas
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The total force of pressure is often underestimated because the area over which it is applied is often overlooked.
Force from Pressure.
The basic relationship for pressure is \(P = \frac{F}{A}\text{,}\) which can be written as \(F = PA\text{.}\) This means that the total force from pressure depends on both the pressure and the area over which it is applied. This can sometimes be unanticipatedly large quantity.
A common demonstration is breaking a piece of wood (like a ruler) using air pressure. Video. The air pressure is approximately 100 kPa (which is 14.7 psi). With only a 30 cm square (about 1 foot) sheet of paper, you get a total force of \(F = (100,000 \text{ Pa}) \cdot (0.3 \text{ m}^2) = 9,000 \text{ N}\) (just over 2000 pounds). In the demo, you’re not getting the full force of air pressure because the paper doesn’t form a vacuum seal with the table, but you can see that the theoretical maximum is much larger than what is needed to break the stick.
1
www.youtube.com/watch?v=UvMmfacVA24
Breathing Under Water.
Action Lab Video
2
www.youtube.com/watch?v=PffSc5ZBXgc