Pressure

For the remainder of this chapter we want to study what happens to fluids and solids, when we apply external forces to them. We will try to stretch or compress objects, and to do this you need to exert forces on these objects.

However, the concept of a force is not quite as useful here as one might at first think. If you apply a force in a single place to a fluid (liquid or gas) material, there is no resistance; the material just gives way. Hence in these materials we talk about the effect of a force applied equally over any area.

This concept of a force per unit area is an extremely important one, one that deserves its own physical quantity. This quantity is pressure:

\[ \rm \mathbf{p = \frac{F}{A}} \]

The SI-unit of pressure can be derived from the SI-units of the force, N, and that of area, m²; it is therefore:

[p] = N/m²; 1 N/m² = 1 Pa (Pascals)

Many other pressure units (bar, Torr, psi, atm, inHg, ...) are in daily use, both in the US and in metric countries. For your convenience, a pressure conversion JavaScript utility is included in our collection of unit conversion engines.

Atmospheric pressure is about 1.013$\cdot$ 10⁵ Pa, which converts to 14.7 psi (pounds per square inch). Even in metric countries, people do not pump their tires up in Pascals, they always use atmospheres.
Gauge pressure vs. actual pressure: Normally when you read a gauge, it gives you the pressure difference between inside and outside. A tire inflated to 32 psi has an actual pressure close to 46.7 psi, because the absolute pressure also includes the air pressure outside the tire, which is 14.7 psi. The pressure near the surface of a lake is 14.7 psi or 1.013$\cdot$ 10⁵ Pa and then increases as you go down. We consider the pressure at the surface to be zero because we have it both inside and outside our ears. As we go up from there, the pressure outside drops and we feel discomfort because of the difference; it happens even faster as we go down.