“Pressure” is a word we all know and use. You probably have a commonsense idea of what pressure is. For example, you feel the effects of varying pressure against your eardrums when you swim underwater or take off in an airplane. Cans of whipped cream are “pressurized” to make the contents squirt out when you press the nozzle. It’s hard to open a “vacuum sealed” jar of jelly the first time, but easy after the seal is broken.

You’ve probably seen water squirting out of a hole in the side of a container, as in FIGURE 14.2. Notice that the water emerges at greater speed from a hole at greater depth. And you’ve probably felt the air squirting out of a hole in a bicycle tire or inflatable air mattress. These observations suggest that

• “Something” pushes the water or air sideways, out of the hole.

• In a liquid, the “something” is larger at greater depths. In a gas, the “something” appears to be the same everywhere.

Our goal is to turn these everyday observations into a precise definition of pressure.

FIGURE 14.2 Water pressure pushes the water sideways, out of the holes.

FIGURE 14.3 shows a fluid—either a liquid or a gas—pressing against a small area $A$ with force $\vec{F}$. This is the force that pushes the fluid out of a hole. In the absence of a hole, $\vec{F}$ pushes against the wall of the container. Let’s define the pressure at this point in the fluid to be the ratio of the force to the area on which the force is exerted:

Notice that pressure is a scalar, not a vector. You can see, from Equation 14.2, that a fluid exerts a force of magnitude

on a surface of area A. The force is perpendicular to the surface.

FIGURE 14.3 The fluid presses against area $A$ with force $\vec{F}$.

From its definition, pressure has units of $\text{N}\text{/}{\text{m}}^2$. The SI unit of pressure is the pascal, defined as

This unit is named for the 17th-century French scientist Blaise Pascal, who was one of the first to study fluids. Large pressures are often given in kilopascals, where $1\text{kPa}=1000\text{Pa}$.

Equation 14.2 is the basis for the simple pressure-measuring device shown in FIGURE 14.4a. Because the spring constant $k$ and the area $A$ are known, we can determine the pressure by measuring the compression of the spring. Once we’ve built such a device, we can place it in various liquids and gases to learn about pressure. Figure 14.4b shows what we can learn from a series of simple experiments.

FIGURE 14.4 Learning about pressure.

The first statement in Figure 14.4b is especially important. Pressure exists at all points within a fluid, not just at the walls of the container. You may recall that tension exists at all points in a string, not only at its ends where it is tied to an object. We understood tension as the different parts of the string pulling against each other. Pressure is an analogous idea, except that the different parts of a fluid are pushing against each other.