You've likely encountered the concept of pressure in multiple contexts, such as in discussions of blood pressure or atmospheric pressure. Pressure plays a vital role in physiology, medicine, and meteorology, among other fields. In physics, pressure is defined as the amount of force applied per unit area:

Here, [latex]F[/latex] is the magnitude of the applied force, and [latex]A[/latex] is the area over which the force is distributed, perpendicular to the surface.

Pressure

Pressure is a scalar quantity that expresses how concentrated a force is when applied to a surface. Mathematically:

The same force can have very different effects depending on the contact area. For example, a gentle push with a finger spreads over a broad area, producing low pressure. In contrast, a needle tip applies the same force over a tiny area, creating high pressure that can pierce skin (see Figure 77.1). The SI unit of pressure is the pascal (Pa):

Other common pressure units include:

• millibar (mb): used in meteorology; [latex]100~\text{mb} = 1 \times 10^4~\text{Pa}[/latex]
• pounds per square inch (psi): used in tire pressure and engineering
• millimeters of mercury (mm Hg): used in measuring blood pressure

Importantly, the force due to pressure in a fluid is always exerted perpendicular to the surface. This is because fluids cannot resist shearing (sideways) forces, so they can’t exert them either. Though pressure is a scalar, the forces it generates have well-defined directions—always perpendicular to surfaces (see Figure 77.2).

Similarly, in a swimming pool, pressure from the water acts on a swimmer’s body from all directions (see Figure 77.3). The deeper the swimmer, the greater the pressure exerted from below, contributing to buoyancy.

Interactive Exploration: Gas Properties

The following interactive simulation allows you to explore how gas particles create pressure. As the particles move and collide with the walls of the container, they exert forces on those walls. When many particles collide over an area, the result is what we measure as pressure. Use the simulation to connect the equation [latex]P = \frac{F}{A}[/latex] with the microscopic behavior of gas particles. Focus especially on how changing the number of particles, temperature, volume, and container size affects pressure.

Guided Exploration

As you interact with the simulation, try to answer the following questions:

1. Add gas particles to the container. What happens to the pressure as more particles are added?
2. Increase the temperature of the gas. How does the motion of the particles change? What happens to the pressure?
3. Decrease the volume of the container while keeping the amount of gas the same. What happens to the pressure? Explain this in terms of particle collisions with the walls.
4. Observe the particles colliding with the walls of the container. How does this microscopic motion explain pressure as force per unit area?
5. Compare a gas at low temperature with the same gas at high temperature. Which one produces greater pressure, and why?
6. How does this simulation help explain why pressure inside a tire, air tank, or balloon acts in all directions?

After completing the exploration, return to the text and connect your observations to the definition of pressure and to the examples involving air tanks, tires, and fluids.

Healthcare Connection

A blood pressure cuff, or sphygmomanometer, is a direct application of pressure as force per unit area. The cuff is an inflatable bladder wrapped around the arm; as it fills with air, it applies a squeezing force over the area of contact with the arm, and this pressure is transmitted through the tissue to compress the brachial artery underneath. By slowly releasing the cuff pressure and listening for or detecting the characteristic sounds of blood beginning to flow again, clinicians can determine the systolic and diastolic pressures in the artery, one of the most common and important measurements in all of medicine.

Section Summary

• Pressure is the force per unit perpendicular area over which the force is applied:
  [latex]P = \frac{F}{A}[/latex]
• The SI unit of pressure is the pascal: [latex]1~\text{Pa} = 1~\text{N/m}^2[/latex].
• Fluids exert pressure equally in all directions, always perpendicular to the surface they contact.

Conceptual Questions

8. How is pressure related to the sharpness of a knife and its ability to cut?
9. Why does a dull hypodermic needle hurt more than a sharp one?
10. The outward force on one end of an air tank was calculated in Example 77.1. How is this force balanced? (The tank does not accelerate, so the force must be balanced.)
11. Why is force exerted by static fluids always perpendicular to a surface?
12. In a remote location near the North Pole, an iceberg floats in a lake. Next to the lake (assume it is not frozen) sits a comparably sized glacier sitting on land. If both chunks of ice should melt due to rising global temperatures (and the melted ice all goes into the lake), which ice chunk would give the greatest increase in the level of the lake water, if any?
13. How do jogging on soft ground and wearing padded shoes reduce the pressures to which the feet and legs are subjected?
14. Toe dancing (as in ballet) is much harder on toes than normal dancing or walking. Explain in terms of pressure.
15. How do you convert pressure units like millimeters of mercury, centimeters of water, and inches of mercury into units like newtons per meter squared without resorting to a table of pressure conversion factors?

Problems & Exercises

11. As a woman walks, her entire weight is momentarily placed on one heel of her high-heeled shoes. Calculate the pressure exerted on the floor by the heel if it has an area of [latex]1\text{.}\text{50}\phantom{\rule{0.25em}{0ex}}{\text{cm}}^{2}[/latex] and the woman’s mass is 55.0 kg. Express the pressure in Pa. (In the early days of commercial flight, women were not allowed to wear high-heeled shoes because aircraft floors were too thin to withstand such large pressures.)
12. The pressure exerted by a phonograph needle on a record is surprisingly large. If the equivalent of 1.00 g is supported by a needle, the tip of which is a circle 0.200 mm in radius, what pressure is exerted on the record in [latex]{\text{N/m}}^{2}[/latex]?
13. Nail tips exert tremendous pressures when they are hit by hammers because they exert a large force over a small area. What force must be exerted on a nail with a circular tip of 1.00 mm diameter to create a pressure of [latex]3\text{.}\text{00}×{\text{10}}^{9}\phantom{\rule{0.25em}{0ex}}{\text{N/m}}^{2}[/latex]? (This high pressure is possible because the hammer striking the nail is brought to rest in such a short distance.)

Glossary

pressure

the force per unit area perpendicular to the force, over which the force acts