# 4.29: Pressure in Fluids

**At Grade**Created by: CK-12

**Practice**Pressure in Fluids

Did you ever use a bicycle pump like the one seen in the opening image? When you push down on the handle, it forces air out through the hose, and the air enters the tire through a tiny opening. Like other **fluids** (liquids and gases), air can flow and take the shape of its container. The air that enters the tire from the pump quickly spreads out to fill the entire tire evenly. As the tire fills with air, it feels firmer. That’s because the air exerts pressure against the inside surface of the tire.

### Why Fluids Exert Pressure

All fluids exert pressure like the air inside a tire. The particles of fluids are constantly moving in all directions at random. As the particles move, they keep bumping into each other and into anything else in their path. These collisions cause pressure, and the pressure is exerted equally in all directions. When particles are crowded together in one part of an enclosed space, such as the air particles first entering a tire, they quickly spread out to fill all the available space. That’s because particles of fluids always move from an area of higher pressure to an area of lower pressure. This explains why air entering a tire through a tiny opening quickly fills the entire tire.

### Pressure, Force, and Area

**Pressure** is defined as the amount of force acting on a given area. Therefore, pressure can be represented by this equation:

\begin{align*}\mathrm{Pressure=\frac{Force}{Area}}\end{align*}

**Pressure** shows how concentrated the force is on a given area. The smaller the area to which force is applied, the greater the pressure is. Think about pressing a pushpin, like the one in the **Figure** below, into a bulletin board. You apply force with your thumb to the broad head of the pushpin. However, the force that the pushpin applies to the bulletin board acts only over the tiny point of the pin. This is a much smaller area, so the pressure the point applies to the bulletin board is much greater than the pressure you apply with your thumb. As a result, the pin penetrates the bulletin board with ease.

### SI Unit for Pressure

In the above equation for pressure, force is expressed in Newtons (N) and area is expressed in square meters (m^{2}). Therefore, pressure is expressed in N/m^{2}, which is the SI unit for pressure. This unit is also called the **Pascal (Pa)**. It is named for the scientist Blaise Pascal whose discoveries about pressure in fluids led to a law of the same name. Pressure may also be expressed in the kilopascal (kPa), which equals 1000 Pascals. For example, the correct air pressure inside a mountain bike tire is usually about 200 kPa.

### Calculating Pressure or Force

When you know how much force is acting on a given area, you can calculate the pressure that is being applied to the area using the equation for pressure given above. For example, assume that a rock weighs 5000 N and is resting on the ground on an area of 0.5 m^{2}. The pressure exerted on the ground by the rock is:

\begin{align*}\text{Pressure}=\frac{5000 \ \text{N}}{0.5 \ \text{m}^2}=10000 \ \text{N/m}^2=10000 \ \text{Pa, or } 10 \ \text{kPa}\end{align*}

Sometimes pressure but not force is known. To calculate force, the equation for pressure can be rewritten as:

Force = Pressure × Area

For example, suppose another rock exerts 10 kPa of pressure over an area of 0.4 m^{2}. How much does the rock weigh? Change 10 kPa (10,000 Pa) to 10,000 N/m^{2}. Then substitute this value for pressure in the force equation as follows:

Force (Weight) = 10,000 N/m^{2} × 0.4 m^{2} = 4,000 N

**Q**: The break-dancer in the **Figure** below has a weight of 800 N. He is balancing on the palm of one hand. If the palm of his hand has an area of 0.02 m^{2}, how much pressure is he exerting on the ground?

**A**: Use the equation for pressure:

\begin{align*}\text{Pressure}=\frac{800 \ \text{N}}{0.02 \ \text{m}^2} = 40000 \ \text{Pa, or } 40 \ \text{kPa}\end{align*}

**Q**: If the break-dancer lies down on the ground on his back, his weight is spread over an area of 0.75 m^{2}. How much pressure does he exert on the ground in this position?

**A**: On his back, the pressure he exerts is:

\begin{align*}\text{Pressure}=\frac{800 \ \text{N}}{0.75 \ \text{m}^2}=1100 \ \text{Pa, or } 1.1 \ \text{kPa}\end{align*}

### Factors That Affect Fluid Pressure

Two factors influence the pressure of fluids. They are the depth of the fluid and its density.

- A fluid exerts more pressure at greater depths. Deeper in a fluid, all of the fluid above it results in more weight pressing down. This causes greater pressure the deeper you go.

- Denser fluids such as water exert more pressure than less dense fluids such as air. The particles of denser fluids are closer together, so there are more collisions of particles in a given area. The difference in density of water and air is illustrated in the
**Figure**below.

### Summary

- All fluids exert pressure because their particles are constantly moving and bumping into things.
- Pressure is defined as the amount of force acting on a given area. It measures how concentrated a force is.
- The SI unit for pressure is the Pascal (Pa), or N/m
^{2}. - To calculate pressure, divide force in Newtons (N) by area in square meters (m
^{2}).

### Review

- Why do fluids exert pressure?
- Explain how a pushpin concentrates the force you apply to it.
- What is the SI unit for pressure?
- A large box weighing 700 N is resting on the ground on an area of 1 m
^{2}. How much pressure is the box exerting on the ground? - What factors influence fluid pressure?

### Explore More

Watch the demonstration showing how a siphon works. Then answer the questions below.

- Why does the liquid move into the siphon when air is removed from the siphon by the pipette?
- How does the liquid flow uphill out of the upper cup?
- Why doesn’t the liquid in the siphon flow back down into the upper cup as well as down into the lower cup?

### Resources

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### Image Attributions

- Explain why fluids exert pressure.
- Relate pressure to force and area.
- Identify the SI unit for pressure.
- Show how to calculate pressure.
- Name factors that affect fluid pressure.

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