Pressure in Fluids

Welcome, students! 🌊 In this lesson, you will learn why a swimming pool feels “heavier” the deeper you go, why your ears feel pressure underwater, and why dams are built thicker at the bottom. These are all real-world effects of pressure in fluids. By the end of this lesson, you should be able to explain what pressure means, how it acts in liquids and gases, and how it connects to the rest of Fluid Statics.

What Pressure Means in a Fluid

Pressure is the amount of force acting on a surface per unit area. In symbols, pressure is written as $p$ and is defined by

$$p=\frac{F}{A}$$

where $F$ is the force acting perpendicular to the surface and $A$ is the area.

This idea is easy to see in everyday life. If you press your hand on a table with the same force, your hand spreads that force over a large area, so the pressure is small. If you press the same force using a thumbtack, the area is tiny, so the pressure is much larger. That is why thumbtacks push into a board so easily 🔩.

In fluids, pressure is especially important because fluids can flow and change shape. A fluid is a substance that can move and does not keep a fixed shape, such as a liquid or a gas. Fluid pressure acts in all directions at a point, not just downward. This is a key idea in fluid statics.

Another important point is that pressure is a scalar quantity. That means it has magnitude but not a single direction like force does. Even though the fluid pushes in many directions, the pressure value at a point is one number.

Pressure in Liquids and Gases

Pressure exists in both liquids and gases, but it behaves differently depending on the fluid.

In a gas like air, pressure comes from the motion of gas particles colliding with surfaces. Air pressure is what makes weather systems important and is also what your body experiences every day. At sea level, the atmospheric pressure is about $101{,}325\,\text{Pa}$, or $101.325\,\text{kPa}$.

In a liquid, pressure is caused by the weight of the liquid above a point. Imagine a point deep in a tank of water. There is water above it, and that water has weight. The deeper the point, the more water is above it, so the greater the pressure.

This is why pressure increases with depth. If you have ever gone swimming, you may have noticed your ears feeling squeezed as you dive deeper. That sensation is the greater water pressure acting on your body 🏊.

Pressure in a fluid is measured in pascals, where $1\,\text{Pa}=1\,\text{N/m}^2$. This unit means one newton of force spread over one square meter of area.

Why Pressure Acts in All Directions

A fluid at rest cannot support shear stress in the same way a solid can. Because of this, pressure at a point in a stationary fluid acts equally in all directions.

This can be understood with a simple thought experiment. Suppose a small cube of fluid is sitting still inside a larger fluid. If the pressure on one side were larger than the opposite side, the cube would accelerate and the fluid would move. Since the fluid is at rest, the pressures must balance.

This explains several practical results:

Water pushes on the sides of a tank, not just the bottom.
A submerged object feels pressure from every side.
The pressure at a point in a fluid at rest does not depend on direction.

This is one of the most important ideas in Fluid Statics because it helps explain how fluid forces are distributed on walls, dams, and containers.

Gauge Pressure and Absolute Pressure

When people measure fluid pressure, they often use either absolute pressure or gauge pressure.

Absolute pressure is measured relative to a perfect vacuum. It includes atmospheric pressure.

Gauge pressure is measured relative to atmospheric pressure. It tells you how much pressure is above atmospheric pressure.

The relationship is

$$p_{\text{absolute}}=p_{\text{atmospheric}}+p_{\text{gauge}}$$

This is important in many real situations. For example, when a car tire is said to be inflated to $220\,\text{kPa}$, that usually means gauge pressure. The actual pressure inside the tire is higher because atmospheric pressure is also acting outside the tire.

A good example is a sealed container of gas. If the gas pressure inside is greater than atmospheric pressure, the gauge pressure is positive. If the inside pressure is below atmospheric pressure, the gauge pressure is negative.

Real-World Examples of Fluid Pressure

Fluid pressure is everywhere around you 🌍.

At rest in a lake, pressure increases with depth, which is why deep-sea equipment must be very strong. A submarine must be designed to withstand large pressures as it dives deeper into the ocean.

In a building, water pressure from the municipal supply helps water flow to taps and showers. If a tank is placed high above the building, gravity creates enough pressure for water to move downward through pipes.

In medicine, blood pressure is a fluid-pressure measurement in arteries. It is often written as systolic over diastolic pressure, such as $120/80\,\text{mmHg}$. This is another example of pressure measurement in a fluid.

In engineering, dams are built thicker at the bottom because water pressure is greater at greater depths. That design helps the structure resist the larger force near the base.

Connecting Pressure to Forces on Surfaces

Pressure is closely linked to force. If pressure is spread over a large area, the total force can still be big.

The relation can be rearranged from $p=\frac{F}{A}$ to get

$$F=pA$$

This is very useful in fluid statics. If a wall is underwater, pressure on the wall creates a force. Since pressure increases with depth, the lower part of the wall experiences greater pressure than the upper part.

Here is a simple example. Suppose a flat underwater panel has area $A=2\,\text{m}^2$ and the pressure on it is $p=3000\,\text{Pa}$. Then the force on the panel is

$$F=pA=(3000)(2)=6000\,\text{N}$$

That is the same idea used in many hydraulic systems, where pressure applied to a fluid can create large forces on pistons.

Pressure Measurement and Why It Matters

Pressure is measured with devices called pressure gauges and manometers. These tools are part of the practical side of Fluid Statics.

A pressure gauge measures the pressure of a fluid relative to atmospheric pressure. A manometer usually compares pressures by using a column of liquid. The difference in height of the liquid columns tells us the pressure difference.

Even though manometry is a separate tool, it is built on the same pressure ideas in this lesson. The pressure at a given depth in a fluid depends on the fluid density, gravity, and depth. That is why pressure measurements can be connected to liquid columns.

In everyday work, engineers use pressure measurements to check pipelines, tanks, boilers, tire inflation, and medical devices. Accurate pressure information helps keep systems safe and working properly.

Summary of the Main Ideas

Pressure in fluids has a few core features:

Pressure is force per area, $p=\frac{F}{A}$.
Pressure exists in both liquids and gases.
In a fluid at rest, pressure acts in all directions.
Pressure in a liquid increases with depth.
Pressure can be measured as absolute pressure or gauge pressure.
Pressure is linked to force on surfaces using $F=pA$.

These ideas are the foundation for later topics in Fluid Statics, especially hydrostatic variation and pressure measurement. If you understand pressure well, you will have an easier time with manometry, buoyancy, and forces on submerged surfaces.

Conclusion

Pressure in fluids explains why fluids push on objects, why deeper water feels stronger, and why pressure measurements matter in engineering and daily life. The central idea is simple but powerful: pressure is force per unit area, and in a fluid at rest it acts in all directions. In liquids, pressure increases with depth because of the weight of the fluid above. This connects directly to hydrostatics, manometers, and many real-world systems. Keep practicing these ideas, students, because they are essential for Thermofluids 1 and for understanding how fluids behave in the world around you.

Study Notes

Pressure is defined as $p=\frac{F}{A}$.
Pressure unit: $\text{Pa}$, where $1\,\text{Pa}=1\,\text{N/m}^2$.
In a stationary fluid, pressure acts equally in all directions.
Liquid pressure increases with depth because of the weight of the fluid above.
Atmospheric pressure at sea level is about $101.325\,\text{kPa}$.
Absolute pressure and gauge pressure are related by $p_{\text{absolute}}=p_{\text{atmospheric}}+p_{\text{gauge}}$.
Force from pressure is found using $F=pA$.
Pressure in fluids is the base idea behind hydrostatics, manometry, and many engineering applications.