Pressure in Fluids

Understand fluid pressure, atmospheric pressure, and how pressure varies with depth.

1. Concept Overview

Fluids exert pressure in all directions. This pressure comes from the continuous motion of fluid molecules and the weight of the fluid above any point. The deeper you go into a fluid, the greater the pressure becomes because more fluid is stacked above you.

Atmospheric pressure works the same way—the air above us acts like a fluid layer, creating pressure on every surface.

2. Definition

Pressure in Fluids: The normal force exerted per unit area by a fluid. It is given by \( P = \dfrac{F}{A} \), where \(F\) is the force and \(A\) is the area.

3. Understanding Fluid Pressure

3.1. Fluids Exert Pressure in All Directions

Unlike solids, fluids spread out evenly and push on surfaces in every direction—upward, downward, and sideways. This is why water pushes equally on all surfaces of a submerged object.

3.2. Pressure Depends on Depth

As depth increases in a fluid, pressure increases because more fluid is above that point. The deeper the point, the heavier the column of fluid pressing down.

3.3. Formula for Pressure at a Depth

The pressure due to a liquid column is given by:

\( P = h \rho g \)

Where:

  • \(h\): depth
  • \(\rho\): density of the fluid
  • \(g\): acceleration due to gravity

4. Atmospheric Pressure

4.1. Air Acts Like a Fluid

Even though air is invisible, it behaves like a fluid made of moving molecules. The weight of the air above us creates atmospheric pressure.

4.2. Meaning of Atmospheric Pressure

Atmospheric pressure at sea level is approximately \( 1.01 \times 10^5 \) pascal. This pressure pushes on everything around us—even our bodies—yet we don’t feel crushed because internal body pressure balances it.

4.3. Variation With Height

Atmospheric pressure decreases as we go higher because there is less air above. This is why mountain regions have lower pressure.

5. Pressure in a Liquid Column

5.1. Linear Increase With Depth

The pressure increases linearly with depth. If you go twice as deep, the pressure doubles. This is seen when divers feel increasing force with depth.

5.2. Independence From Shape of Container

For a given depth, pressure is the same regardless of the shape or width of the container. Only depth, density, and gravity matter.

6. Pascal’s Observation

Pascal noticed that pressure applied at one point in a fluid is transmitted equally in all directions. This sets the foundation for hydraulic machines and fluid pressure applications.

7. Examples to Build Intuition

7.1. Water Pressure in Swimming

When you swim deeper underwater, you feel more pressure on your ears. This happens because the pressure increases with depth.

7.2. Leaking Container

A hole near the bottom of a container throws water out faster than a hole near the top. The deeper hole is under greater pressure.

7.3. Suction by a Straw

When you suck air from a straw, the pressure inside it decreases. Atmospheric pressure on the drink then pushes the liquid up into the straw.