Pressure in Fluids and Atmospheric Pressure

Pressure in Fluids and Atmospheric Pressure

A fluid is any substance that can flow — this includes both liquids and gases. Fluids exert pressure on surfaces and objects immersed in them, and this pressure increases with depth.

Pressure in a Fluid

The pressure exerted by a fluid at any point acts equally in all directions at that point. This is because fluid particles are in constant random motion and collide with surfaces from all angles.

The pressure in a column of fluid depends on three factors:

• The height (depth) of the fluid column
• The density of the fluid
• The gravitational field strength

The equation is:

pressure due to a column of liquid = height of column x density of liquid x gravitational field strength

p = h x rho x g

Where:

• p = pressure (pascals, Pa)
• h = height of the liquid column (metres, m)
• rho = density of the liquid (kg/m cubed)
• g = gravitational field strength (N/kg) — on Earth, g = 9.8 N/kg

Example: What is the pressure at the bottom of a swimming pool 2 m deep? (Density of water = 1,000 kg/m cubed)

p = h x rho x g = 2 x 1,000 x 9.8 = 19,600 Pa (19.6 kPa)

This is the pressure due to the water only. The total pressure at the bottom also includes atmospheric pressure acting on the surface.

Key Points About Fluid Pressure

• Pressure increases with depth — this is why dams are thicker at the bottom, and why deep-sea divers need special equipment
• Pressure does not depend on the shape of the container — only on the depth
• A more dense fluid produces greater pressure at the same depth (e.g. mercury produces more pressure than water)
• Pressure acts on all surfaces in contact with the fluid — including upward pressure on the underside of objects (this causes upthrust)

Upthrust and Floating

An object submerged in a fluid experiences a greater pressure on its bottom surface than on its top surface (because the bottom is deeper). This pressure difference creates an upward force called upthrust.

An object floats when the upthrust equals its weight. An object sinks when its weight exceeds the upthrust.

• Objects that are less dense than the fluid will float
• Objects that are more dense than the fluid will sink

A steel ship floats because its hull is shaped to displace a large volume of water, creating enough upthrust to support the weight despite steel being denser than water.

Atmospheric Pressure

The atmosphere is a thin layer of gas surrounding the Earth. The weight of the air above us creates atmospheric pressure at the surface.

• At sea level, atmospheric pressure is approximately 101,000 Pa (101 kPa, or about 1 atmosphere)
• Atmospheric pressure decreases with altitude — at higher altitudes, there is less air above, so less weight pressing down
• The atmosphere gets less dense with increasing altitude — the particles are more spread out

Atmospheric pressure acts on all surfaces. We do not normally feel it because it acts equally from all directions, and our bodies are adapted to it.

The Magdeburg hemispheres demonstrated atmospheric pressure dramatically — two metal hemispheres were placed together and the air was pumped out. Teams of horses could not pull them apart because the atmospheric pressure on the outside held them together with no air pressure inside to push them apart.

Pressure in Everyday Life

• Drinking through a straw — you reduce the air pressure inside the straw by sucking; atmospheric pressure on the surface of the drink then pushes the liquid up
• Suction cups — pressing out the air creates low pressure inside; atmospheric pressure holds the cup to the surface
• Barometers measure atmospheric pressure and are used in weather forecasting; falling pressure often indicates approaching storms

The General Pressure Equation

For any force acting on a surface:

pressure = force normal to a surface / area of that surface

p = F / A

Where:

• p = pressure (Pa)
• F = force perpendicular to the surface (N)
• A = area (m squared)

This explains why sharp objects (small area) exert high pressure, and why snowshoes (large area) prevent sinking into snow.

Exam Tips

• Use p = h x rho x g for pressure in a LIQUID; use p = F / A for a force on a surface — do not mix them up
• When explaining floating, always refer to upthrust equalling weight, not just "density"
• For atmospheric pressure questions, always explain that there is less air above at higher altitudes, so less weight and therefore less pressure