AP® Physics 1: Algebra-Based · Unit 8 · Topic 8.2
Pressure in a Column of Fluid
Pressure in a fluid increases with depth because deeper fluid has more fluid stacked above it pushing down. The pressure from that column alone is P = rho g h, depending only on density, gravity, and depth.
Picture any point underwater. Above it sits a column of fluid reaching up to the surface, and that fluid has weight. The deeper the point, the taller the column above it, the more weight pressing down, and the higher the pressure. This is why your ears ache at the bottom of a pool but feel fine near the surface: at the deep end there is simply more water stacked over your eardrums. The relationship is P = rho g h, where rho is the fluid's density, g is 9.8 m/s2, and h is depth below the surface. This gives the pressure contributed by the fluid column itself, added on top of whatever pressure already exists at the surface, usually atmospheric pressure.
The key insight is that this formula has no term for width, shape, or total volume. A skinny test tube and a wide swimming pool filled with water to the same depth produce the exact same pressure at the bottom. That is because pressure comes from the weight of the fluid directly above a point, per unit area, not from the fluid off to the side. A wider container has more total water, but it also has a wider base to spread that weight over, so the ratio of weight to area stays fixed.
This idea sets up everything else in the fluids unit. Buoyancy comes from the pressure difference between the top and bottom of a submerged object, which exists only because pressure grows with depth. Graphed against depth, pressure in a liquid like a lake rises as a straight line, since rho stays constant. The atmosphere's pressure also increases toward the ground, but air compresses and gets denser lower down, so its graph curves instead of staying linear.
Key terms
- Pressure
- Force per unit area exerted by a fluid, measured in pascals, where 1 Pa = 1 N/m2.
- Fluid column
- The vertical stack of fluid directly above a given point, whose weight creates pressure at that point.
- Density (rho)
- Mass per unit volume of a fluid, a fixed property for a given liquid like water at constant temperature.
- Absolute pressure
- The total pressure at a depth, equal to atmospheric pressure plus the pressure from the fluid column above.
Watch it explained
- How it worksHow does the weight of the fluid stacked overhead build up pressure with depth?
- Worked exampleFind the water pressure 12 m beneath the surface of a lake.
- Common mistakeWhy doesn't the width of the container change the pressure at a given depth?
- Going furtherWhat does a graph of pressure against depth look like for a lake and for the atmosphere?
Check yourself
End of topic.