Hydrostatic Pressure
Any fluid pushes harder the deeper you go, because at greater depth there's more fluid piled up above you, adding its weight. This pressure depends only on how deep you are and what the fluid is — it doesn't matter if the container is wide, narrow, or a weird shape.
The formula
P = ρ · g · h
- P — pressure (Pa): the extra push the fluid exerts at that depth
- ρ — density (kg/m³): how much mass is packed into each cubic meter of the fluid
- g — gravitational acceleration (m/s²): how strongly gravity pulls, about 9.8 near Earth's surface
- h — depth (m): how far below the fluid's surface you are
Worked example
Water has a density of 1000 kilograms per cubic meter. How much pressure does 0.5 meters of water add, using 9.8 for gravity?
- ρ = 1000 kg/m³
- g = 9.8 m/s²
- h = 0.5 m
- P = ρ · g · h
- P = 1000 kg/m³ · 9.8 m/s² · 0.5 m
P = 4900 Pa
Test yourself
Using the same water, what pressure does 1.0 meter of depth add instead of 0.5 meters?
- Correct answer: 9800 Pa
- 4900 Pa
- 2450 Pa
Correct! Doubling the depth doubles the pressure: 1000 kg/m³ × 9.8 m/s² × 1.0 m = 9800 Pa.
A wide tub and a narrow tube are both filled with water to the same depth. Which has more pressure at the bottom?
- the narrow tube
- the wide tub
- Correct answer: they're the same
Exactly! Pressure only depends on depth and density, not on the container's shape or width.
Where you see this
A concrete gravity dam is built with a base far thicker than its top, because water pushes harder the deeper it gets — every 10 meters of water depth adds about 98,000 pascals, roughly a whole extra atmosphere. A diver feels the same law as an ache in the ears long before anything else: descend just a few meters in a pool and the added pressure is already noticeable on the eardrums.
Common mistakes
A natural guess is that a wider column of water must push harder on the bottom — there is more water weighing down. In truth the pressure at a given depth is identical in a wide tub and a thin tube filled to the same height: P = ρ · g · h contains no width, no container shape, no total volume. A second slip is expecting pressure to grow with the square of depth — it grows in a straight line, so doubling the depth exactly doubles the pressure.
How it connects
What does the pushing is simply the weight of the fluid piled above — the same gravity that governs free fall, now pressing sideways as well as down. This is the foundation of the whole fluids unit: Pascal's law asks what happens when such pressure is applied to an enclosed fluid and squeezed, and Archimedes' principle grows out of the depth difference between an object's bottom and its top.