The Crushing Weight of Fluid
Hydrostatic pressure is the pressure exerted by a fluid at equilibrium at a given point within the fluid, purely due to the force of gravity. Hydrostatic pressure increases in direct proportion to depth measured from the surface because of the increasing weight of fluid exerting downward force from above.
This principle dictates the engineering of massive underwater structures. It is why dams must be built significantly thicker at the bottom than at the top, why submarines require heavily reinforced titanium or steel pressure hulls to dive deep into the ocean, and why your ears begin to hurt when you dive to the bottom of a deep swimming pool.
Pascal's Paradox
One of the most counter-intuitive aspects of hydrostatic pressure is known as Pascal's Paradox. The hydrostatic pressure at a certain depth depends only on the fluid density, gravity, and the depth. The total volume, weight, or shape of the container holds absolutely no relevance. A tiny, thin vertical pipe filled with 10 meters of water will generate the exact same pressure at the bottom as a massive lake that is 10 meters deep.
The Formula
Example Calculation
Calculate the staggering hydrostatic pressure exerted on a military submarine at a depth of $1000 , \text{meters}$ in the ocean (seawater density $\approx 1025 , \text{kg/m}^3$).
- Multiply Density $\cdot$ Gravity $\cdot$ Depth: $1025 \cdot 9.81 \cdot 1000 = 10,055,250 , \text{Pa}$.
This is roughly $10 , \text{MPa}$ (Megapascals) of pressure, or about 100 times standard atmospheric pressure crushing inward on the submarine's hull from every direction.