Pressure in still fluids
Pressure is force spread over area, and in a fluid it grows with depth — nothing else about the container matters.
Pressure
Pressure is force per area, P = F/A, measured in pascals (1 Pa = 1 N/m^2). Fluid pressure pushes perpendicular to every surface it touches, equally in all directions. Gauge pressure is what a tire gauge reads — the amount above atmospheric — while absolute pressure adds the 1.01e5 Pa of the atmosphere on top.
P = \frac{F}{A}Hydrostatic pressure
In a liquid at rest, pressure grows linearly with depth: P = P0 + rho*g*h, where rho is the fluid density and h is the depth below the surface. The pressure depends only on depth and fluid — not on the container's shape or the total volume of water — which is why connected tanks of any geometry fill to the same height.
P = P_0 + \rho g hWorked example
A diver descends 10 m in fresh water (rho = 1000 kg/m^3). The gauge pressure is rho*g*h = (1000)(9.8)(10) = 98,000 Pa, about 98 kPa — roughly one atmosphere. Adding the air's 1.01e5 Pa, the absolute pressure is about 2.0e5 Pa: two atmospheres total at 10 m down.
P = P_0 + \rho g h \approx 1.0\times 10^5 + 9.8\times 10^4 = 2.0\times 10^5\ \text{Pa}Flashcard
Pressure equals force per unit area
Check your understanding
What gauge pressure does a swimmer feel 5.0 m below the surface of a lake?