Fluid Pressure
Fluid pressure is the force exerted per unit area by a fluid on any surface in contact with it, arising from the continuous collisions of fluid molecules. In a static fluid, pressure at a given depth depends on the fluid's density, gravitational acceleration, and the depth below the free surface. It is fundamental to hydraulics, hydrostatics, and the design of dams, pipelines, and pressure vessels.
Key Formula
P = P0 + ρ × g × h
LaTeX: P = P_0 + \rho g h
| Symbol | Meaning | Unit |
|---|---|---|
| P | Absolute pressure at depth h | Pa (Pascal) |
| P₀ | Pressure at the surface (atmospheric) | Pa |
| ρ | Density of the fluid | kg/m³ |
| g | Acceleration due to gravity | m/s² |
| h | Depth below the free surface | m |
Worked Example
Problem
A diver descends to a depth of 20 m in seawater (density = 1025 kg/m³). Atmospheric pressure at the surface is 101 325 Pa. What is the absolute pressure at that depth? (g = 9.81 m/s²)
Solution
Step 1 — Identify known values: ρ = 1025 kg/m³, g = 9.81 m/s², h = 20 m, P₀ = 101 325 Pa. Step 2 — Calculate gauge pressure: ρgh = 1025 × 9.81 × 20 = 201 105 Pa. Step 3 — Add atmospheric pressure: P = 101 325 + 201 105 = 302 430 Pa.
Answer
P ≈ 302 430 Pa ≈ 3.02 atm
Fluid Pressure at Various Depths in Common Fluids (g = 9.81 m/s²)
| Fluid | Density (kg/m³) | Depth (m) | Gauge Pressure (Pa) | Gauge Pressure (atm) |
|---|---|---|---|---|
| Freshwater | 1000 | 10 | 98 100 | 0.97 |
| Seawater | 1025 | 10 | 100 553 | 0.99 |
| Seawater | 1025 | 100 | 1 005 525 | 9.93 |
| Mercury | 13 600 | 1 | 133 416 | 1.32 |
| Engine oil | 870 | 5 | 42 644 | 0.42 |
Interactive Tools
Wikimedia Commons, CC BY-SA
Related Terms
Bernoulli's Equation
Bernoulli's Equation is a statement of energy conservation for steady, incompressible, inviscid fluid flow along a streamline, relating fluid pressure, kinetic energy per unit volume, and potential energy per unit volume. It shows that an increase in flow speed corresponds to a decrease in pressure, explaining phenomena such as lift on aerofoils and the operation of carburettors. Derived by Daniel Bernoulli in 1738, it remains one of the most widely applied principles in fluid dynamics.
Capillary Action
Capillary action is the spontaneous rise (or depression) of a liquid in a narrow tube or porous medium against or with gravity, driven by the interplay between adhesive forces (liquid to solid) and cohesive forces (liquid to liquid), as characterised by surface tension. When adhesion exceeds cohesion — as in water in glass — the liquid rises and forms a concave meniscus; when cohesion exceeds adhesion — as in mercury in glass — the liquid is depressed and forms a convex meniscus. Capillary action is vital in plant water transport, paper chromatography, inkjet printing, and soil hydrology.
Drag Force
Drag force is the resistive force exerted by a fluid on a body moving through it, acting opposite to the direction of relative motion and composed of pressure drag (form drag) and skin-friction drag. For objects moving at moderate to high speeds, drag is proportional to the square of velocity, the fluid density, the frontal area, and a dimensionless drag coefficient that depends on shape and flow regime. Understanding and minimising drag is critical in vehicle and aircraft design, sports engineering, and offshore structure analysis.
From Latin "pressura" (a pressing), derived from "premere" (to press). The modern scientific sense was formalised in the 17th century by Blaise Pascal, whose name is honoured in the SI unit of pressure.