Mechanical
Fluid Pressure
Hydrostatic and dynamic pressure in liquids and gases
Fluid pressure is force per unit area exerted by a fluid on its container or any surface. Hydrostatic pressure depends on depth and density (P = rho g h), independent of container shape. Dynamic pressure (q = 0.5 rho v squared) arises from fluid motion. Total head combines static, dynamic, and elevation terms via Bernoulli's equation. Critical to pipe sizing, dam design, hydraulics, aerodynamics, and pneumatic systems.
- HydrostaticP = rho g h — depth times density times gravity
- Dynamicq = 0.5 rho v squared — kinetic energy per volume
- BernoulliP + 0.5 rho v squared + rho g h = constant
- UnitsPascal (Pa), psi, bar, atm
- Pascal's lawConfined fluid transmits pressure equally
- Atmospheric~101.3 kPa at sea level
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Why fluid pressure matters
- Hydraulics. Brakes, jacks, presses, heavy machinery.
- Plumbing. Sizing pipes, pumps, water supply.
- Aerodynamics. Lift, drag, airspeed measurement.
- Civil. Dam design, retaining walls, foundations.
- Process industry. Reactors, pipelines, vessels.
- Medicine. Blood pressure, ventilator design.
- Weather. Atmospheric pressure drives wind and storms.
Common misconceptions
- Pressure depends on shape. Only depth, density, gravity matter for hydrostatic.
- Bernoulli always applies. Requires incompressible inviscid steady streamline flow.
- Static and dynamic add directly. Stagnation point only — not arbitrary locations.
- Gauge equals absolute. Differ by atmospheric pressure (~101 kPa).
- Liquid pressure pushes only down. Acts equally in all directions at a point.
- Air has no weight. Atmospheric column weighs 10.3 meters of water at sea level.
Frequently asked questions
What is fluid pressure?
Force per unit area exerted by a fluid on a surface. Measured in pascals (newtons per square meter). Caused by molecular collisions in gases and weight of fluid above in liquids. Acts equally in all directions at a point (isotropic) when the fluid is at rest. The pressure scalar relates to stress in continuum mechanics.
How is hydrostatic pressure calculated?
P = rho g h. Density times gravity times depth. A column of water 10 meters deep adds about 98 kilopascals, roughly one atmosphere. Independent of container shape (hydrostatic paradox): a thin tube and a wide tank produce identical pressure at equal depth. Add atmospheric pressure to get absolute pressure.
What is dynamic pressure?
q = 0.5 rho v squared. Kinetic energy per unit volume of moving fluid. Pitot tubes measure it on aircraft to compute airspeed. Distinct from static pressure (the pressure measured perpendicular to flow). Stagnation pressure equals static plus dynamic at a point where flow is brought to rest.
What does Bernoulli's equation say?
Along a streamline of incompressible inviscid flow, the sum of static pressure, dynamic pressure, and gravitational potential per volume stays constant. P plus half rho v squared plus rho g h equals constant. Faster flow means lower pressure, explaining lift on wings and the venturi effect in carburetors.
What is Pascal's law?
Pressure applied to a confined fluid transmits equally in all directions throughout the fluid. Foundation of hydraulics. A small force on a small piston creates large force on a large piston (force amplification proportional to area ratio). Hydraulic brakes, jacks, and excavators all exploit it.
How is pressure measured?
Many devices. Manometer (U-tube of liquid). Bourdon tube (curved tube straightens under pressure). Diaphragm gauges. Strain-gauge transducers (piezoresistive silicon). Capacitive sensors. Piezoelectric for dynamic pressures. Each suited to a range and frequency. Calibration against known references is essential for accuracy.
What's gauge versus absolute pressure?
Absolute pressure references vacuum (zero). Gauge pressure references local atmospheric pressure (zero at ambient). Most pressure gauges read gauge. Tire pressure of 32 psi gauge equals about 46.7 psi absolute. Vacuum gauges read negative gauge or use absolute scale. Always specify which reference when reporting values.