Fluid Dynamics
We can predict the orbit of a planet centuries ahead, but we still can't fully explain the swirl of smoke rising from a candle.
By Greg Goodwin · Published October 16, 2026 · Updated October 24, 2026
Cheat Sheet
- Scope: the study of how liquids and gases move, and the forces they exert on objects.
- Bernoulli's principle (1738): along a streamline in steady flow, faster-moving fluid has lower pressure.
- Reynolds number (1883): a ratio that predicts whether flow will be smooth (laminar) or chaotic (turbulent).
- Navier-Stokes equations (1822-1845): the governing equations of fluid motion; whether smooth solutions always exist in 3D is a $1 million Millennium Prize problem.
- Boundary layer: Ludwig Prandtl's 1904 insight that friction effects are concentrated in a thin layer near a surface.
- Dimples on golf balls: they trip the boundary layer into turbulence, which reduces drag and lets the ball fly farther.
The 60-Second Version
Fluid dynamics studies how liquids and gases move, from blood in an artery to air over an airplane wing to a hurricane crossing the ocean. The basic ideas come from conservation laws: mass, momentum, and energy are neither created nor destroyed. Pressure differences push fluid along, while viscosity resists the flow. At low speeds, flow is smooth and orderly, called laminar; at higher speeds, it breaks into chaotic eddies, called turbulence, which is difficult to predict. Engineers use equations, wind tunnels, and large computer simulations to design vehicles, pipelines, and buildings. The fundamental equations, named after Navier and Stokes, are well established, but mathematicians have not proven whether they always have well-behaved solutions in three dimensions.
The Long Version
Pressure, Speed, and Bernoulli
In 1738, Daniel Bernoulli published results showing that, for steady flow of a fluid without friction, an increase in speed comes with a decrease in pressure. This principle explains why a fast stream of air across a strawberry-shaped opening can draw liquid upward in a perfume atomizer. It is often invoked to explain how wings produce lift, but a full explanation also involves the wing deflecting air downward, as described by Newton's third law, and the circulation of air around the wing. The two descriptions are consistent when properly applied.
Smooth and Turbulent Flow
Osborne Reynolds, in experiments with dye in water pipes in 1883, found that flow changed character at a critical value of a ratio now called the Reynolds number, which compares inertial forces with viscous forces. Low values indicate smooth laminar flow, while high values lead to turbulence. A water faucet turned gently produces a glassy stream, and turned up it becomes chaotic. Turbulence increases mixing and drag, which can be harmful for vehicles and useful in engines and chemical reactors.
The Boundary Layer
In 1904, Ludwig Prandtl realized that even for fluids with low viscosity, friction matters in a thin layer next to surfaces. This boundary layer determines drag and whether flow separates from the surface, which causes a stall on a wing. The idea unified theory and practice, and it underlies modern aerodynamics. Designers use it to shape cars, aircraft, and even golf balls; dimples on the ball cause a turbulent boundary layer that clings longer to the surface and shrinks the wake behind it.
The Hard Equations
The Navier-Stokes equations describe fluid motion in terms of velocity, pressure, density, and viscosity. They can be solved exactly only in simple cases. Mathematicians do not yet know if, in three dimensions, solutions that start smooth must stay smooth, or if they can develop singularities. The Clay Mathematics Institute offers a $1 million prize for resolving the question. Meanwhile, engineers rely on numerical methods that approximate the equations on powerful computers.
Everywhere in Nature and Technology
Fluid dynamics governs weather forecasts, ocean circulation, and the flight of birds and insects. It guides the design of blood pumps, ship hulls, wind turbines, and spacecraft re-entry. It also matters for understanding how the heart and arteries work, and how pollution spreads through air and water. Computational fluid dynamics has largely replaced physical testing in the early stages of many designs.
Why People Care
Almost everything that moves through air or water depends on fluid dynamics. It shapes how efficiently we travel, how accurately we forecast storms, and how well we design machines, yet it still contains deep unsolved problems.
Glossary
- Viscosity
- A fluid's internal resistance to flow; honey has a higher viscosity than water.
- Laminar flow
- Smooth flow in which the fluid moves in parallel layers.
- Turbulence
- Irregular, swirling flow with eddies at many scales.
- Drag
- The force resisting an object's motion through a fluid.
- Computational fluid dynamics (CFD)
- Using computer simulations to solve fluid flow problems numerically.
Go Deeper
More to Explore
- Gravity
The force that keeps you in your chair, the Moon in the sky, and physicists awake at night.
- Optics and Light
Rainbows, eyeglasses, fiber-optic internet, and telescopes all come down to how light bends.
- The Standard Model of Particle Physics
Physicists predicted the Higgs boson in 1964, then waited until 2012 and a giant collider at CERN to actually catch it.
- Electromagnetism
Light, radio waves, and the current running through a phone charger are, at a fundamental level, all exactly the same physical phenomenon.
- Nuclear Energy
Nuclear plants make electricity with no direct greenhouse gas emissions, yet Chernobyl and Fukushima still shape energy policy.