The Navier-Stokes equations include the fluid version of Newton's second law

The Navier-Stokes equations are fundamentally accurate but unsolved in 3D

The equations model fluids and have been shown to have solutions for all systems in two dimensions. Averaging and approximations let the equations be used in climate models, aerodynamics, and medicine, though their use in some systems produces nonsensical answers.

Newton's laws describe how objects resist acceleration and respond to forces

Newton’s first law defines inertia as the tendency of an object to maintain its velocity. His second law connects external force, inertia, and acceleration, while his third law states that forces come in pairs—every action has an equal and opposite reaction.

The Reynolds number is the ratio of viscous and inertial forces in fluids

It can approximate fluid behavior in simple systems by non-dimensionalizing—removing the units within—the Navier-Stokes equations. A value close to zero indicates that the fluid will exhibit laminar flow, while a large number suggests that turbulence will occur.

Turbulence has been called the most important unsolved problem in classical physics

Despite being the most common type of fluid flow in our world, scientists have struggled to model turbulent flow accurately. Though behaving unpredictably, understanding inertia and viscosity can help determine whether turbulence will occur.

When experiencing turbulence, fluid elements undergo stretching and folding

Simulations show patches of fluid particles, such as splashes of milk, bend under turbulent flow, creating curvature that grows linearly then exponentially. This accelerated deformation enhances folding and mixing faster than other methods, such as stirring or beating.

Viscosity is a fluid's resistance to flow, which varies with temperature

Liquids become less viscous as temperature increases, while gases become more viscous and therefore flow more slowly. The increased gas collisions at higher temperatures contribute to greater friction between streamlines, increasing viscosity.

Conservation laws identify physical properties that remain unchanged in systems

The total amounts of properties like energy, charge, and angular momentum within a system have been experimentally observed to remain constant, even as changes occur. Particle interactions also conserve specific quantities, such as baryon and lepton numbers. Inconsistencies in these values within isolated systems have historically hinted at the existence of new physics.

Modified Newtonian dynamics revises gravity to eliminate the need for dark matter

Rather than imagining that an undiscovered particle is responsible for discrepancies in the orbits of stars and galaxies, MOND suggests that the mathematics underlying Newton's laws of gravity and force change beyond a certain scale. However, the suggested revisions struggle to explain relativistic effects involving gravity, including gravitational lensing and gravitational waves.

Explore a simplified breakdown of the Einstein field equations

Often depicted as one formula, Einstein's equation represents a suite of 16 nonlinear partial differential equations, which can be simplified to six unique ones, that relate the geometry of spacetime to the presence of mass and energy.

Friction is the force that resists the sliding of surfaces along one another

Friction always acts to resist movement and is determined by how rough the surfaces are and how hard they are pressed together. In the case of fluids, friction arises from the relative motion between adjacent fluid layers, which act like sliding surfaces.

Winter Olympic sports highlight various laws and principles of physics

Figure skaters leverage the conservation of angular momentum during spins by tightening their bodies, and the skintight suits used in ski jumping help reduce drag. Centripetal force allows speedskaters to make tight turns, while friction on skis helps ski mountaineers climb slopes. No action can violate the conservation of energy.

In a closed space, acceleration cannot be distinguished from gravity

Just as pressing into a door when in a car makes a turn resembles the feeling of being pushed from the side, Albert Einstein’s equivalence principle states that being in a gravitational field feels the same as when a floor accelerates up against you, as in a rocket.

Virtual particles are bookkeeping tools used to describe force interactions

Physicists mathematically describe the electromagnetic, weak nuclear, and strong nuclear forces as the result of these particles being exchanged between particles of matter. Despite not being real, observable particles, this method has provided experimental predictions with an accuracy of over 12 decimal places.

Differences in air pressure above and below an airplane's wing allow it to fly

The bending of air around a surface causes it to flow more quickly, reducing the pressure exerted by the airflow. In a commercial airplane, the pressure difference between air diverted above the wing and air flowing undiverted below it creates enough lift to overcome gravity.

While the sun's gravity keeps the planets in orbit, their gravity also pulls on the sun, causing it and everything else in the solar system to orbit around a mutual balance point called the barycenter—the true center of the solar system.

Physicists detect the sound of heat in superfluids, theorized since 1938

Referred to as "second sound," the flow of heat in a superfluid resembles a sound wave bouncing back and forth. The heat-mapping techniques used to make the detection may improve the study of neutron stars and superconductors.

The universe only evolves toward increasing disorder, providing a direction to time

Within physics, the second law of thermodynamics states that entropy always increases, as seen by a concentrated drop of dye slowly diffusing throughout a cup of water, increasing disorder. Because such processes do not unfold in reverse, entropy may be what provides time with a single direction, unlike space.

Hurricanes spin due to differences in air and ground speed as they move across Earth

The movement of an object across latitudes causes it to take a curved trajectory because its speed no longer matches that of the ground beneath it. This phenomenon, called the Coriolis effect, explains why hurricanes spin counterclockwise in the Northern Hemisphere and clockwise in the Southern Hemisphere.

Transpiration drives water movement through a plant’s vascular system

Water evaporates from the leaves, creating tension that pulls more water upward from the roots through the xylem—the equivalent of plant blood vessels. This process is supported by water molecules sticking to each other (cohesion) and xylem walls (adhesion).

The weight of Earth's atmosphere is equivalent to a 33-foot deep, global ocean

Because air is made up of gas molecules with mass, it is not weightless. On the planet's surface, we are effectively living in what is the equivalent of the bottom of an invisible ocean of these particles pressing against us, just as water molecules do when we are submerged.

Convection flows in Earth’s mantle drive the movement of tectonic plates

These processes transfer heat from Earth’s core to the surface via rising magma plumes, while cooler, denser rock falls into the mantle at rates similar to human fingernail growth. These rates are determined by combining seismic data with computer simulations to model Earth’s interior.

The magnetic constant sets the strength of magnetic fields

The permeability of free space, or μ₀, contributes to the speed of light in the universe—a fundamental constant. It also helps quantify how the movement of electric charges generates a magnetic field and vice versa.

Hurricanes, which rely on air consistently spinning in the same direction, cannot cross the equator because air curves in opposite directions north and south of it.

The difference between cash flow and profit, explained

While cash flow is the net balance of cash moving in and out of a business, profit is the remaining balance after subtracting a business's operating expenses from its revenue.

O-rings contain fluid within a system

These donut-shaped components, typically made of rubber, block the escape of liquids and gases in low-pressure systems by forming a seal when compressed within a groove. In high-pressure systems, the O-ring is forced into a gap, blocking any leakage.

An analysis of the logistic map, which shows how chaos can emerge from simple equations

When modeling systems such as the predator-prey cycle of an organism's population in an ecosystem, the logistic map function shows the population normally settles into an equilibrium value. However, at high reproduction and starvation rates, multiple such values arise, making it difficult to accurately model long-term population growth in some environments.

Chaos theory—informally known as the butterfly effect—is the reason why weather forecasts are presented with probabilities rather than certainties.

What does blood do?

Blood's primary purpose is to ferry oxygen and nutrients to cells in need while collecting cell waste and byproducts for removal. It also enables the body's repair and immune systems to traverse our internal landscape to address cell damage or external invaders, such as viruses and parasites. Zooming out from the exact roles of blood's various cells, the fluid connective tissue also assists with maintaining homeostasis via temperature regulation and pH balance.

The deadliest aspect of volcanic eruptions is often not lava, but pyroclastic flows—avalanches of ash, gas, and rock that can move more than half the speed of sound.

Pure water does not conduct electricity because this flow of energy requires the movement of charged particles, and water is a neutral molecule.

The boiling temperature of water decreases with increasing elevation because the molecules need less energy to overcome the lower atmospheric pressure associated with thinner air.

Most of the observable universe's volume consists of voids and supervoids—enormous regions of space with little to no galaxies, stars, or light.

How fusion—which releases energy when two lighter atoms combine to form a heavier atom—differs from fission

English mathematician Ada Lovelace wrote the first computer algorithm a century before computers existed and hypothesized that computing devices would one day be able to compose music—foreseeing the generative AI systems of today.

How Amazon operates a 'flywheel' business model, a self-reinforcing cycle that drives continuous growth

For centuries, Niagara Falls has been a magnet for daredevils seeking to conquer one of nature's most powerful wonders, with its 200-foot drop and water rushing at 32 feet per second with 280 tons of force.

As of 2025, the most cited papers in science include a review of graphene, methods to improve image recognition, streamlining electron density calculations, and optimizing protein studies.

The 19th-century painters of the Hudson River School were among the first American romantics, with portraits that displayed the natural beauty of the young country.

After 25 people used virtual reality headsets to practice flying with virtual wings—flapping their arms—their visual cortex responded to the wings almost as if they were real arms, treating them as body parts.

The word 'jazz' evolved from 'jasm,' 19th-century American slang for 'energy'

Ebola infects and disables immune cells, triggering a cascade of events that leads to small blood clots throughout the body, weakening blood vessels and interrupting blood flow to key organs.

The price of gas is a composite made up of several different factors, with the federal gas tax making up less than 20% of what drivers pay at the pump.

Browse a detailed visual analysis of over 200,000 similes—comparisons that often use 'like' or 'as'—from popular fiction to see how frequently writers the same idiomatic expressions.

Venture capital is a form of funding provided to early-stage companies with high growth potential, typically in exchange for an equity (or ownership) stake

Tattoos remain visible on your skin thanks to immune cells called macrophages

Gerrymandering works through two techniques: cracking opposing voters across districts to dilute their power, and packing them into a few to waste their votes in lopsided majorities.

Play the role of a student in a game where you try to navigate college and remain debt-free, selecting different income levels, high school experience, race, ethnicity, and more.

SpongeBob exemplifies Aristotle's philosophy for living well because he understands that happiness doesn't come from external factors like money, recognition, or power.

Salvador Dalí believed he was his own dead brother, who had died nine months before he was born

The US Constitution is widely regarded as the longest-standing written national constitution still in force—see how it has influenced rights worldwide.