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

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

The first equation is the fluid version of the conservation of mass, which prevents incompressible fluids from gaining or losing matter. The second equation replaces acceleration and inertia, which is resistance to acceleration, with fluid pressure and viscosity.

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.

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.

View the transition from laminar to turbulent flow

Using a dye released in the water, streamlines, which are parallel to one another and consistent at low flow velocities, become visible. As the water moves more quickly, viscosity cannot suppress the velocity change, and streamlines become chaotic, creating turbulence.

The R0 value is how epidemiologists quantify disease contagiousness

The basic reproduction number indicates the average number of people a person with a disease will infect. Measles is the most contagious disease, with an R0 of 12-18, though vaccines have significantly reduced the number of susceptible individuals.

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.

How 'vibes' factor into scientists' decisions about using certain units

Although there are absolute quantities from which units can be defined, such as the speed of light and the corresponding light year for distance, the usefulness of units comes from their ability to easily communicate values, rather than how fundamental their origins are. For example, while Kelvin measures absolute temperature, Celsius is scaled to the temperatures of boiling and freezing water, making them more practical for everyday usage.

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.

What is the Gini coefficient?

The Gini coefficient is a measure of income inequality on a scale from 0 to 1. A value of 0 indicates perfect equality, where everyone has the same income, while a value of 1 indicates perfect inequality, where one person has all the income and...

Swimming in schools helps some fish conserve energy in turbulent flows

Scientists studying groups of giant danios swimming in turbulent waters found that the fish used up to 79% less energy than they did when swimming individually in the same conditions. The same fish were found to use the same amount of energy in turbulent and calm water when in schools.

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.

Their 1901 Wind Tunnel system revolutionized the study of aeronautics

Only the second to be built in the US, the wind tunnel allowed the brothers to study how air moves around more than 200 different wing shapes. This data helped them refine a key math equation, long held as the standard, that had been based only on one wing shape.

Zero-g rides get their name from the weightless sensation of being turned upside down

Inversions are when riders are flipped upside down on rides. Zero-g rolls involve turning 360 degrees with inversions, resulting in a temporary experience of zero g-force for passengers.

Ranked-choice voting redistributes ballots until a candidate wins a majority

In ranked-choice voting, voters rank candidates in order of preference. If no one wins a majority, the lowest-ranked candidate is eliminated, and their votes are reassigned until a candidate surpasses 50%, avoiding separate runoff elections.

Blood leaves the heart at speeds around 12-16 miles per hour

Blood is pumped around the body through the circulatory system, aka the cardiovascular system. This system comprises the heart, arteries, veins, and capillaries. This video is the first in a multi-part series on the circulatory system, focusing on the role of the heart, the pump that powers the entire system.

General relativity describes a singularity as the final moment in time

Using Penrose diagrams—mathematical structures that compress all of space and time—physicists can observe the path of light and which events can affect one another. The space-time maps help visualize the structure of black holes and describe what happens when objects fall in.

Unlike hurricanes, tornadoes are not ranked based on measured wind speed

Technological limitations prevent direct measurements of wind speeds where tornadoes make contact with the ground. Instead, the Enhanced Fujita scale assigns a rating with a range of speeds based on how much damage a tornado caused to various types of structures. These types are more extensive than the original Fujita scale.

The 'butterfly effect' is the informal name for chaos theory

In mathematics, chaos theory involves complex systems that are highly sensitive to their initial conditions. Originally discovered when analyzing weather data, slight variations in the data input into such systems create drastically different results, despite following known physical laws.

Why the ratios of helium isotopes are analyzed to investigate ocean circulation

Volcanic activity on the seafloor produces high ratios of helium-3 to helium-4, which can be tracked in ocean samples more easily than other elements because helium is nonreactive. Water from deep ocean currents can also be distinguished from air-exposed surface water sources by comparing these ratios, since atmospheric helium ratios are much lower.

For the same cost, turbines with three blades are the most resilient

Odd-numbered blade values more evenly distribute wind loads across the face of rotors, reducing bending and twisting forces on the turbine that cause wear. Modeling shows that three blades optimize efficiency and cost for everyday wind speeds.

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.

Reels have strongly influenced NASCAR’s social media strategy

With viewership and attendance tanking from 2008 to 2018, NASCAR knew it needed better marketing to reach the next generation of fans, so it designed a new social media and content creation strategy. Using these new methods, it achieved 27% follower growth in three years.

Watch a simulated flight through Jupiter's Great Red Spot

Since its discovery over 350 years ago, the anticyclonic storm—with a high-pressure center and flows opposite to the low-pressure system underneath it—has fascinated astronomers due to its size, which is larger than Earth's, and its prominent features, including winds that surpass 250 miles per hour.

A recession is commonly defined as two straight quarters of shrinking GDP

Recessions are sustained downturns in the economy. They’re significant, widespread, and there’s no single, surefire way to define or predict them.

A FIRE number is the amount of money someone needs in retirement

To calculate one’s FIRE number, FIRE followers typically multiply their expected annual expenses in retirement by 25.

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

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.

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

To reduce wrinkles in clothing, research recommends gentle wash cycles with more water and tumble drying with smaller loads and longer times.

Some coin denominations have ridges etched on their sides, partly to prevent counterfeiting, in a practice called 'reeding.'

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.

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

Corals are themselves not coral reefs—the term refers to the tiny marine invertebrates that build the rigid reef.

Ebola is a filovirus, meaning it resembles a thread under a microscope, though it sometimes twists and can resemble a bowl of spaghetti.

The term 'algorithm' originated from the Latinized name of al-Khwārizmī, a 9th-century mathematician whose works introduced Arabic numerals and the decimal-based numeral system to Europe and whose treatise 'Al-Jabr' gave algebra its name.

The first steps to rebuilding your credit score include getting to know exactly what's on your credit report and figuring out how far you are from the '700 club,' or 'good score' range.

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.

Iran's Revolutionary Guard Corps is independent of Iran's regular army and is one of the most powerful and influential military-political organizations in the Middle East.

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.

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

Some renewable energy sources may weaken the resiliency of electric grids by removing outage buffers provided by coal- and natural gas-fired plants, which provide the system with more time to find a new power source if a plant goes down.

The syncytiotrophoblast is the outer layer of the placenta and the largest human cell, spanning an area about twice that of a king-sized bedsheet.

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.

Use this calculator to find the dollar value of your mental load, from meal planning to coordinating after-school care for your children.

The rivalry between Alexander Hamilton and Thomas Jefferson centered on federalism—the question of how much power the federal government should hold relative to the states.

The Nasdaq's 'Magnificent 7' companies are responsible for roughly 40% of the Nasdaq 100 index's gains, while the remaining 93 companies account for the other 60%.

In 2026, Finland was named the world's happiest country for the ninth consecutive year based on its wealth, social safety network, and high life expectancy, among other factors.

Brian Wilson wrote the Beach Boys' 'Don't Worry Baby' for the Ronettes, but the legendary girl group rejected it.

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.