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Bernoulli's principlelaw

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Daniel Bernoulli published the principle in his book 'Hydrodynamica' (1738), formulating the law of conservation of energy for a moving fluid. Initially, he was thinking about blood flow and water movement in pipes. The equation relates pressure, speed, and height along a streamline (particle trajectory) in an inviscid incompressible fluid. Key: an increase in speed leads to a pressure drop, and vice versa — this is a consequence of the redistribution of kinetic and potential energies.

How it works

An airplane stays in the air: over the curved wing, air flows faster, pressure decreases, and the lower pressure pushes upward. A car's carburetor sprays gasoline similarly: air rushes through a Venturi tube and sucks out the fuel.

💡 A shower curtain 'sticks' to the wall for a moment after turning on: the water jet accelerates in the hose, pressure drops, and the outside air pushes the curtain against the wall.
P + \frac{1}{2} \rho v^2 + \rho g h = \text{const}
P — static pressure (Pa), ρ — fluid density (kg/m³), v — flow velocity (m/s), g — acceleration due to gravity (g ≈ 9.81 m/s²), h — height above reference level (m)
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Discovered by
Daniel BernoulliLeonhard Euler
Related concepts
Waterturbulence
Related laws
law of conservation of energyArchimedes' principle

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arXiv:2602.22211 · 2026-02-25

Freezing Ice and Expanding Space

When scientists accounted for the fact that water under ice constantly moves and mixes, the equations for ice growth suddenly matched those describing the expansion of the entire cosmos. Moreover, a term appeared in these equations that behaves exactly like mysterious dark energy—the very thing that
arXiv:2602.24019 · 2026-02-27

Cosmic Rhythm: From Snowdrifts to Quantum Gas

The bumps of a 'quantum snowdrift' made of cold atoms grow according to exactly the same scenario as a snowdrift in your yard. This universal law works for sand, water, and even cities. The experiment proved: nature is unified from atoms to skyscrapers.
arXiv:2603.09060 · 2026-03-10

The Quantum Mpemba Paradox: Why Hotter Cools Faster

In the quantum world, a system initially farther from equilibrium can settle down faster. Physicists found that suppressing the dominant rhythm of chaos sharply accelerates the growth of disorder and the approach to equilibrium. Moreover, by breaking time symmetry, they achieved an almost instantane
arXiv:2603.11788 · 2026-03-12

How Rain Launches Microplastics into the Air

Physicists have discovered that rain lifts plastic particles into the air, especially those that repel water. Upon impact, they get coated in water and turn into airborne beads that wind scatters across the planet. This changes our understanding of how plastic travels from the ocean into our lungs.
arXiv:2603.15896 · 2026-03-16

Interstellar Comet: Water 14 Times Heavier Than Earth's

Spectroscopic analysis of comet 3I/ATLAS by Webb revealed an anomalously high deuterium content. This chemical marker suggests the comet was born in the bitter cold of a distant star system.
arXiv:2603.20445 · 2026-03-20

How Bacteria Battle on Water Planets

Researchers applied Earth’s competition models to bacteria on hycean planets—worlds with deep oceans and hydrogen skies. Light-eating microbes grab the surface, like weeds taking over a garden. Viruses can crash the system or boost diversity. On worlds with one side always facing their star, life is
arXiv:2603.22491 · 2026-03-23

Enceladus's Ocean — A Perfect Heat Pump

Water salinity drives Enceladus's ocean currents. When salt concentration is very low or very high, circulation speeds up, carrying heat to the poles and thinning the ice. This finding narrows down the ocean's possible properties and brings us closer to finding life.
arXiv:2603.22602 · 2026-03-23

Quantum Leap to Calm

In a new study, physicists explained the quantum Mpemba effect: a system with higher initial energy reaches equilibrium faster. By creating a thermodynamic model based on the principle of fastest entropy growth and applying machine learning, they identified the decisive parameter. The discovery prom
arXiv:2603.24522 · 2026-03-25

Diamond Sensor Catches Magnetic Signal from a Living Cell

Instead of quickly fading glowing markers, scientists used magnetic nanoparticles and diamond sensors. This 'compass' picks up magnetic signals from cells without interference, making it possible to observe even weak processes in a single living cell. This opens new possibilities for diagnostics and
arXiv:2604.04094 · 2026-04-05

A Quantum Recipe for Free Will

The 'Agent Choice via Quantum Flux' model reconciles free choice with physics: one decision is embodied by many quantum states—like soup made by different chefs. This leaves room for genuine choice where only predetermination was seen before.
arXiv:2604.06450 · 2026-04-07

Carbon nanotubes with calcium trap hydrogen

Hydrogen fuel is clean, but keeping it in a tank is tricky—molecules are too small and slip away. Scientists found a fix: put calcium atoms inside carbon tubes so they snag hydrogen like Velcro. This brings us closer to lightweight, safe hydrogen tanks for cars.
arXiv:2604.07110 · 2026-04-08

Quantum Rainbow: How a Tiny Computer Sorts Mountains of Data

Researchers have proved that even a tiny quantum processor can outperform massive classical computers in sorting and analyzing big data. The 'quantum sketch' algorithm was successfully used to decode genes in individual cells and to gauge the sentiment of movie reviews. All of this was accomplished
arXiv:2604.07639 · 2026-04-08

The Sun Conducts Ice Ages

New research settles an old debate: ice ages are controlled not by complex chemistry but by sunlight. A simple model links the flow of solar heat to ice volume, accurately reproducing 800,000 years of data. The ocean, like a mute, dampens the slow 400,000-year cycle, making the 100,000-year cycle th
arXiv:2604.12143 · 2026-04-13

Dance of Ions: How Quantum Vortices Are Born

By controlling ion rotation, scientists created a skyrmion — a stable magnetic vortex. The full picture of spins has been revealed with 87% accuracy, paving the way to quantum materials and ultra-dense memory.
arXiv:2604.13872 · 2026-04-15

Wings in a Minute: How AI Became an Aerodynamic Genius

A new AI training method: first learn from 30,000 shapes, then fine-tune for the task. Just 450 examples reduce error to 0.36%. This speeds up the search for the best aerodynamic solutions.
arXiv:2604.18062 · 2026-04-20

How Stellar Flares Change the Atmosphere of Faraway Planets

The study examines how radiation from stellar flares affects the air of young planets. Scientists modeled a year of chemical changes and found that moderate flares have a strong impact. Atmospheres with high water vapor content are particularly vulnerable. This discovery is important for correctly i
arXiv:2604.20325 · 2026-04-22

Diagnosis for Distant Worlds: How Not to Mistake Life for Noise

The search for extraterrestrial life is like an unreliable medical test: a single positive result means nothing if the error rate is unknown. A new approach sidesteps this problem by dividing worlds into groups—much like patients with different risk factors. Statistical comparison dramatically reduc
arXiv:2605.02969 · 2026-05-03

Atmosphere found on a small icy body beyond Neptune

Astronomers have for the first time found an atmosphere on a small object (612533) 2002 XV93 in the Kuiper Belt. Previously, it was thought that only large bodies could retain gases, but this icy ball 250 km in diameter proved otherwise. The discovery forces a fresh look at the hidden activity of sm
arXiv:2605.02243 · 2026-05-04

The Secret of the Metallic Comet from Another Star System

After its close approach to the Sun, comet 3I/ATLAS ejected an abnormally large amount of nickel and iron into its tail. These metals hid deep inside as volatile compounds with carbon monoxide. When heat seeped beneath the surface, the compounds evaporated, freeing the atoms. This mechanism unveils
arXiv:2605.07652 · 2026-05-08

Quantum Batteries: Instant Charging with Squeezed Light

The new scheme uses a light-filled cavity where photon pairs, like sharp jolts, instantaneously transfer energy to a chain of qubit cells. Quantum links inside the cells suppress leakage, making the battery immune to noise and defects.
arXiv:2605.14582 · 2026-05-14

River as a Mirror of the Universe

Researchers found that a lab-made river’s cross-section perfectly mirrors the form predicted by a cosmological equation for a negatively curved universe. Normally, this equation tracks how the Universe’s size evolves over time. Surprisingly, water sculpts its channel to maximize bottom friction, and
arXiv:2605.14670v1 · 2026-05-14

How Not to Mistake Life for Lifeless Chemistry

On Saturn's moon Enceladus, scientists search for signs of life in the subsurface ocean. Non-living processes create similar signatures. Researchers developed a method to estimate the non-biological background and showed: without precise geophysical data, distinguishing living from non-living is imp
arXiv:2605.15337 · 2026-05-14

Martian Spores: How Life Could Have Flown to Earth

Scientists simulated the journey of microbes inside a Martian fragment. The spores survived harsh ultraviolet radiation, and computer calculations showed the trip takes only a year. This makes the idea of interplanetary spread of life more plausible.
arXiv:2605.15595 · 2026-05-15

The Chemical Signature of Life: How to Find It by Its Elements

Scientists have revealed a universal recipe for living matter: it contains more oxygen, hydrogen, sulfur, and nitrogen relative to carbon. This pattern holds for any organism and isn't tied to specific biomolecules. The chemical signature of life is universal—future missions could search for it on o
arXiv:2605.19252 · 2026-05-19

Quantum Droplets: Precision Unattainable

New interval quantum mechanics describes states not as points, but as 'quantum droplets' — regions of possible values. Measurement squeezes the droplet, and paradoxes like Schrödinger's cat simply do not arise in the real, imprecise world.
arXiv:2605.19706 · 2026-05-19

A Vortex's Silent Patch Reveals Its Speed

Physicists have found that the shape of a water vortex's sound shadow can precisely measure its rotation speed. The main surprise: the mathematics of an ordinary sink plug and a giant black hole are the same.
arXiv:2605.20354 · 2026-05-19

The Ice Centaur Riddle: What Is Chiron Hiding?

Chiron releases methane from its depths, carbon dioxide from the surface, and carbon monoxide is locked inside. This reshapes models of how icy bodies behave.
arXiv:2605.23038 · 2026-05-21

Quantum Mpemba: Strong Entanglement Melts Faster

Physicists have discovered that under environmental influence, a strong quantum bond between particles breaks down faster than a weak one. The reason is excess energy in highly entangled states. This counterintuitive effect helps manage fragile quantum systems.
arXiv:2605.23197 · 2026-05-22

The City as an Organism: Nature’s Lessons for Roads Without Gridlock

Nature’s arteries—river systems, leaf veins—have operated flawlessly for millions of years. A new study reveals how to transfer this brilliant engineering to city roads. The result: networks that grow, adapt, and require almost no maintenance.
arXiv:2605.23766 · 2026-05-22

Stellar Orthography: How ExoVeil Reads Missed Planets

Traditionally, astronomers caught planets by waiting for multiple passes across stars. ExoVeil breaks this mold: a transformer neural network learns to predict the star's normal twinkling and spots even a lone shadow. A blind analysis of Kepler data revealed 179 new candidates, and on TESS data with
arXiv:2606.02778v3 · 2026-06-01

Molecular Rope in the Cradle of Planets

In the disk of TW Hydrae, resembling the early Solar System, HC5N has been detected — the longest carbon chain in such an object. The ALMA discovery shows that prebiotic compounds are not destroyed in the planetary forge. Models point to an excess of carbon, linking the disk's chemistry with interst
arXiv:2606.02815v1 · 2026-06-01

Neptune's False Note: Nereid — Not an Interloper, but a Last Survivor

Neptune's third-largest moon, Nereid, was long counted among the icy intruders from the Kuiper Belt. But its unique infrared spectrum, captured by the James Webb Space Telescope, is unlike any other: crystalline water ice with a reddish tint and traces of carbon dioxide hint at a birth near the plan
arXiv:2606.02818v1 · 2026-06-01

Hearing Precision: How to Predict the Capabilities of Quantum Sensors from the Sound of a Kettle

A quantum system can act as an ultra-sensitive sensor, but its ultimate precision used to be calculated by fully reconstructing all properties — a laborious process. Now scientists have shown that a few simple measurements suffice: a machine learning algorithm predicts precision based on particle co
arXiv:2606.02986 · 2026-06-02

Erythrulose: The First Sugar Baked in an Interstellar Furnace

Spectral lines of erythrulose (C₄H₈O₄), caught by the Yebes 40m and IRAM 30m radio telescopes, betrayed the presence of this sugar in the cloud G+0.693. For the first time, we see how, in the interstellar medium, on the surface of icy dust grains, components of nucleic acids are born from glycolalde
arXiv:2606.03313v1 · 2026-06-02

Bees of Dark Clouds: How Ions Weave Carbon Rings in Space

In the PIRENEA ion trap, a cosmic dance was recreated: benzyl-type ions intertwine with alkylnaphthalenes, birthing a photostable acenaphthylene cation. This solves the mystery of cyanoacenaphthylene in the TMC-1 cloud and rewrites the rules for assembling aromatic compounds in the cold depths of sp
arXiv:2606.03575v1 · 2026-06-02

Steam from Scorching Rocks: Silicon Gas in the Atmosphere of TWA5B

The CRIRES+ spectrograph on the Very Large Telescope captured the faint light of the young super-Jupiter TWA5B and resolved the SiO lines—the main carrier of gaseous silicon. The detection with a signal-to-noise ratio of 7.5 means: silicon almost entirely floats in the gas phase, not locked in silic
arXiv:2606.03824v1 · 2026-06-02

Diamond Detective: Magnetic Dance Reveals the Secrets of Liquids

A diamond plate with magnetic particles on DNA strands analyzes liquid by the trembling of particles. Their movement changes with thickness and composition: in syrup—slow, in alcohol—fast. The diamond reads the magnetic echo and creates a precise portrait of the liquid—no reagents, no waiting.
arXiv:2606.04064 · 2026-06-02

Comet Spice: How a Late Influx of Matter Reshaped the Outer Solar System

Carbonaceous chondrites that fall to Earth carry a double isotopic signature. Measurements of silicon, iron, magnesium, and chromium tell us that the stuff of Jupiter and Saturn came from two reservoirs, with a late addition of comet dust making up more than a third. Even more surprising, CI chondri
arXiv:2606.04529v1 · 2026-06-03

Lead Archives: Ancient Minerals vs. Higgsino

Dark matter is physics' greatest intrigue. Paleodetection opens a new chapter: million-year-old minerals, like laurionite (PbClOH), preserve traces of dark particles. Thanks to massive lead nuclei and exceptional purity, crystals can detect the Higgsino — the superpartner of the Higgs boson, whose s
arXiv:2606.05299v1 · 2026-06-03

Ultraviolet Trap: How TRAPPIST-1 Star Fakes Signs of Life

TRAPPIST-1 e is a rocky planet in the habitable zone of a red dwarf, one of astrobiologists' prime targets. But decoding its atmosphere requires a precise ultraviolet 'autograph' of the star. Simulations showed: different UV spectra dramatically alter the chemical portrait, producing deceptive pairs
arXiv:2606.05451v1 · 2026-06-03

The Quantum Mpemba Paradox: Asymmetry Accelerates Order

Scientists have discovered that in quantum systems where conservation laws split states into isolated 'pockets,' a strong disturbance of equilibrium recovers faster than a weak one—just like hot water sometimes freezes sooner than cold. Meanwhile, some imbalances vanish in a flash, while others get
arXiv:2606.06653 · 2026-06-04

Cosmic Tan: How Stellar Flares Repaint Water Worlds

Atmospheres of many sub-Neptunes are shrouded in dense organic hazes that hide their true composition. In lab experiments, such hazes were recreated from water vapor, methane, and carbon dioxide, then irradiated with ultraviolet light, mimicking flares from red dwarfs. It turned out that after irrad
arXiv:2606.06691v1 · 2026-06-04

Freo Doctor: How Wind Governs the Fate of Meteorites

The bright flash of a bolide is just the first act. After an asteroid or comet fades, dark flight begins: the invisible drift of fragments to the ground. That's when wind sows chaos, shifting the impact point by hundreds of meters. The team of Devillepoix and Cupák deployed the WRF model to calculat
arXiv:2606.07144v1 · 2026-06-05

Heavy water ice found in planet-forming disk

The Webb telescope directly observed heavy water ice for the first time in a planetary disk—the birthplace of planets. There's unexpectedly a lot of it, pointing to a turbulent history of the ice that might explain the origin of Earth's oceans.
arXiv:2606.10888 · 2026-06-09

Mysterious Trace on Titan's Surface

Titan's dense haze long concealed its surface. But in infrared light, the JWST telescope discerned a narrow dark band — a chemical fingerprint of an unknown substance. A similar, but broader, one was found on Pluto. This discovery brings us closer to unraveling the composition of distant icy worlds.
arXiv:2606.13350 · 2026-06-11

Visitors from the Abyss: How Passing Planets Shaped Earth's Fate

Hundreds of rogue planets lurk on the outskirts of the Solar System. Their close encounters with Earth—even without a collision—cause waves, eruptions, and climate shifts. This explains past mass extinctions.
arXiv:2606.17105 · 2026-06-14

A Planet's Rotation Revealed Its Fiery Secrets

Astronomers studied WASP-121 b, a gas giant always facing its star with one side. As the planet transited the star, they detected changes in light absorption: the eastern limb was hotter than the western, which destroys water and leaves carbon monoxide. This opens a method for scanning weather on su
arXiv:2606.19487 · 2026-06-17

How Confirmation Bias Helps You Think Faster

We often blame ourselves for noticing only what matches our expectations. But a mathematical model inspired by the laws of the microworld showed that this habit drastically reduces errors and requires less memory. It's not foolishness, but a calculated strategy.
arXiv:2606.23325 · 2026-06-22

James Webb Fishes Out an Invisible Planet from a Dusty Disk

A third giant planet has been found around Beta Pictoris—not in an image, but through chemical traces in light: methane, water, and carbon monoxide. It is 2–4 times more massive than Jupiter and sits so far out that a year there lasts over a century. Its gravity shapes the inner edge of the dusty di
arXiv:2606.23789 · 2026-06-22

Quantum Drones Scan Ruins with Magnetic Vision

After earthquakes or explosions, every hour counts. New research proposes using drones with incredibly sensitive quantum magnetometers to peer beneath rubble. Scientists simulated the collapse of a concrete parking structure and showed that weak magnetic fields from steel rebar can reveal where void
arXiv:2606.25957 · 2026-06-24

Traces of Mind: What We Miss in the Search for Aliens

Between searching for life and technology, there is a gap: how to notice intelligence without machines? Noosignatures — any ordered traces of a thinking being — fill this void. From a paw print to a signal without a key: a new method expands the chances of finding alien intelligence even where life
arXiv:2606.28437 · 2026-06-26

Can life travel between stars on icy comets?

Data from JWST and SPHEREx on comet 3I/ATLAS revealed that natural spread of life in ice is possible if microbes periodically thaw. But intentional sending of life by another civilization is nearly impossible — the impact would be too hot. The work proposes a method to search for life on such wander
arXiv:2607.00202 · 2026-06-30

Cosmic Carving: Birth of a Bloated Neptune from a Jupiter

Astronomers discovered exoplanet TOI-2195 A b – a hot Neptune with a mass 1.5 times that of Neptune, but a radius almost as large as Jupiter's. Orbital analysis suggests a likely polar orbit. Modeling indicates the planet may have formed as a cold Jupiter, losing up to 90% of its mass during highly
arXiv:2607.01315v1 · 2026-07-01

Smoldering Giant: Methane and Haze over a Dead Star

The James Webb Space Telescope has peered into a previously unseen world: the atmosphere of the giant planet WD 1856 b, orbiting a white dwarf. The transit spectrum from 0.5 to 5.0 μm revealed hydrocarbons, including methane with a significance of 17:1 to 30:1, thick aerosols, and thermal glow from
arXiv:2607.01316v1 · 2026-07-01

Light Trap for Nanoparticles

Special surfaces, optimized by computer algorithms, capture and hold the tiniest particles with the force of light. This technology is essential for ultrasensitive sensors, precise assembly of microdevices, and even manipulation of individual atoms in quantum systems.
arXiv:2607.02352 · 2026-07-02

Gravitational Infancy: Record Orbits in the Cradle of HD 114082

310 light-years from Earth, astronomers have found a remarkable system: a 15 million-year-old star surrounded by two transiting gas giants with record-long orbits of 225 and 314 days. Observations with TESS, CHEOPS, and ground-based telescopes measured their radii and set upper limits on their masse
arXiv:2607.02685v1 · 2026-07-02

Cosmic Debt: How a Planet's Mass Locks Civilizations Forever

Scientists from Blue Marble Space combined geophysics, atmosphere, and rocket dynamics to find the limits of chemical escape from exoplanets. A payload of 1,000 kg — like that of the Voyager probes — was used as a benchmark. It turned out that for a planet more massive than about 11.5 M⊕, the number
arXiv:2607.02691v1 · 2026-07-02

Quasi-interstellar objects: when the Solar System meets its own exiles

The discovery of 1I/‘Oumuamua made us wonder: could some interstellar wanderers actually be our own comets, ejected from the Oort cloud and returning millions of years later? Simulations show that such ‘quasi-interstellar objects’ are indeed possible, but they have unique characteristics: extremely
arXiv:2607.04216v1 · 2026-07-05

The Unmixed Cocktail: Why Double Diffusion Is Powerless in the Interiors of Giant Planets

A new study has, for the first time, self-consistently incorporated the recipe of double diffusion into an evolutionary code of planets and traced the fate of Jupiter and Saturn from the moment of formation. It turns out that even a thousandfold enhancement of mixing does not lead to significant sme
arXiv:2607.04629v1 · 2026-07-06

The Icy Moons' Double Breath: JWST Unravels the Mystery of Uranus's Carbon Dioxide

Spectrograph NIRSpec aboard the JWST telescope has discerned a complex mosaic of carbon dioxide and carbon monoxide bands on Ariel, Umbriel, Titania, and Oberon. Comparison with laboratory ices at cryogenic temperatures revealed signatures of crystalline CO₂, clathrates, and carbonates. The observed
arXiv:2607.05600v2 · 2026-07-06

Quantum Mpemba effect: hot cools faster, but only near absolute zero

The Mpemba effect, known from kitchen experiments with water, is reimagined in a quantum model. It turns out that at the level of individual particles, hot cools faster only at temperatures close to absolute zero, where quantum tunneling operates. Reverse paradoxes also emerge, unthinkable in the or
arXiv:2607.06071 · 2026-07-07