# Thury Hydrodynamics Compendium The Thury Hydrodynamics Compendium is the flagship article of the Apex Spine: an index of combination, built on three gases and one refusal. [[Hydrogen]] and [[Oxygen]] are the reactive pair — between them they make [[Water]], the [[Oxyhydrogen|oxyhydrogen]] family, and by extension most of the chemistry a working technician ever touches. [[Helium]] and [[Helium-3]] are the boundary: they combine with nothing, and by refusing they define what reactivity means. Everything on the spine hangs between those two poles, and the medium that carries it is fluid. <!-- NAMESAKE: the Eugene "Denny" Thury section is written by MTN by hand. Leave this slot for him. --> ## The reaction canon Two ignoble gases and one extremely noble one. [[Combustion]] of hydrogen in oxygen is the canon's founding event — a [[Redox]] reaction whose [[Energy]] has flown rockets and now runs a [[Fuel_cell]] without a flame — and its product is the substance every other article here eventually returns to. Run it backwards with [[Electrolysis]] and you have storage rather than release. Against that, the noble branch: [[Helium]] holds its [[Electron_shell]] closed, and [[Helium-3]], one [[Neutron]] lighter, becomes interesting precisely where chemistry stops and [[Nuclear_fusion]] begins. The canon is therefore not a list of substances but a spectrum of willingness. ## Why the spine is fluid Gases and liquids are how these reactions are delivered, mixed, stored, and lost. That makes [[Fluid_dynamics]] the connective tissue: [[Viscosity]] and the [[Reynolds_number]] decide the regime, [[Turbulence]] decides the mixing, [[Vorticity]] decides what the flow is actually doing, and [[Buoyancy]] and [[Hydrostatics]] decide what floats and what presses. The compendium's claim is that a technician in any of the eight Centers is working the same physics under different names — coolant, [[Two-phase_flow|two-phase]] steam, blood, tile drainage, fuel. See the [[PORTAL_WT!Thury_Hydrodynamics_Compendium|Compendium portal]] for the eight bridges. ## How to read it The Apex Spine holds the canon; the Compendium portal holds the applications. The book shelf on [[PORTAL_Thury_Hydrodynamics_Apex_Spine|the spine]] pairs each branch with an open textbook, and each book seeds its own stub articles, so the compendium grows by reading rather than by assertion. Nothing here is finished: unbuilt links are deliberate forward-references. The rest of the page is written in summary style, the way Wikipedia writes a broad article. It runs in six parts, from the physics of the medium, through water and the two branches of the canon, to water at work and the water of the Earth and of [[Minnesota]]. Each section is a short summary of a subject that has its own full article, named in the line under the heading: follow that link for the depth and the sources. Each section ends by naming the neighbors it connects to, so the page can be read straight through as one argument or entered anywhere. Every section also carries one microsim, and the thirty-five together are a set. They were built for this page from the same open textbooks the spine reads — the physics was solved or looked up beforehand and baked into each file, so the browser only interpolates, draws, and answers the sliders — and every one carries the same three lines: the equation it obeys, a readout of the numbers it is computing, and a caption that changes with the state you put it in. Drag to orbit, press *r* to reset, *space* to pause. Where a sim simplifies the physics it says so on screen with the word *illustrative*. The See-also articles under each hatnote inherit these sims as variants, so a reader who follows a link into the depth finds the same instrument, retuned. **On the spine:** [[Hydrogen]] · [[Oxygen]] · [[Helium]] · [[Helium-3]] · [[Fluid_dynamics]]. ## Part I — The medium ### Fluid dynamics *Main article: [[Fluid_dynamics]] · See also: [[Reynolds_number]], [[Navier–Stokes_equations]]* Fluid dynamics is the physics of liquids and gases in motion, and it is the medium of this whole spine. Its laws are the conservation of mass, momentum and [[Energy|energy]] written for a continuous fluid; for most everyday flows they take the form of the [[Navier–Stokes_equations|Navier–Stokes equations]]. One number does more than any other to sort flows into kinds: the [[Reynolds_number|Reynolds number]], the ratio of a flow's inertia to its [[Viscosity|viscosity]]. At low values a flow creeps and stays orderly; at high values it sheds vortices and turns turbulent. Behind a cylinder the change is a sequence anyone can watch: a symmetric creeping flow, then a closed pair of eddies, then, just above a Reynolds number of about 47, the alternating shedding of the Kármán vortex street, whose frequency stays near a fifth of the stream speed over the cylinder's diameter across an enormous range.[^smyth] Every later section is fluid dynamics in a particular setting: at rest, in a pipe, near a wall, near the speed of sound, in a magnetic field, on a rotating planet, or behind a dam. <div class="wt-sim" data-src="https://wikitube-3d-microsims.netlify.app/thury/Fluid_dynamics.html" data-title="Fluid dynamics"></div> *Try: choose Re = 10, 40, 100 and 180 and watch the same cylinder go from creeping flow to a steady pair of eddies to a vortex street. The flow was solved beforehand on a lattice; the dye rides the stored velocity field and the readout gives the Strouhal number.* Connects to: [[#Fluids at rest|Fluids at rest]] · [[#Energy along a streamline|Energy along a streamline]] · [[#Thick fluids and pipe flow|Thick fluids and pipe flow]] · [[#Turbulence|Turbulence]] · [[#When flow becomes unstable|When flow becomes unstable]] · [[#Geophysical fluid dynamics|Geophysical fluid dynamics]] ### Fluids at rest *Main article: [[Hydrostatics]] · See also: [[Buoyancy]]* Before water moves, it presses. In a fluid at rest, pressure rises with depth in proportion to the fluid's [[Density|density]] and to [[Gravity|gravity]], and at any point it pushes equally in every direction. The total push on a dam wall therefore grows with the square of the depth, and it acts two thirds of the way down.[^barmeir105] [[Buoyancy]] follows directly: a body in a fluid is pushed up by a force equal to the weight of the fluid it displaces, so the fraction of a floating block that sits under water is just the ratio of its density to the fluid's. That one rule sets the thrust on a dam, the [[Hydraulic_head|head]] that drives a turbine, and the weight of a great lake on its bed. [[Hydrostatics]] is the zero-speed limit of fluid dynamics, the reference state against which every moving flow is measured. <div class="wt-sim" data-src="https://wikitube-3d-microsims.netlify.app/thury/Hydrostatics.html" data-title="Hydrostatics"></div> *Try: deepen the reservoir and watch the pressure arrows on the wall grow; change the block's density until it sinks, then switch the fluid to mercury and watch it float again.* Connects to: [[#Fluid dynamics|Fluid dynamics]] · [[#Hydropower|Hydropower]] · [[#Dams and reservoirs|Dams and reservoirs]] · [[#Lake Superior|Lake Superior]] ### Energy along a streamline *Main article: [[Bernoulli's_principle]] · See also: [[Venturi_effect]], [[Continuity_equation]]* Set still water moving and pressure starts to trade against speed. [[Bernoulli's_principle|Bernoulli's principle]] says that along a streamline in a steady, frictionless, incompressible flow, the sum of pressure, kinetic energy and potential energy per unit volume stays constant: where the flow speeds up, its pressure falls. It is energy conservation for a moving fluid. Pair it with continuity — the same volume per second passes every cross-section — and a Venturi tube becomes a flow meter: the throat is faster by the square of the diameter ratio, and the pressure drop between inlet and throat gives the discharge.[^liburdy] The principle explains the low pressure that lets cavitation start and the speed water gains falling through a penstock. Its conditions matter, because friction, turbulence and compressibility each break it, and much of the rest of Part I is about what happens when they do. <div class="wt-sim" data-src="https://wikitube-3d-microsims.netlify.app/thury/Bernoulli's_principle.html" data-title="Bernoulli's principle"></div> *Try: narrow the throat and watch the six manometer columns: the throat column drops by exactly the kinetic energy the tracers gain.* Connects to: [[#Fluid dynamics|Fluid dynamics]] · [[#Fluids at rest|Fluids at rest]] · [[#Boundary layers and drag|Boundary layers and drag]] · [[#Cavitation|Cavitation]] ### Thick fluids and pipe flow *Main article: [[Viscosity]] · See also: [[Hagen–Poiseuille_equation]], [[Non-Newtonian_fluid]]* [[Viscosity]] is a fluid's resistance to shearing, the internal friction that makes honey pour slowly and water quickly. It is what brings a flow to rest against a wall, and it is the quantity the Reynolds number weighs inertia against. In a narrow pipe, viscosity gives the smooth [[Laminar_flow|laminar flow]] described by the Hagen–Poiseuille equation, in which, for a given pressure drop, the flow rate rises with the fourth power of the pipe's radius and the velocity profile is an exact parabola.[^barmeir105] Past a Reynolds number near 2,000 the profile flattens and the fluid churns, and the fourth-power law no longer holds.[^miedema] Some fluids, called non-Newtonian, change their viscosity with how fast they are sheared. At the far end of the spine sits superfluid helium, a liquid that flows with no viscosity at all. <div class="wt-sim" data-src="https://wikitube-3d-microsims.netlify.app/thury/Viscosity.html" data-title="Viscosity"></div> *Try: push water, oil, glycerol and honey through the same pipe; read the flow rate as you double the radius, and watch the parabola flatten when the water turns turbulent.* Connects to: [[#Fluid dynamics|Fluid dynamics]] · [[#Turbulence|Turbulence]] · [[#Superfluidity|Superfluidity]] · [[#Flow through the ground|Flow through the ground]] ### Boundary layers and drag *Main article: [[Boundary_layer]] · See also: [[Drag_(physics)]], [[Kármán_vortex_street]]* Next to any surface a moving fluid is held still, and its speed climbs from zero at the wall to the full stream speed across a thin sheet called the [[Boundary_layer|boundary layer]]. Ludwig Prandtl's insight in 1904 was that the rest of the flow can often be treated as if viscosity did not exist, provided this thin layer is handled separately. The layer thickens with the square root of the distance along a plate while it is laminar; near a local Reynolds number of 500,000 it turns turbulent, thickens faster, and its profile fills out.[^liburdy] The friction [[Drag_(physics)|drag]] on a hull, a wing or a pipe wall is made here, and so is most of the [[Vorticity|vorticity]] in an ordinary flow. When the layer separates from a surface, it leaves a wake of eddies behind it: the start of the vortex street that trails a cylinder. <div class="wt-sim" data-src="https://wikitube-3d-microsims.netlify.app/thury/Boundary_layer.html" data-title="Boundary layer"></div> *Try: raise the free-stream speed and watch the transition point move toward the leading edge; the profile rakes change shape and the drag readout jumps.* Connects to: [[#Turbulence|Turbulence]] · [[#Energy along a streamline|Energy along a streamline]] · [[#Cavitation|Cavitation]] ### Turbulence *Main article: [[Turbulence]] · See also: [[Reynolds_number]]* [[Turbulence]] is the flow regime in which motion turns chaotic at many scales at once: eddies inside eddies, carrying momentum and heat far faster than molecular [[Diffusion|diffusion]] could. It is the normal state of rivers, wakes, smoke plumes and the air over a wing. Energy enters at the largest eddies and cascades down to the smallest, where viscosity turns it into heat; between the two, Kolmogorov's law says the energy at each scale falls off as the wavenumber to the minus five-thirds, and the ratio of the largest eddy to the smallest grows as the Reynolds number to the three-quarters.[^miedema] The equations that govern it are deterministic, yet their turbulent solutions cannot be predicted in detail, which leaves turbulence one of the great open problems of classical physics. On the spine it decides how fast a flame mixes its fuel, how a river scours its bed and how heat leaves a machine. <div class="wt-sim" data-src="https://wikitube-3d-microsims.netlify.app/thury/Turbulence.html" data-title="Turbulence"></div> *Try: raise the Reynolds number and watch the smallest eddies shrink while the spectrum panel keeps its minus-five-thirds slope; the law-of-the-wall panel shows the same pipe going laminar below 2,040.* Connects to: [[#Vorticity|Vorticity]] · [[#When flow becomes unstable|When flow becomes unstable]] · [[#Combustion|Combustion]] ### Vorticity *Main article: [[Vorticity]] · See also: [[Quantum_vortex]]* [[Vorticity]] is the local spin of a fluid: how fast a tiny parcel rotates about its own center as it is carried along. Mathematically it is the curl of the [[Velocity|velocity]] field. It is not the same as a curving path. A parcel can travel around a wide circle without spinning, and one moving in a straight line through a shear layer can spin hard. The Rankine vortex makes the distinction visible: inside its core the fluid turns as a solid body and every parcel spins, while outside the core the fluid circles the axis with no vorticity at all and a floating cross keeps pointing the same way as it goes round.[^smyth] Vorticity is made at walls, carried and stretched by the flow, and gathered into [[Vortex|vortices]]. The same idea runs from a bathtub drain to a hurricane, and in a superfluid it comes only in fixed quanta. <div class="wt-sim" data-src="https://wikitube-3d-microsims.netlify.app/thury/Vorticity.html" data-title="Vorticity"></div> *Try: watch the orange crosses inside the core turn with the fluid while the white ones outside circle the axis without turning; widen the core and the dip in the free surface deepens.* Connects to: [[#Turbulence|Turbulence]] · [[#Superfluidity|Superfluidity]] · [[#Geophysical fluid dynamics|Geophysical fluid dynamics]] ### When flow becomes unstable *Main article: [[Hydrodynamic_stability]] · See also: [[Kelvin–Helmholtz_instability]], [[Rayleigh–Bénard_convection]]* A flow can obey its equations perfectly and still refuse to stay as it is. [[Hydrodynamic_stability|Hydrodynamic stability]] asks whether a small disturbance dies away or grows. In his 1883 pipe experiments Osborne Reynolds saw smooth flow give way to turbulence near a Reynolds number of 2,000, and modern experiments place the point above which pipe turbulence sustains itself at about 2,040.[^avila2023] Where two layers slide past each other, the [[Kelvin–Helmholtz_instability|Kelvin–Helmholtz instability]] rolls the interface into billows unless stratification holds it, which it does once the Richardson number passes a quarter; where heavy fluid rests on light, the Rayleigh–Taylor instability pulls it down in fingers that mushroom and mix;[^barmeir105] where a layer is heated from below, [[Rayleigh–Bénard_convection|Rayleigh–Bénard convection]] breaks it into cells. Instability is how order becomes turbulence, and how patterns first appear. <div class="wt-sim" data-src="https://wikitube-3d-microsims.netlify.app/thury/Hydrodynamic_stability.html" data-title="Hydrodynamic stability"></div> *Try: scrub time through the four movies (each a two-dimensional simulation solved beforehand): the shear layer rolling up, the same layer held by stratification, heavy-over-light falling, and a heated layer breaking into cells.* Connects to: [[#Fluid dynamics|Fluid dynamics]] · [[#Turbulence|Turbulence]] · [[#Helium-3 and fusion|Helium-3 and fusion]] ### When water hits hard *Main article: [[Compressible_flow]] · See also: [[Hydraulic_shock]], [[Mach_number]]* Most of this spine treats water and air as incompressible, and at low speed that works: a flow can often be treated so while its Mach number stays below about 0.3.[^britannica-cf] Near the speed of [[Sound|sound]], density changes grow large and [[Compressible_flow|compressible flow]] takes over. Pressure then travels as waves, a flow can choke in a narrow passage, and supersonic gas speeds up in a widening nozzle rather than a narrowing one. Across a shock wave, pressure, temperature and density jump almost at once, and one number, the Mach number ahead of it, fixes every ratio across it.[^barmeir108] Liquids feel it too: closing a valve quickly on flowing water sends a pressure surge down the pipe at about 1,400 metres a second, the water hammer that a penstock must survive and that a hydraulic ram puts to work.[^clemson] <div class="wt-sim" data-src="https://wikitube-3d-microsims.netlify.app/thury/Compressible_flow.html" data-title="Compressible flow"></div> *Try: lower the back pressure on the nozzle: the throat chokes at Mach 1, a shock appears in the diverging section and walks toward the exit, and finally the whole nozzle runs supersonic.* Connects to: [[#Hydroelectricity|Hydroelectricity]] · [[#Open channels and the hydraulic jump|Open channels and the hydraulic jump]] · [[#Water that pumps itself|Water that pumps itself]] ## Part II — The substance: water ### Water *Main article: [[Properties_of_water]] · See also: [[Phases_of_ice]], [[Supercooling]]* [[Water]] is the product of the reaction canon and the strangest common substance on the spine. Most of its [[Properties_of_water|oddities]] trace to one cause, the [[Hydrogen_bond|hydrogen bond]], which links its molecules into a shifting network. That network is why ice floats on its own liquid, why liquid water is densest a few degrees above freezing, and why water holds so much heat and dissolves so much. On a pressure–temperature map the three ordinary phases meet at the triple point, the liquid can be carried far below freezing without freezing if nothing seeds the ice, and above 647 K and 22 MPa there is no longer any difference between liquid and vapor.[^averill] Every other part of the spine returns to it: as the exhaust of the reactive branch, as the working fluid of hydropower, and as the subject of hydrology. <div class="wt-sim" data-src="https://wikitube-3d-microsims.netlify.app/thury/Properties_of_water.html" data-title="Properties of water"></div> *Try: drag the state point across the phase map to find ice, liquid, vapor, the supercooled band and the supercritical fluid; the right-hand curve shows the density peaking near 4 °C.* Connects to: [[#Two liquids|Two liquids]] · [[#The hydrogen bond|The hydrogen bond]] · [[#Electrolysis: the canon in reverse|Electrolysis]] · [[#Hydrology|Hydrology]] ### Two liquids *Main article: [[Liquid–liquid_critical_point]] · See also: [[Polyamorphism]]* Water may be two liquids. In 1992 computer simulations suggested that deeply supercooled water hides a second [[Critical_point_(thermodynamics)|critical point]], below which it separates into a low-density liquid with an open, tetrahedral network and a high-density liquid packed more tightly.[^poole1992] The point lies where supercooled water normally freezes within microseconds, so for three decades it could not be measured. In 2026 a Stockholm-led team reported experimental evidence of the [[Liquid–liquid_critical_point|liquid–liquid critical point]], placing it near 210 K (about −63 °C) and 1,000 bar.[^you2026][^physicstoday2026] Other researchers say the question is not yet closed.[^physicstoday2026] It is the Compendium's founding surprise: the most familiar liquid on Earth still held a critical point that no one had seen. <div class="wt-sim" data-src="https://wikitube-3d-microsims.netlify.app/thury/Liquid%E2%80%93liquid_critical_point.html" data-title="Liquid–liquid critical point"></div> *Try: each cell is a patch of water that is either open (light) or dense (dark). Cool the lattice past the critical coupling and the patches condense into two liquids; tilt the pressure bias and one of them wins.* Connects to: [[#Water|Water]] · [[#The hydrogen bond|The hydrogen bond]] · [[#Superfluidity|Superfluidity]] ### The hydrogen bond *Main article: [[Hydrogen_bond]]* The [[Hydrogen_bond|hydrogen bond]] is the attraction between a hydrogen atom bound to an electronegative atom, such as [[Oxygen|oxygen]], and a lone pair of electrons on a neighboring molecule. It is much weaker than the bonds inside a water molecule, about 21 kilojoules per mole against 463, but stronger than most other attractions between molecules, and water forms a network of them that is always breaking and re-forming within picoseconds.[^openstax] In ice every molecule donates two bonds and accepts two, which builds the open hexagonal lattice that floats; in the liquid the count falls toward three and a half at the freezing point and lower as the water warms. That network gives water its high boiling point, and it is what the two-liquid picture is about: in the low-density liquid the network is ordered and tetrahedral, in the high-density liquid it has collapsed. Hydrogen bonding also helps carry protons through the wet membranes of fuel cells. <div class="wt-sim" data-src="https://wikitube-3d-microsims.netlify.app/thury/Hydrogen_bond.html" data-title="Hydrogen bond"></div> *Try: warm the box of molecules from ice to hot water and count the gold hydrogen bonds per molecule as the lattice loosens and the density rises past the ice value.* Connects to: [[#Water|Water]] · [[#Two liquids|Two liquids]] · [[#Fuel cells: the same reaction without a flame|Fuel cells]] ## Part III — The reactive branch: hydrogen and oxygen ### Combustion *Main article: [[Combustion]] · See also: [[Oxyhydrogen]]* [[Combustion]] is rapid oxidation that releases energy as heat and light, and hydrogen burning in oxygen is the founding event of the canon: two gases combine into water and nothing else, releasing 286 kilojoules for every mole of liquid water they make.[^haverkort] A mixture of the two, [[Oxyhydrogen|oxyhydrogen]], burns with an intense flame. How fast any flame burns depends on how quickly fuel and oxidizer mix, and that is a question of flow: a laminar hydrogen–air flame advances at about two metres a second, and in most real burners and engines [[Turbulence|turbulence]] wrinkles the front and multiplies that speed. Burning hydrogen in a heat engine also wastes most of its energy as heat; the fuel cell, two sections on, does far better.[^murphy16] <div class="wt-sim" data-src="https://wikitube-3d-microsims.netlify.app/thury/Combustion.html" data-title="Combustion"></div> *Try: lean the mixture until the flame lifts off, then add turbulence and watch the front wrinkle and the flame shorten as it burns faster.* Connects to: [[#Turbulence|Turbulence]] · [[#Electrolysis: the canon in reverse|Electrolysis]] · [[#Fuel cells: the same reaction without a flame|Fuel cells]] ### Electrolysis: the canon in reverse *Main article: [[Electrolysis_of_water]] · See also: [[Oxygen_evolution]], [[Photocatalytic_water_splitting]]* Run the canon backwards and you have storage instead of release. [[Electrolysis_of_water|Electrolysis of water]] uses an electric current to split water into hydrogen and oxygen at two electrodes, two volumes of the one for every volume of the other. Thermodynamics sets the floor: 1.23 volts to drive the reaction and 1.48 volts to drive it without drawing heat from the surroundings, and every kilowatt-hour above that is loss.[^haverkort] Making a kilogram of hydrogen this way takes at least 39.4 kilowatt-hours, measured by hydrogen's higher heating value, and practical electrolyzers keep about 65–80% of their input energy in the hydrogen they make.[^murphy16] The hydrogen is only as clean as the electricity behind it, so electrolysis ties the canon to the [[Electrical_grid|grid]], and in Minnesota to wind and falling water. <div class="wt-sim" data-src="https://wikitube-3d-microsims.netlify.app/thury/Electrolysis_of_water.html" data-title="Electrolysis of water"></div> *Try: raise the current density and watch the cell voltage climb up the polarization curve while the readout turns volts into kilowatt-hours per kilogram of hydrogen.* Connects to: [[#Water|Water]] · [[#Fuel cells: the same reaction without a flame|Fuel cells]] · [[#The hydrogen economy|The hydrogen economy]] · [[#Hydroelectricity|Hydroelectricity]] ### Fuel cells: the same reaction without a flame *Main article: [[Fuel_cell]] · See also: [[Oxygen_reduction_reaction]]* A [[Fuel_cell|fuel cell]] runs the founding reaction without a flame. Hydrogen gives up its electrons at one electrode; the electrons travel through an outside circuit as an [[Electric_current|electric current]], and in the common proton-exchange type the hydrogen ions cross a membrane to meet oxygen at the other electrode, where water forms. Because the energy leaves as electricity rather than heat, a fuel cell converts around 65% of the fuel's energy, far more than an engine burning the same hydrogen.[^murphy16] Its voltage falls as more current is drawn, first from the cost of getting the reactions started, then from the membrane's resistance, and finally, near the limiting current, from starving the electrodes of reactant.[^haverkort] Its weak points, Murphy notes, are that fuel cells are not particularly robust and have difficulty in cold weather.[^murphy16] <div class="wt-sim" data-src="https://wikitube-3d-microsims.netlify.app/thury/Fuel_cell.html" data-title="Fuel cell"></div> *Try: draw more current and watch the lamp brighten, peak and dim again as the voltage slides down the polarization curve; stack the cells to reach kilowatts.* Connects to: [[#Combustion|Combustion]] · [[#Electrolysis: the canon in reverse|Electrolysis]] · [[#The hydrogen economy|The hydrogen economy]] ### The hydrogen economy *Main article: [[Hydrogen_economy]] · See also: [[Hydrogen_production]], [[Hydrogen_storage]]* The [[Hydrogen_economy|hydrogen economy]] is the reactive branch at the scale of a civilization: hydrogen made from water or fossil fuels, stored, moved and turned back into work. The idea took hold around 1970,[^jones1970] and it has swung between enthusiasm and disappointment since.[^kerlin12][^murphy16] World demand passed 100 million tonnes in 2025, yet low-emissions hydrogen made up less than 1% of production in 2024.[^iea2026][^iea2025] The energy lost at each conversion and the difficulty of storing so light a gas are the main objections: a kilowatt-hour of electricity that goes through an electrolyzer, a compressor and a fuel cell comes back as roughly a third of a kilowatt-hour of work, against about 85% for a battery.[^murphy16] Minnesota's own experiment is at Morris, where the University of Minnesota has made ammonia from wind-powered hydrogen since 2013.[^wcroc2023] <div class="wt-sim" data-src="https://wikitube-3d-microsims.netlify.app/thury/Hydrogen_economy.html" data-title="Hydrogen economy"></div> *Try: follow one kilowatt-hour of electricity through electrolysis, storage and a fuel cell or engine; the dots that drop out red at each stage are the heat that is lost, and the violet bar is a battery for comparison.* Connects to: [[#Electrolysis: the canon in reverse|Electrolysis]] · [[#Fuel cells: the same reaction without a flame|Fuel cells]] · [[#Helium-3 and fusion|Helium-3 and fusion]] · [[#Hydroelectricity|Hydroelectricity]] ## Part IV — The noble branch: helium and helium-3 ### Superfluidity *Main article: [[Superfluidity]] · See also: [[Superfluid_helium-4]], [[Quantum_vortex]], [[Roton]], [[Two-fluid_model]]* Cooled below about 2.17 K, liquid [[Helium|helium-4]] becomes a superfluid. It flows with no viscosity, creeps up the walls of its container, and can rotate only in fixed quanta of circulation, carried by [[Quantum_vortex|quantized vortices]]: spin a bucket of it and the number of vortex lines it threads through itself is set by the spin rate and Planck's constant over the atom's mass, nothing else. In the two-fluid picture the liquid is a mixture of a superfluid with no viscosity and a normal fluid, and the superfluid fraction rises from nothing at the transition toward the whole as the temperature falls. [[Superfluidity]] is quantum mechanics made visible at the scale of a laboratory flask. Helium-3, whose atoms are fermions, turns superfluid only about a thousand times colder, after its atoms have paired. This is the noble branch's refusal carried into flow: the gas that will not react also will not resist. <div class="wt-sim" data-src="https://wikitube-3d-microsims.netlify.app/thury/Superfluidity.html" data-title="Superfluidity"></div> *Try: spin the bucket and count the vortex lines as they settle into a triangular lattice; cool it and read the superfluid fraction; switch to an ordinary liquid and the quanta vanish.* Connects to: [[#Vorticity|Vorticity]] · [[#Two liquids|Two liquids]] · [[#Cryogenics|Cryogenics]] · [[#Helium-3 and fusion|Helium-3 and fusion]] ### Cryogenics *Main article: [[Cryogenics]] · See also: [[Lambda_point]], [[Dilution_refrigerator]], [[Liquid_helium]]* [[Cryogenics]] is the science of very low temperatures, and it is the door into the noble branch. [[Liquid_helium|Liquid helium]] boils at 4.2 K and stays liquid toward absolute zero at ordinary pressure, needing about 25 atmospheres to freeze; below its [[Lambda_point|lambda point]], near 2.17 K, it becomes superfluid, and a [[Dilution_refrigerator|dilution refrigerator]], which dissolves helium-3 into helium-4, reaches far colder still. Each rung down the ladder costs more: the work needed to pump a joule of heat out of a cold body rises as the temperature falls, without limit. Cryogenics also makes hydrogen storable as a liquid, which boils at −253 °C.[^kerlin12] Every experiment on superfluid helium, and much of fusion and space technology, depends on it. <div class="wt-sim" data-src="https://wikitube-3d-microsims.netlify.app/thury/Cryogenics.html" data-title="Cryogenics"></div> *Try: slide the temperature down the ladder from room temperature to a thousandth of a kelvin and watch the state point cross the helium-4 phase map from gas to liquid to superfluid.* Connects to: [[#The hydrogen economy|The hydrogen economy]] · [[#Superfluidity|Superfluidity]] · [[#Helium-3 and fusion|Helium-3 and fusion]] ### Helium-3 and fusion *Main article: [[Nuclear_fusion]] · See also: [[Helium-3]], [[Aneutronic_fusion]]* [[Helium-3]], one neutron lighter than ordinary helium, is where chemistry stops and [[Nuclear_fusion|nuclear fusion]] begins. Fusing light nuclei releases energy, but the nuclei must first get past the electric repulsion between them, which takes extreme temperatures and quantum tunneling. At any temperature only a narrow window of energies, the Gamow peak, is both hot enough to tunnel and populated enough to matter, and the window opens first for deuterium and tritium: near 15 keV their reaction runs well over a hundred times faster than deuterium with helium-3.[^nrl] Helium-3 interests fusion researchers because some of its reactions release few neutrons. It is also scarce: the United States' supply has come chiefly as a by-product of tritium decay.[^nidc] That is why the helium find in northern Minnesota, where Pulsar Helium reported helium-3 in 2025, drew attention, though no commercial technology yet separates helium-3 from helium-4 at scale.[^pulsar] <div class="wt-sim" data-src="https://wikitube-3d-microsims.netlify.app/thury/Nuclear_fusion.html" data-title="Nuclear fusion"></div> *Try: raise the temperature and watch the Gamow window slide up in energy while the three fuel curves separate; the readout gives the ratio of D–T to D–He3 reactivity at the chosen temperature.* Connects to: [[#When flow becomes unstable|When flow becomes unstable]] · [[#The hydrogen economy|The hydrogen economy]] · [[#Superfluidity|Superfluidity]] · [[#Magnetohydrodynamics|Magnetohydrodynamics]] ### Magnetohydrodynamics *Main article: [[Magnetohydrodynamics]] · See also: [[Plasma_(physics)]]* When a fluid conducts electricity, flow and magnetic field push on each other. [[Magnetohydrodynamics]] is the fluid dynamics of liquid metals, salt water and [[Plasma_(physics)|plasmas]] in magnetic fields. Hannes Alfvén predicted its characteristic waves in 1942, and his share of the 1970 Nobel Prize in Physics was awarded for his work in the field.[^alfven1942][^nobel1970] A field across a channel of liquid metal brakes the flow in the middle and flattens its profile, in proportion to the Hartmann number; along a field line the fluid's inertia and the field's tension carry a wave at the Alfvén speed, which in a tokamak plasma runs to thousands of kilometres a second. It describes the dynamo in [[Earth|Earth's]] liquid iron core and the plasma a tokamak holds inside a torus of magnetic field. For the noble branch, it is the physics of containing a fusion fuel that no material wall could touch. <div class="wt-sim" data-src="https://wikitube-3d-microsims.netlify.app/thury/Magnetohydrodynamics.html" data-title="Magnetohydrodynamics"></div> *Try: raise the Hartmann number and watch the channel's velocity profile flatten against the walls; change the medium to see how fast the plucked field lines carry an Alfvén wave.* Connects to: [[#Vorticity|Vorticity]] · [[#Helium-3 and fusion|Helium-3 and fusion]] · [[#Geophysical fluid dynamics|Geophysical fluid dynamics]] ## Part V — Water at work ### Hydropower *Main article: [[Hydropower]] · See also: [[Hydraulic_head]]* [[Hydropower]] is energy taken from falling or flowing water, the oldest way the spine's fluid has worked for people. [[Water_wheel|Water wheels]] ground grain and sawed timber for centuries before [[Water_turbine|turbines]] replaced them. The power available is set by two things, the flow and the [[Hydraulic_head|head]], the height through which the water falls. A Pelton wheel shows how cleanly the energy can be taken: its jet leaves the nozzle at nearly the free-fall speed for the head, and when the buckets run at half the jet speed the water leaves them almost at rest, having given the wheel nearly everything it carried.[^barmeir105] At St. Anthony Falls in Minneapolis, water power drove the sawmills and then the flour mills that built the city.[^nps-ch6] <div class="wt-sim" data-src="https://wikitube-3d-microsims.netlify.app/thury/Hydropower.html" data-title="Hydropower"></div> *Try: run the bucket speed up from stalled to runaway and watch the spent water drop out of the wheel; the efficiency curve peaks at exactly half the jet speed.* Connects to: [[#Fluids at rest|Fluids at rest]] · [[#Hydroelectricity|Hydroelectricity]] · [[#Hydrology|Hydrology]] · [[#Dams and reservoirs|Dams and reservoirs]] ### Dams and reservoirs *Main article: [[Dam]] · See also: [[Spillway]], [[Reservoir]], [[Environmental_impact_of_reservoirs]]* A [[Dam|dam]] is where hydropower gets its head. Holding back a river raises its level and stores the water, and the pressure that rises with depth behind the dam sets the load the structure must carry: the force grows with the square of the depth and the overturning moment about the toe with the cube, so a gravity dam is designed for the last few metres of a full reservoir. Gravity dams resist with their weight, arch dams carry the load into the valley walls, and embankment dams are built of compacted earth or rock. Dams also block fish, flood land and trap sediment, and many are aging; when one fails the reservoir leaves as a wave whose front runs at twice the shallow-water speed of the impounded depth.[^barmeir105] Minnesota has more than 1,150 dams, and in June 2024 the Blue Earth River cut a new channel around the Rapidan Dam.[^mndnr-dams][^blueearth] <div class="wt-sim" data-src="https://wikitube-3d-microsims.netlify.app/thury/Dam.html" data-title="Dam"></div> *Try: raise the reservoir until the tipping moment passes the dam's weight, or press breach, and watch the dam-break wave run down the valley with Ritter's exact solution drawn over the live one.* Connects to: [[#Fluids at rest|Fluids at rest]] · [[#Hydropower|Hydropower]] · [[#Hydroelectricity|Hydroelectricity]] · [[#Open channels and the hydraulic jump|Open channels and the hydraulic jump]] ### Open channels and the hydraulic jump *Main article: [[Hydraulic_jump]] · See also: [[Froude_number]], [[Weir]]* Water racing down a spillway is fast and shallow; the river below is slow and deep. Where the two meet, the flow jumps. In a [[Hydraulic_jump|hydraulic jump]] the surface rises abruptly and the water churns, dissipating much of its [[Energy|energy]]. The jump comes where the flow's [[Froude_number|Froude number]], the open-channel counterpart of the Mach number, passes through one, and the depth ratio across it follows from momentum alone: Bélanger's equation gives the downstream depth from the upstream depth and Froude number, and the energy lost grows with the cube of the rise.[^barmeir105] Engineers force a jump on purpose in the stilling basins below dams to protect the riverbed, and where the tailwater sits sets where the jump stands. A small one forms in any kitchen sink, where the thin, fast sheet from the tap meets a ring of deeper water. <div class="wt-sim" data-src="https://wikitube-3d-microsims.netlify.app/thury/Hydraulic_jump.html" data-title="Hydraulic jump"></div> *Try: raise the inflow Froude number and watch the jump grow from an undular ripple to a steady wall; move the tailwater above or below the conjugate depth and the jump walks upstream or is swept away.* Connects to: [[#Hydropower|Hydropower]] · [[#When water hits hard|When water hits hard]] · [[#Dams and reservoirs|Dams and reservoirs]] ### Cavitation *Main article: [[Cavitation]] · See also: [[Specific_speed]]* [[Cavitation]] is boiling caused by falling pressure rather than rising heat. Where a liquid speeds up, around a propeller tip or across a turbine blade, its pressure can drop below its vapor pressure and bubbles form; the vapor pressure of water climbs steeply with temperature, from about two percent of an atmosphere at room temperature to a full atmosphere at the boil, so warm water cavitates sooner.[^averill] When the bubbles are carried into higher pressure they collapse violently, in microseconds, and the repeated collapse pits metal. Cavitation limits how fast a turbine or pump can run and how high above the water below it can be set. It is Bernoulli's principle turned destructive. <div class="wt-sim" data-src="https://wikitube-3d-microsims.netlify.app/thury/Cavitation.html" data-title="Cavitation"></div> *Try: speed the flow through the Venturi until the throat pressure falls under the red vapor-pressure line; bubbles are born in the throat and collapse in the diffuser. Warm the water and it happens sooner.* Connects to: [[#Hydropower|Hydropower]] · [[#Hydroelectricity|Hydroelectricity]] · [[#Energy along a streamline|Energy along a streamline]] · [[#Boundary layers and drag|Boundary layers and drag]] ### Water that pumps itself *Main article: [[Hydraulic_ram]] · See also: [[Trompe]]* A [[Hydraulic_ram|hydraulic ram]] pumps water uphill with no fuel and no motor. Water runs down a drive pipe and out of a waste valve until it moves fast enough to slam the valve shut. The sudden stop creates a pressure surge, the water hammer of Part I, that drives some of the water up a delivery pipe, and the cycle repeats 30 to 100 times a minute.[^clemson][^practical] A ram can lift water ten feet or more for every foot of fall, but it delivers only a fraction of the water that passes through it.[^clemson] John Whitehurst built one in 1772, and Joseph Michel Montgolfier made it self-acting in 1796.[^lienhard] <div class="wt-sim" data-src="https://wikitube-3d-microsims.netlify.app/thury/Hydraulic_ram.html" data-title="Hydraulic ram"></div> *Try: raise the delivery head and watch the beat slow and the delivered fraction fall; the charts show the surge at the ram and the drive-pipe speed on every stroke.* Connects to: [[#Hydropower|Hydropower]] · [[#When water hits hard|When water hits hard]] ### Hydroelectricity *Main article: [[Hydroelectricity]] · See also: [[Pumped-storage_hydroelectricity]]* [[Hydroelectricity]] turns falling water into electricity. Water under head runs down a [[Penstock|penstock]], spins a turbine, and the turbine drives an [[Electric_generator|electric generator]]; the power is the density of water times gravity times the flow times the net head, less what the penstock's friction takes, and turbine-generator sets return about nine tenths of it.[^kerlin12] On September 5, 1882, the first central hydroelectric station in the United States lit Minneapolis with power from St. Anthony Falls.[^mnopedia1882] A plant with a reservoir can slow its turbines when demand is low and open them when it is high, which makes it a partner for wind and solar power,[^earle92] and a [[Pumped-storage_hydroelectricity|pumped-storage]] plant stores energy by pumping water uphill to let it fall again later. <div class="wt-sim" data-src="https://wikitube-3d-microsims.netlify.app/thury/Hydroelectricity.html" data-title="Hydroelectricity"></div> *Try: run one day in twenty seconds with load-following on and watch the gates follow the morning and evening peaks while the reservoir dips and refills; narrow the penstock and read the head lost to friction.* Connects to: [[#Electrolysis: the canon in reverse|Electrolysis]] · [[#Hydropower|Hydropower]] · [[#The Mississippi|The Mississippi]] · [[#Saint Anthony Falls|Saint Anthony Falls]] ### Hydroponics *Main article: [[Hydroponics]] · See also: [[Capillary_action]], [[Osmosis]], [[Transpiration]]* [[Hydroponics]] grows plants without soil, their roots in water that carries dissolved nutrients.[^umn-ext] It makes water the delivery system for agriculture. The grower supplies [[Nitrogen|nitrogen]], [[Phosphorus|phosphorus]], [[Potassium|potassium]] and trace elements in solution, keeps the pH between about 5.4 and 7 because each element is available to the roots only within its own band of acidity, and sees that the roots get [[Oxygen|oxygen]], of which water holds less the warmer it is.[^umn-ext] William Gericke of the University of California coined the term and described the method in *Science* in 1937.[^osu][^gericke1937] The University of Minnesota reports that controlled-environment agriculture uses only about 10% of the water of conventional farming, which ties the practice to the Compendium's agricultural centers.[^umn-cea] <div class="wt-sim" data-src="https://wikitube-3d-microsims.netlify.app/thury/Hydroponics.html" data-title="Hydroponics"></div> *Try: push the pH out of the band and watch the nutrient bars fall and the ions turn grey; warm the tank and read how much oxygen the water can still hold for the roots.* Connects to: [[#Water|Water]] · [[#Hydrology|Hydrology]] ## Part VI — Earth's fluids, and Minnesota's ### Geophysical fluid dynamics *Main article: [[Geophysical_fluid_dynamics]] · See also: [[Ocean_current]], [[Thermohaline_circulation]]* [[Geophysical_fluid_dynamics|Geophysical fluid dynamics]] is fluid dynamics on a rotating, layered planet. Two facts change everything. The frame rotates, so the [[Coriolis_force|Coriolis effect]] deflects every moving parcel, and at large scale the wind and the currents end up blowing along the pressure contours rather than across them, in the geostrophic balance that fails only at the equator;[^bosboom] and the fluid is layered by density, so any vertical motion must work against buoyancy. The result is flow that behaves almost as if it were two-dimensional and organizes itself into currents, jets and eddies instead of dissolving. It governs the [[Ocean_current|ocean currents]], the slow [[Thermohaline_circulation|thermohaline circulation]], the weather, and the currents and internal waves of a lake as large as Superior. <div class="wt-sim" data-src="https://wikitube-3d-microsims.netlify.app/thury/Geophysical_fluid_dynamics.html" data-title="Geophysical fluid dynamics"></div> *Try: release parcels into a pressure low and watch them loop in inertial circles as they drift along the isobars; move the latitude toward the equator and geostrophy fails, or across it and the spin reverses.* Connects to: [[#Fluid dynamics|Fluid dynamics]] · [[#Vorticity|Vorticity]] · [[#Lake Superior|Lake Superior]] · [[#Waves and tides|Waves and tides]] ### Waves and tides *Main article: [[Wind_wave]] · See also: [[Tide]], [[Tsunami]], [[Tidal_power]]* Wind blowing across water raises [[Wind_wave|wind waves]], and how large they grow depends on how hard the wind blows, how long it blows and how far it blows across open water; a fully developed sea is a spectrum of sinusoids whose significant height grows with the square of the wind speed.[^bosboom] Each wave's speed depends on its length and on the depth: in deep water long waves outrun short ones, and in shallow water every wave slows to the square root of gravity times the depth, which is why a [[Tsunami|tsunami]], set off by a sudden movement of the sea floor and hundreds of kilometres long, rears up as it reaches the shelf. [[Tide|Tides]] are waves too: the slow rise and fall of the sea under the pull of the Moon and the Sun, whose lunar and solar constituents beat against each other to make the fortnightly cycle of spring and neap. An enclosed basin such as a large lake adds its own motion, the seiche, a sloshing of the whole basin that raises the water at one end as it lowers it at the other. <div class="wt-sim" data-src="https://wikitube-3d-microsims.netlify.app/thury/Wind_wave.html" data-title="Wind wave"></div> *Try: raise the wind and read the significant height and peak period as the sea builds; make the water shallow and watch the waves shorten and steepen. The surface is 48 sinusoids summed on the graphics card.* Connects to: [[#Hydropower|Hydropower]] · [[#Geophysical fluid dynamics|Geophysical fluid dynamics]] · [[#Lake Superior|Lake Superior]] ### Hydrology *Main article: [[Hydrology]] · See also: [[Groundwater]], [[Aquifer]]* [[Hydrology]] is the science of where water goes. It keeps a stock-and-flow account of water moving between ocean, ice, [[Groundwater|groundwater]], lakes, soil, rivers and air, and uses it to predict floods, droughts and supply. When rain falls on a catchment the soil takes what it can, at a rate that decays as it wets, and the rest runs off to the stream; the gauge downstream sees the storm arrive late and stretched into a hydrograph whose peak depends on how much of the basin drains at once.[^earle-env] Minnesota is an unusually good place to read the account: from a single ridge near Hibbing, water drains north to Hudson Bay, east to the Gulf of St. Lawrence and south to the Gulf of Mexico.[^hmdb-3waters] Hydrology is where the spine's physics meets the landscape, and where the water made by the reactive branch ends up. <div class="wt-sim" data-src="https://wikitube-3d-microsims.netlify.app/thury/Hydrology.html" data-title="Hydrology"></div> *Try: rain on the catchment and watch each drop soak in or run downhill to the gauge; lengthen the storm past the basin's time of concentration and the hydrograph plateaus.* Connects to: [[#Water|Water]] · [[#Hydropower|Hydropower]] · [[#Lake Superior|Lake Superior]] · [[#The Mississippi|The Mississippi]] · [[#Flow through the ground|Flow through the ground]] ### Flow through the ground *Main article: [[Darcy's_law]] · See also: [[Aquifer]], [[Groundwater]]* Water underground moves through sand and rock, and it moves slowly. [[Darcy's_law|Darcy's law]], found by the engineer Henry Darcy in 1856 from experiments on the sand filters of Dijon, says that the flow through a porous material is proportional to the drop in [[Hydraulic_head|hydraulic head]] and to the material's hydraulic conductivity, which runs from metres a day in gravel to a millimetre a year in clay.[^woessner41] In a worked example in Steven Earle's *Physical Geology*, groundwater would take nearly four years to travel 100 m.[^earle14] The same law tells how fast water reaches a well from an [[Aquifer|aquifer]], how a clay lens bends the flow around itself, and how fast oil flows toward a well in a reservoir. <div class="wt-sim" data-src="https://wikitube-3d-microsims.netlify.app/thury/Darcy's_law.html" data-title="Darcy's law"></div> *Try: choose the geology and watch the flow paths crowd around a clay lens or race through gravel; the head field was solved beforehand, and the tracers cross the aquifer in years per second.* Connects to: [[#Hydrology|Hydrology]] · [[#Thick fluids and pipe flow|Thick fluids and pipe flow]] · [[#Lake Agassiz and the Red River|Lake Agassiz and the Red River]] ### Lake Superior *Main article: [[Lake_Superior]] · See also: [[Seiche]], [[WT!Minnesota_Great_Lakes_Basin]]* [[Lake_Superior|Lake Superior]] is the largest freshwater lake on Earth by surface area and the head of the Great Lakes chain shared by Minnesota, Wisconsin, Michigan and Ontario. It is cold, deep and slow to change, and it is large enough to show the physics of a rotating, stratified fluid in its own currents, its seasonal turnover and its seiches: a basin 560 kilometres long and 147 metres deep on average rocks end to end with a period near eight hours, which Merian's formula gives from the length and the depth alone, and which the gauges at Duluth and the east end record at about 7.9.[^bosboom] Minnesota's North Shore streams drop off the rim of an ancient rift into it. For the spine it is the Great Lakes basin, one of the three directions in which Minnesota's water leaves the state. <div class="wt-sim" data-src="https://wikitube-3d-microsims.netlify.app/thury/Lake_Superior.html" data-title="Lake Superior"></div> *Try: pile the water up with a wind and let go: the two ends of the lake swing in opposition for the first mode and in step for the second; change the season to see the thermocline that lies between the sun-warmed surface and the cold below.* Connects to: [[#Fluids at rest|Fluids at rest]] · [[#Geophysical fluid dynamics|Geophysical fluid dynamics]] · [[#Hydrology|Hydrology]] · [[#Waves and tides|Waves and tides]] ### The Mississippi *Main article: [[Mississippi_River]] · See also: [[WT!Minnesota_Gulf_of_Mexico_Basin]], [[WT!Minnesota_Hudson_Bay_Basin]]* The [[Mississippi_River|Mississippi River]] begins at Lake Itasca in northern Minnesota and carries the state's southern drainage to the Gulf of Mexico.[^dnr-water] Between Minneapolis and St. Paul it once dropped more than 100 feet in less than 15 miles, and that fall made the region's first industrial power.[^anfinson2003] Its tributary, the [[Minnesota_River|Minnesota River]], runs in the broad valley cut by Glacial River Warren when Lake Agassiz drained south. Federal dams at the headwaters, built in the 1880s, regulate its flow.[^mnopedia-headwaters] <div class="wt-sim" data-src="https://wikitube-3d-microsims.netlify.app/thury/Mississippi_River.html" data-title="Mississippi River"></div> *Try: move the rain around the Hill of Three Waters and watch each drop choose Hudson Bay, Lake Superior or the Gulf; the profile below runs the river from Itasca to the sea with the falls marked.* Connects to: [[#Hydroelectricity|Hydroelectricity]] · [[#Hydrology|Hydrology]] · [[#Saint Anthony Falls|Saint Anthony Falls]] · [[#Lake Agassiz and the Red River|Lake Agassiz and the Red River]] ### Saint Anthony Falls *Main article: [[Saint_Anthony_Falls]] · See also: [[St._Anthony_Falls_Hydroelectric_Development]], [[Saint_Anthony_Falls_Laboratory]]* [[Saint_Anthony_Falls|Saint Anthony Falls]] is where Minnesota's water first went to work. Among its Dakota names is Owahmenah, falling water; Louis Hennepin named it for St. Anthony of Padua in 1680.[^anfinson2003] Its power drove the mills that made Minneapolis the "Flour Milling Capital of the World" from 1880 for fifty years, and in 1882 it lit the first central hydroelectric station in the United States.[^mhs-flour][^mnopedia1882] Hard limestone over soft sandstone had let the falls retreat upstream for thousands of years, about ten miles from near Fort Snelling, as the plunging water washed out the sandstone and the undercut cap broke off; after the riverbed collapsed into the Eastman tunnel in 1869, engineers held them in place.[^nps-ch6] The University of Minnesota's St. Anthony Falls Laboratory has studied flowing water beside them since 1938.[^heitkamp] <div class="wt-sim" data-src="https://wikitube-3d-microsims.netlify.app/thury/Saint_Anthony_Falls.html" data-title="Saint Anthony Falls"></div> *Try: run the clock back twelve thousand years and watch the falls walk upstream through the gorge section as the sandstone washes out from under the limestone; the timeline marks Hennepin, the tunnel, the power station and the laboratory.* Connects to: [[#Hydroelectricity|Hydroelectricity]] · [[#The Mississippi|The Mississippi]] · [[#Open channels and the hydraulic jump|Open channels and the hydraulic jump]] ### Lake Agassiz and the Red River *Main article: [[Lake_Agassiz]] · See also: [[Red_River_of_the_North]], [[Tile_drainage]]* About 13,000 years ago, meltwater from the retreating ice sheet pooled into [[Lake_Agassiz|Lake Agassiz]], a lake larger than all of today's Great Lakes combined. About 11,700 years ago it broke through its southern moraine near Browns Valley and poured south as Glacial River Warren, carving the valley the Minnesota River now follows and starting the waterfall that became Saint Anthony Falls.[^mnopedia-drain][^usgs-miss] When the lake finally drained north it left the flat lakebed of the [[Red_River_of_the_North|Red River]] valley, where the river falls less than half a foot per mile below Grand Forks and its spring floods spread wide.[^usgs2005] Upper and Lower Red Lake and Lake of the Woods are what remains of it in Minnesota.[^dnr-lowlands] <div class="wt-sim" data-src="https://wikitube-3d-microsims.netlify.app/thury/Lake_Agassiz.html" data-title="Lake Agassiz"></div> *Try: play the clock from 13,000 to 8,000 years ago and watch the ice edge retreat, the lake fill to the Browns Valley sill and spill south as River Warren, then drop and drain north when the ice uncovers Hudson Bay; the chart tracks the lake's area against the Great Lakes.* Connects to: [[#Hydrology|Hydrology]] · [[#The Mississippi|The Mississippi]] · [[#Saint Anthony Falls|Saint Anthony Falls]] · [[#Flow through the ground|Flow through the ground]] ## Minnesota *This section is specific to Wikitube.* Minnesota counts 11,842 lakes of ten acres or more and 69,200 miles of natural rivers and streams, including 680 miles of the [[Mississippi_River|Mississippi]] from its source at Lake Itasca.[^dnr-water] The state's water has been worked as hard as it has been admired. On September 5, 1882, the Minnesota Brush Electric Company switched on a hydroelectric station on Upton Island below [[Saint_Anthony_Falls|Saint Anthony Falls]], and centralized hydroelectric power came on for the first time in the United States, in downtown Minneapolis, twenty-five days ahead of Appleton, Wisconsin.[^mnopedia1882] Beside the same falls, the University of Minnesota's St. Anthony Falls Laboratory was dedicated in 1938 under its first director, Lorenz G. Straub, built with Works Progress Administration funds.[^heitkamp] The helium find belongs to the same landscape. Helium was first encountered by accident at the site near Babbitt in 2011; Pulsar Helium licensed it in 2021 and in 2024 reported laboratory concentrations of 8.7 to 14.5 percent helium, against a commercial threshold commonly put near 0.3 percent.[^kaxe] In October 2025 the company reported helium-3 at concentrations up to 14.5 parts per billion in the same well, with a helium-3 to helium-4 ratio of about 0.09 times the atmospheric ratio, verified independently at Woods Hole Oceanographic Institution, and stated plainly that no commercial technology yet separates helium-3 from helium-4 at scale.[^pulsar] That caveat is the lesson: helium-3 is scarce because the United States' supply has come chiefly as a by-product of tritium decay, and a natural source is only useful once the separation problem is solved.[^nidc] ## References [^avila2023]: Avila, Marc; Barkley, Dwight; Hof, Björn (2023). "Transition to turbulence in pipe flow." *Annual Review of Fluid Mechanics* 55: 575–602. https://doi.org/10.1146/annurev-fluid-120720-025957 [^britannica-cf]: Encyclopaedia Britannica. "Compressible fluid flow." https://www.britannica.com/science/compressible-fluid-flow [^clemson]: Smith, W. B. (2019). "Homemade Hydraulic Ram Pump for Livestock Water." Clemson University Land-Grant Press, LGP 1017. https://lgpress.clemson.edu/publication/homemade-hydraulic-ram-pump-for-livestock-water/ [^practical]: Practical Action. "Hydraulic Ram Pumps." Technical brief. https://sswm.info/sites/default/files/reference_attachments/PRACTICAL%20ACTION%204000%20Hydraulic%20Ram%20Pumps.pdf [^lienhard]: Lienhard, John H. "Hydraulic Ram." *The Engines of Our Ingenuity*, episode 2116. University of Houston. https://engines.egr.uh.edu/episode/2116 [^poole1992]: Poole, Peter H.; Sciortino, Francesco; Essmann, Ulrich; Stanley, H. Eugene (1992). "Phase behaviour of metastable water." *Nature* 360: 324–328. https://doi.org/10.1038/360324a0 [^you2026]: You, S.; Ladd Parada, M.; Nam, K.; et al. (2026). "Experimental evidence of a liquid-liquid critical point in supercooled water." *Science* 391: 1387. https://doi.org/10.1126/science.aec0018 [^physicstoday2026]: Wells, Sarah (May 7, 2026). "Experiment closes in on a second critical point of water." *Physics Today*. https://physicstoday.aip.org/news/experiment-closes-in-on-a-second-critical-point-of-water [^murphy16]: Murphy, Tom W., Jr. (2021). *Energy and Human Ambitions on a Finite Planet*. eScholarship, University of California. §16.5 "Hydrogen." https://escholarship.org/uc/item/9js5291m [^kerlin12]: Kerlin, Thomas W. (2013). *Future Energy: Opportunities and Challenges*. International Society of Automation (CC BY 4.0 edition, University of Tennessee). Chapter 12, "Hydrogen"; pp. 236–241, hydropower. https://trace.tennessee.edu/ [^jones1970]: Jones, Lawrence W. (1970). *Toward a liquid hydrogen fuel economy*. University of Michigan, report UMR2320. https://hdl.handle.net/2027.42/5800 [^iea2025]: International Energy Agency (2025). *Global Hydrogen Review 2025*, Executive summary. https://www.iea.org/reports/global-hydrogen-review-2025/executive-summary [^iea2026]: International Energy Agency (2026). *Global Hydrogen Review 2026*, "Demand." https://www.iea.org/reports/global-hydrogen-review-2026/demand [^wcroc2023]: University of Minnesota West Central Research and Outreach Center (April 27, 2023). "Taking the Lead in Green Ammonia." https://wcroc.cfans.umn.edu/news/lead-green-ammonia [^nidc]: U.S. Department of Energy Isotope Program. "Supply and Demand of Helium-3." https://www.isotopes.gov/Supply-and-Demand-of-Helium-3 [^pulsar]: Pulsar Helium Inc. (October 1, 2025). "Pulsar Helium announces Helium-3 Discovery at Jetstream #1, Topaz Project, Minnesota." Company release. https://pulsarhelium.com/investors/news/news-details/2025/Pulsar-Helium-announces-Helium-3-Discovery-at-Jetstream-1-Topaz-Project-Minnesota-October-2025/default.aspx [^kaxe]: KAXE Northern Community Radio (July 8, 2024). "What to know about Minnesota's richest-in-the-world helium deposit." https://www.kaxe.org/local-news/2024-07-08/all-about-mn-richest-ever-helium-discovery-babbitt [^alfven1942]: Alfvén, H. (1942). "Existence of electromagnetic-hydrodynamic waves." *Nature* 150: 405–406. https://doi.org/10.1038/150405d0 [^nobel1970]: Nobel Prize Outreach. "The Nobel Prize in Physics 1970." https://www.nobelprize.org/prizes/physics/1970/summary/ [^nps-ch6]: National Park Service, Mississippi National River and Recreation Area. "River of History — Chapter 6." https://home.nps.gov/miss/learn/historyculture/river-of-hisory-chapter-6.htm [^mndnr-dams]: Minnesota Department of Natural Resources. 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Pp. 25–38, the thermodynamics of water splitting (1.23 V, 1.48 V) and electrode kinetics. [^averill]: Averill, Bruce; Eldredge, Patricia. *Chemistry: Principles, Patterns, and Applications* (open textbook, Portal Books 050). Pp. 884–889, phase diagrams and the vapor pressure of water. [^openstax]: OpenStax. *Chemistry 2e* (open textbook, Portal Books 051). Pp. 502–508, intermolecular forces and the hydrogen bond. [^nrl]: Naval Research Laboratory (2019). *NRL Plasma Formulary*, "Fusion" section: Maxwell-averaged reactivities of D–T, D–D and D–³He versus temperature. https://www.nrl.navy.mil/ ## Wikipedia : Wikitube **Wikitube-only (local `WT!` article):** [Wikitube](https://en.wikitube.io/wiki/WT!Thury_Hydrodynamics_Compendium) ## Previous hub tags Hubs: `Life_Physics`, `Systems`. Portals: [[PORTAL_Thury_Hydrodynamics_Apex_Spine]], [[PORTAL_WT!Thury_Hydrodynamics_Compendium]], [[PORTAL_Centers_of_Excellence]]. --- *Apex Spine wave · 2026-09-10 · flagship · spine prose: 35 sections in six parts (plan: `_registry/plans/THURY_COMPENDIUM_SECTIONS.md`) · microsim-first rewrite 2026-09-11: 35 three.js microsims, one per section, built by the Wikitube microsim framework (`Style Guide and Worklist/MICROSIM_GUIDE/`, specs in `specs/sims/`); sim URLs point at `/thury/` on the sim site and go live with the next production deploy.*