Objects in fluids have forces and motions {fluid dynamics}|.
thrust
Forward force {thrust, fluid} pushes objects through fluid.
drag
Friction {drag} retards moving objects in fluid. Drag rises as velocity increases.
velocity
If thrust stays constant, velocity rises and drag increases, until force balance makes no more acceleration, at terminal velocity. Example is feather falling through air under gravity.
energies
At pipe points, energies are kinetic energy from fluid flow, potential energy from liquid standing in open pipes, and/or energy from outside forces and pressures. Pipe fluids have energy conservation, by Bernoulli's theorem. For streamline flow, sum of pressure P and kinetic energy KE per volume V is constant: P + (KE / V) = constant. P * V = PE, so (PE / V) + (KE / V) = KE + PE = constant total energy.
pressure
Outside force can exert pressure on fluid. Force moves fluid small distance, and kinetic energy distributes throughout fluid, increasing fluid pressure. Outside pressure P is kinetic energy per volume and is force F times distance s divided by volume V: P = KE / V = (F * s) / V.
depth
At fluid depth, gravity causes pressure. Stationary pressure P is potential energy per volume and is density d times gravity acceleration g times depth h: P = PE / V = (m*g*h) / V = (m/V) * g * h = d * g * h.
flow
Fluid flow causes kinetic energy, which exerts pressure in flow direction. Directed pressure P is kinetic energy divided by volume and is half density d times velocity v squared: P = KE / V = (0.5 * m * v^2) / V = 0.5 * (m/V) * v^2 = 0.5 * d * v^2.
Rotating one cylinder inside another causes intervening liquid to flow {Couette-Taylor flow}. First, flow streamlines. At faster speed, fluid cylinder separates into separate layers along cylinder axis, so fluid goes up and down in cylinder. At higher frequency, flow is chaotic, with no defined frequencies.
At fluid boundaries {no-slip condition}, fluid does not slip.
Mixtures of large organic positive ions and inorganic negative ions {ionic liquid}| can be liquid at room temperature, because large charge is spread over large space, so crystal is loose. Liquid has polar and non-polar parts, so it can dissolve organic materials.
non-turbulent flow {laminar flow}|.
Material can become fluid {liquefaction}|.
After torpedo goes 50 meters per second in water, water pressure is low enough to allow water vapor to make vapor cavity around object {supercavitation, fluid}|, allowing high speed.
Wax surfaces repel water very well {superhydrophobicity}|.
City water pressure {water pressure}| is 30 to 50 pounds per square inch, which can lift water 25 to 30 meters.
Friction {drag, fluid}| slows objects moving through fluid. Drag increases if velocity increases. Pipe walls retard fluid flow by friction one millimeter into fluid.
Wing induces drag as it lifts {lifting line theory}.
Drag rises as velocity increases, while forward force stays constant, until forces balance with no more acceleration {terminal velocity}|. Feathers fall through air under gravity with terminal velocity.
Material density and water density have ratio {specific gravity}|. Specific gravity is one for water. Metals have higher specific gravities and sink in water. Wood has lower specific gravity and floats in water. Density D multiplied by gravity acceleration g is weight m*g per volume V {specific weight}: d*g = (m / V) * g = m*g / V.
Instruments {hydrometer}| can measure specific gravity.
Forces between molecules make fluid stick together {viscosity}|.
causes
In liquids, van der Waals forces cause viscosity. In gases, non-ideal molecular collisions cause viscosity.
pressure
Gas viscosity increases if pressure increases.
temperature
Temperature increase increases gas viscosity and decreases liquid viscosity.
factors
Fluid viscosity depends on fluid density, pressure, temperature, and velocity. In pipe, pipe-opening size affects viscosity. Intermolecular forces tend to pull fluid sideways in pipes and contribute to turbulence. Fluid sideways pressure P equals viscosity V times velocity change dv divided by length change dl: P = v * dV/dl.
Pipe flow with incompressible fluid has two regions. A thin layer {boundary layer} touches tube or obstruction and has viscous effects, because surface interacts thermally and mechanically with fluid. Center has flow with no turbulence.
Temperature, viscosity, and fluid depth relate {Rayleigh number}. Reynolds number and Rayleigh number together account for flow effects, viscosity, thermal conductivity, linear-expansion or volume-expansion coefficient, fluid depth, and temperature gradient.
Fluids have ratios {Reynolds number} of internal force to viscous force. Reynolds number measures fluid momentum change. If Reynolds number is small, smooth pipe decreases drag, because flow is laminar. If Reynolds number is high, vortices in smooth pipe increase drag.
Fluids have attractive electric forces among molecules {cohesion}|. Surface tension has cohesion.
Inside fluid, cohesive forces are symmetric and cancel each other. At fluid surfaces, cohesion pulls molecules closer together {surface tension}|, to make surface density more than inside density. Increased-surface-density layer width is 20 molecules. Air above fluid has small density and has little attraction for fluid. Surface chemical potential is greater than inside fluid, because net force is more, and fluid is denser and so more organized.
floating
Surface tension can make density great enough to float objects, such as steel pins.
examples
Glue, waterproofing, detergents, wicks in candles, blotters, towels, bubbles, milk drops, camphor dance, soap film, salts, and needles on water illustrate surface tension.
drops
Droplets have more surface area and high surface tension.
factors
Solute can lower solvent-molecule cohesion by disrupting cohesive forces and lowering chemical potential. Soaps and detergents lessen water surface tension by blocking water-molecule attractions. However, ions in water increase surface tension by increasing electric forces.
Gravity causes fluid molecules to press on molecules below {pressure, fluid} {fluid pressure}|. Deeper molecules have more pressure, because more molecules are above them. Pressure P, force F per area A, at point below fluid surface is density d times depth h times gravity acceleration g: P = F / A = (m * g) * (h / V) = (m / V) * g * h = d * g * h. Pressure is directly proportional to gravity acceleration, because acceleration times mass is force. Pressure is directly proportional to density, because density relates to molecule mass. Pressure is directly proportional to depth, because depth relates to molecule number. Pressure does not depend on total surface area, because pressure is force per unit area.
fluid level
Liquids rise to equal heights at all openings to atmosphere, because pressures and potential energies are equal at liquid surfaces.
cause
Random molecule motions cause fluid pressure. Random motion exerts force and pressure equally in all directions, even upward or at angle. Container wall slope has no effect. Pressure is the same at all points at same depth. The net effect of random motions is that pressure is perpendicular to fluid surface, because random motions are symmetric around perpendicular.
temperature
Temperature increase increases fluid pressure, because molecules move faster.
density
More and/or heavier molecules have higher density and exert more pressure.
gas
Gas has random translational kinetic energy per unit volume, making force per unit area on container walls. Random translational kinetic energy depends on mass and molecule average velocity. If volume decreases, pressure goes up. If temperature decreases, pressure goes down. If pressure decreases, volume goes up. If pressure increases, temperature goes up.
Because pressure transmits equally throughout fluids, pressure sum, and energy sum, is constant {Bernoulli's theorem} {Bernoulli theorem} {Bernoulli's principle}. At pipe points, energy conserves. Pressure stays constant throughout fluid.
If fluid goes through narrower pipe area, fluid speeds up, because mass cannot build up. Higher speed makes more kinetic energy and directed pressure. Sideways pressure decreases, to conserve energy. If fluid slows, kinetic energy goes down, and potential energy and sideways pressure increase.
examples
Fountains, tanks with holes, aspirators, sprayers, Venturi meters, wings, pipes, rubber tubes, and curve balls demonstrate Bernoulli's principle.
In confined fluids, force in one direction can transmit pressure to all directions {hydraulics}|. Increased pressure changes into increased random molecule motions. For example, pushing a piston in a long thin cylinder can do work on fluid and increase molecule random kinetic energy, which can do work on a piston in a short wide cylinder.
area
At depth, force per area pressure is the same throughout confined fluid. Small force acting over long distance on small area can make big force acting over short distance on large area, because energy in and energy out are equal. Large area can apply large total force.
examples
Dams, breathing using lung double cavity, manometer, Bourdon gauge, barometer, hydraulic brakes, hydraulic lifts, syringe, and fluid tank show hydraulic effects.
Simple-fluid hydrodynamics {hydrodynamics}| has no viscosity or heat exchange and follows Euler equation: mass m per volume V times acceleration g equals negative of pressure P gradient perpendicular to velocity vector: (m / V) * g = - dP / ds.
Equal areas have same pressure in confined fluid {Pascal's principle} {Pascal principle}.
Fluid discharge velocity from small hole at depth below open surface is square root of two times gravity acceleration g times depth h {Torricelli's theorem} {Torricelli theorem}: (2*g*h)^0.5.
Removing gas molecules {vacuum, gas}| reduces pressure. Vacuum pumps remove gas molecules.
Oil with iron filings {magnetorheological fluid} can turn solid in magnetic field.
Fluids {electrorheological fluid} can become solid, or have lower viscosity, in high electric fields.
Fluid mildly heated from bottom at first has temperature gradient with no net flow. More heat creates alternating hexagonal cells that allow hot fluid to rise and cold fluid to fall. Even more heat makes turbulent motion, with no net flow {Bénard problem}.
Heated fluids can have convection {Rayleigh-Bénard convection} with circular motions.
Two surfaces can stick to each other {adhesion, surface}|.
Fluids have electric forces between molecules and container surfaces. Fluids that physically adhere to surface can rise in small-diameter tubes {capillary rise}|. Clinging force pulls fluid up tube sides. Fluid rises until potential-energy increase balances air pressure.
When fluids leave holes, fluid tends to flow around hole edge {Coanda effect}.
If fluid is adhesive, fluid curves up container walls {meniscus}|. If fluid is not adhesive, fluid curves down container walls.
Van der Waals forces can cause molecules to bind to surfaces {physisorption}|. Vibrations then cause molecules to leave surface, within 10^-8 seconds, heating surface. Surface chemical bonds do not form or break.
Chemical bonds between surface molecules and fluid molecules can bind molecules to surfaces chemically {chemisorption}|. Molecule stays at surface from 1 to 1000 seconds and then has desorption. Chemisorption has activation energy. At low pressure and low absorption, chemisorption fraction depends on pressure. At high pressure or for strong electrical forces, chemisorption fraction depends on pressure inverse.
Chemisorbed molecules stay at surface from 1 second to 1000 seconds and then leave {desorption, surface}|, heating surface. Surface chemical bonds break. Desorption has activation energy.
Objects in fluids have more pressure on bottom surface than on top surface {buoyancy}|, because bottom surface is deeper in fluid. The greater force on bottom pushes object up. Buoyancy equals difference between object-bottom pressure and object-top pressure. Buoyant force is in opposite direction from gravity. Objects that sink have more force than fluid weight pushed up. Objects that sink are denser than fluid.
If objects float in fluid, fluid weight pushed up around object equals upward buoyant force on object {Archimedes principle, buoyancy}|.
Object in fluid pushes fluid out {displacement, fluid}|. Fluid tries to return to original position by gravity. Displaced fluid and object both want to occupy same place. Equilibrium happens when both forces push down equally.
Objects can sink until buoyant force balances gravity {floating}|. Displaced fluid and object both want to occupy same place, so object is at equilibrium when fluid force pushing down equals object force pushing down. Object that floats is less dense, including air spaces, than fluid. Submarines, fish, boats, balloons, and ice cubes demonstrate buoyancy. If floating-object mass center is not along buoyant-force line, object rotates around mass center.
Fluid mass can go past point or through area over time {fluid flow}|.
pipe
Fluid velocity at different pipe radii differs. Highest velocity is in center. Velocity is zero at pipe walls.
conservation
Same fluid amount at one point must be at another point. Otherwise, fluid builds. Same fluid volume passes any point, during time. At pipe points, inflow equals outflow.
pressure
Around pipe loops, pressures add to zero.
rate
Flow rate increases with increase in molecule velocity, temperature, pressure, and/or mean free path. Flow rate decreases with increase in cross-sectional area, molecule mass, and/or molecule collision frequency.
Flow in pipes can have constant velocity at each radius, with no sideways motion {streamline flow}|.
Flow in pipes can have sideways motion or different velocities at same pipe radius {turbulent flow}|. Trapped gases in fluid can cause turbulence.
High-speed flow and/or pipe edges can pull fluid apart, making vacuum spaces {cavitation, fluid}|.
Fluids have flow rate through area {flux, fluid}|. Flux is energy, mass, momentum, or charge change D divided by cross-sectional area A times time t: D / (A * t).
pipe
In pipes, masses entering and leaving cross-sectional areas are equal. Otherwise, fluid builds, or vacuum happens. Mass m flowing through pipe equals fluid density d times fluid velocity v times cross-sectional area A: m = d*v*A. For liquid, fluid density is constant, and fluid velocity going in vi times cross-sectional area at entrance Ai equals fluid velocity going out vo times cross-sectional area at exit Ao: vi * Ai = vo * Ao. For gas, fluid density varies, and fluid density at entrance di times fluid velocity going in vi times cross-sectional area at entrance Ai equals fluid density at exit do times fluid velocity going out vo times cross-sectional area at exit Ao: di * vi * Ai = do * vo * Ao.
Flux equals constant times gradient {Fick's first law of diffusion} {Fick first law of diffusion}: dm / (A * dt) = dC / ds, where m is mass, A is cross-sectional area, t is time, C is concentration difference, and s is distance.
Pressure, temperature, concentration, or force change over time relates to quantity change over distance {Fick's second law of diffusion} {Fick second law of diffusion}: dP / dt = dm / ds, where P is pressure, t is time, m is mass, and s is distance.
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Date Modified: 2022.0225