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Principle in fluid mechanics
where Δ p {\displaystyle \Delta p} is the hydrostatic pressure (given in pascals in the SI system), or the difference in pressure at two points within a
Pascal's_law
Relation between gas pressure and volume
Boyle's law, also referred to as the Boyle–Mariotte law or Mariotte's law (especially in France), is an empirical gas law that describes the relationship
Boyle's_law
SI derived unit of pressure
generally measure atmospheric pressure in hectopascals (hPa), equal to 100 pascals or 1 millibar. Exceptions include Canada, which uses kilopascals (kPa)
Pascal_(unit)
Relationship between volume and temperature of a gas at constant pressure
Charles's law (also known as the law of volumes) is an experimental gas law that describes how gases tend to expand when heated. A modern statement of
Charles's_law
French polymath (1623–1662)
Blaise Pascal (19 June 1623 – 19 August 1662) was a French mathematician, physicist, inventor, philosopher, and Catholic writer. Pascal was a child prodigy
Blaise_Pascal
Scientific law that a closed system's mass remains constant
In physics and chemistry, the law of conservation of mass or principle of mass conservation states that for any system which is closed to all incoming
Conservation_of_mass
Liquid, gas, or other continuously deforming and flowing material
stress is a function of strain rate. A consequence of this behavior is Pascal's law which describes the role of pressure in characterizing a fluid's state
Fluid
Relationship between pressure and temperature of a gas at constant volume
Gay-Lussac's law usually refers to Joseph-Louis Gay-Lussac's law of combining volumes of gases, discovered in 1808 and published in 1809. However, it
Gay-Lussac's_law
Branch of physics
Isaac Newton (investigated viscosity) and Blaise Pascal (researched hydrostatics, formulated Pascal's law), and was continued by Daniel Bernoulli with the
Fluid_mechanics
Force needed to pull a spring grows linearly with distance
divided by an area; it is therefore measured in units of pressure, namely pascals (Pa, or N/m2, or kg/(m·s2). The elements of the strain tensor ε are dimensionless
Hooke's_law
Argument for the belief in God
Culture. 1 (3): 130–140. Retrieved 29 September 2019. Orr, D. W. (1992). "Pascals wager and economics in a hotter time". Ecological Economics. 6 (1): 1–6
Pascal's_wager
Branch of fluid mechanics that studies fluids at rest
reservoir.[citation needed] Pascal made contributions to developments in both hydrostatics and hydrodynamics. Pascal's law is a fundamental principle of
Hydrostatics
Law of physics and chemistry
The law of conservation of energy states that the total energy of an isolated system remains constant; it is said to be conserved over time. In the case
Conservation_of_energy
Type of machine that uses liquid fluid power to perform work
tubes, or pipes. Hydraulic systems, like pneumatic systems, are based on Pascal's law which states that any pressure applied to a fluid inside a closed system
Hydraulic_machinery
Type of fluid
\right)^{\top }\right)} This constitutive equation is also called the Newton law of viscosity. The total stress tensor σ {\displaystyle {\boldsymbol {\sigma
Newtonian_fluid
Buoyancy principle in fluid dynamics
weight of the fluid that the body displaces. Archimedes' principle is a law of physics fundamental to fluid mechanics. It was formulated by Archimedes
Archimedes'_principle
Law describing the pressure drop in an incompressible and Newtonian fluid
equation, also known as the Hagen–Poiseuille law, Poiseuille law or Poiseuille equation, is a physical law that gives the pressure drop in an incompressible
Hagen–Poiseuille_equation
Upward force that opposes the weight of an object immersed in fluid
principle is named after Archimedes of Syracuse, who first discovered this law in 212 BC. For objects, floating and sunken, and in gases as well as liquids
Buoyancy
Human male external reproductive organ
varied between 2–3 to 60–80 mL/Min implies the most ideal milieu to apply Pascal's law in the entire human body; the overall structure is unique. Penile measurements
Human_penis
Manometric unit of pressure
is defined as exactly 133.322387415 pascals, or approximately 1 torr = 1/760 atmosphere = 101325/760 pascals. It is denoted mmHg or mm Hg. Although
Millimetre_of_mercury
Type of fluid
mechanics, a non-Newtonian fluid is a fluid that does not follow Newton's law of viscosity; that is, it has variable viscosity dependent on stress. In
Non-Newtonian_fluid
Relative deformation of a physical body
{\partial u_{x}}{\partial x}}dx} For an isotropic material that obeys Hooke's law, a normal stress will cause a normal strain. Normal strains produce dilations
Strain_(mechanics)
Principle relating to fluid dynamics
Bernoulli's principle can be derived directly from Isaac Newton's second law of motion. When a small volume of fluid is flowing horizontally from a region
Bernoulli's_principle
State of matter
the primary component of hydraulic systems, which take advantage of Pascal's law to provide fluid power. Devices such as pumps and waterwheels have been
Liquid
Property of substances whose particles stick together
Bernoulli's principle Navier–Stokes equations Poiseuille equation · Pascal's law Viscosity (Newtonian · non-Newtonian) Buoyancy · Mixing · Pressure Liquids
Cohesion_(chemistry)
Deflection of a spinning object moving through a fluid
The wake and trailing air-flow are deflected; according to Newton's third law of motion there must be a reaction force in the opposite direction. The air's
Magnus_effect
Equation in fluid dynamics
{\langle v\rangle }^{2}.} The wall shear stress has the SI unit of pascals (Pa). The friction factor fD is not a constant: it depends on such things
Darcy–Weisbach_equation
Force distributed over an area
a unit of force divided by a unit of area; the SI unit of pressure, the pascal (Pa), for example, is one newton per square metre (N/m2); similarly, the
Pressure
State of matter
Bernoulli's principle Navier–Stokes equations Poiseuille equation · Pascal's law Viscosity (Newtonian · non-Newtonian) Buoyancy · Mixing · Pressure Liquids
Plasma_(physics)
Physical quantity
first formulated, in a slightly extended form, by Blaise Pascal, and is now called Pascal's law.[citation needed] In a fluid at rest, all frictional and
Hydrostatic_pressure
Failure Theory in continuum mechanics
Bernoulli's principle Navier–Stokes equations Poiseuille equation · Pascal's law Viscosity (Newtonian · non-Newtonian) Buoyancy · Mixing · Pressure Liquids
Von_Mises_yield_criterion
Theorem in fluid mechanics
equation Morison equation Navier–Stokes equations Oseen flow Pascal's law Poiseuille's law Potential flow Pressure Static pressure Pressure head Relativistic
Torricelli's_law
Study of the deformation of bodies in the presence of frictional effects
for two cylinders in steady rolling contact using Coulomb’s dry friction law (see below). These are applied to railway locomotive traction, and for understanding
Frictional_contact_mechanics
Aspects of fluid mechanics involving fluid flow
conservation laws, specifically, conservation of mass, conservation of linear momentum, and conservation of energy (also known as the first law of thermodynamics)
Fluid_dynamics
Physical property when materials or objects return to original shape after deformation
caused by the stretching of polymer chains when forces are applied. Hooke's law states that the force required to deform elastic objects should be directly
Elasticity_(physics)
Bernoulli's principle Navier–Stokes equations Poiseuille equation · Pascal's law Viscosity (Newtonian · non-Newtonian) Buoyancy · Mixing · Pressure Liquids
List of equations in fluid mechanics
List_of_equations_in_fluid_mechanics
American film producer and business executive (born 1958)
Newcomer, Eric; Sakoui, Anousha (February 11, 2015). "Sony's Pascal Defends Paying Women Like J-Law Less". BloombergBusiness. Bloomberg L.P. Archived from the
Amy_Pascal
Resistance of a fluid to shear deformation
Newton's law of viscosity is not a fundamental law of nature, but rather a constitutive equation (like Hooke's law, Fick's law, and Ohm's law) which serves
Viscosity
Physical quantity that expresses internal forces in a continuous material
therefore its coordinates are measured in the same units as pressure: namely, pascals (Pa, that is, newtons per square metre) in the International System, or
Stress_(mechanics)
Chilean and American actor (born 1975)
Tale of a Doctor Fleeing U.S. Law". The New York Times. Tinoco, Armando (April 11, 2023). "Sarah Paulson Helped Pedro Pascal Early In His Career Giving Him
Pedro_Pascal
Device to detect water temperature and pressure
Because the pressure is roughly proportional to depth according to Pascal's law, temperature measurements can be correlated to the depth at which they
Bathythermograph
Classic magic trick performed by stage magicians
bottle is a simple demonstration of hydrostatics, specifically Pascal's law. Pascal's law states that any pressure applied at any point in a continuous
Inexhaustible_bottle
Branch of mechanics concerned with solid materials and their behaviors
1660: Hooke's law by Robert Hooke 1687: Isaac Newton published "Philosophiae Naturalis Principia Mathematica" which contains Newton's laws of motion 1750:
Solid_mechanics
Ability of a liquid to flow in narrow spaces
and Moloch horridus. The height h of a liquid column is given by Jurin's law h = 2 γ cos θ ρ g r , {\displaystyle h={{2\gamma \cos {\theta }} \over
Capillary_action
Know Pedro Pascal Played In The Law & Order Universe". Looper. Retrieved May 17, 2024. Gordon, Ilana (July 11, 2023). "The 15 best Pedro Pascal movies and
Pedro Pascal on screen and stage
Pedro_Pascal_on_screen_and_stage
Equation describing the transport of some quantity
equations are a stronger, local form of conservation laws. For example, a weak version of the law of conservation of energy states that energy can neither
Continuity_equation
Concept in fluid dynamics
Bernoulli's principle Navier–Stokes equations Poiseuille equation · Pascal's law Viscosity (Newtonian · non-Newtonian) Buoyancy · Mixing · Pressure Liquids
No-slip_condition
Tendency of a liquid surface to shrink to reduce surface area
the necessary "wall tension" of the surface layer according to Laplace's law. Another way to view surface tension is in terms of energy. A molecule in
Surface_tension
Model of electrically conducting fluids
Cauchy momentum equation), an equation of state, Ampère's law, Faraday's law, and Ohm's law. As with any fluid description of a kinetic system, a closure
Magnetohydrodynamics
Process of a gas escaping through a small hole
is larger than the mean free path of the gas, flow obeys the Sampson flow law. In medical terminology, an effusion refers to accumulation of fluid in an
Effusion
Equation of the state of a hypothetical ideal gas
units, p is measured in pascals, V in cubic metres, T in kelvins, and kB = 1.38×10−23 J⋅K−1 in SI units. Combining the laws of Charles, Boyle, and Gay-Lussac
Ideal_gas_law
State of matter
such a way that the strain is directly proportional to the stress (Hooke's law). The coefficient of the proportion is called the modulus of elasticity or
Solid
Mathematical model of how solid objects deform
are: Cauchy momentum equation, which is an expression of Newton's second law. In convective form it is written as: ∇ ⋅ σ + F = ρ u ¨ {\displaystyle {\boldsymbol
Linear_elasticity
Equations of motion for viscous fluids
pressure, temperature and density. They arise from applying Newton's second law to fluid motion, together with the assumption that the stress in the fluid
Navier–Stokes_equations
Line integral of the fluid velocity around a closed curve
change over time, the law must be modified to include a term known as Maxwell's correction. Maxwell's equations Biot–Savart law in aerodynamics Kelvin's
Circulation_(physics)
Empirical law on the variance of species in a habitat
Taylor's power law is an empirical law in ecology that relates the variance of the number of individuals of a species per unit area of habitat to the
Taylor's_law
Liquid that is attracted by poles of a magnet
speaker's magnet. Since ferrofluids are paramagnetic, they obey Curie's law and thus become less magnetic at higher temperatures. A strong magnet placed
Ferrofluid
Equation describing the evolution of the vorticity of a fluid particle as it flows
\nabla \rho } . You can make sense of this by considering the ideal gas law p = ρRT (which is valid if the Reynolds number is large enough that viscous
Vorticity_equation
Medical condition of the prostate gland
testicular and prostatic veins are connected. According to Bernoulli's and Pascal's laws, fluid flowing through connected columns has the same pressure. BPH
Prostatic_congestion
Process of pushing material through a die to create long symmetrical-shaped objects
Bernoulli's principle Navier–Stokes equations Poiseuille equation · Pascal's law Viscosity (Newtonian · non-Newtonian) Buoyancy · Mixing · Pressure Liquids
Extrusion
Transformation of a body from a reference configuration to a current configuration
(relative deformation) is expressed by constitutive equations, e.g., Hooke's law for linear elastic materials. Deformations which cease to exist after the
Deformation_(physics)
Applied engineering involving liquids
through the same pressure (or exact change of pressure) at both locations. Pascal's law or principle states that for an incompressible fluid at rest, the difference
Hydraulics
Control device that converts force into hydraulic pressure
Master-slave (technology) Brake fluid pressure sensor List of auto parts Pascal's law "Master Cylinders". Majorsell Limited. "Chapter 7 : Basic Hydraulic System
Master_cylinder
French tax officer and mathematician
Étienne Pascal (French: [etjɛn paskal]; 2 May 1588 – 24 September 1651) was a French chief tax officer and the father of Blaise Pascal (1623–1662). Pascal was
Étienne_Pascal
Study of the flow of matter, primarily in a fluid state
inactive as of July 2025 (link) Rühs, Patrick A.; Bergfreund, Jotam; Bertsch, Pascal; Gstöhl, Stefan J.; Fischer, Peter (2021). "Complex fluids in animal survival
Rheology
Set of laboratory techniques for separation of mixtures
Bernoulli's principle Navier–Stokes equations Poiseuille equation · Pascal's law Viscosity (Newtonian · non-Newtonian) Buoyancy · Mixing · Pressure Liquids
Chromatography
In physics, the first law of thermodynamics is an expression of the conservation of total energy of a system. The increase of the energy of a system is
First law of thermodynamics (fluid mechanics)
First_law_of_thermodynamics_(fluid_mechanics)
Medical condition
been much controversy concerning the most ideal milieu for applying Pascal's law as it relates to this area of study. Because many males are not responding
Venous_leak
Term in fluid mechanics
but some authors choose to use static pressure in some situations. Pascal's law Stagnation pressure Standard conditions for temperature and pressure
Static_pressure
Strain caused by an external load
is isotropic (or orthotropic) and homogeneous. The material obeys Hooke's law (it is linearly elastic and will not deform plastically). The beam is initially
Bending
Medical injection device
bladders". 1650: Blaise Pascal invented a syringe (not necessarily hypodermic) as an application of what is now called Pascal's law. 1844: Irish physician
Syringe
Equations for calculations of the Darcy friction factor
4}}} . Johann Nikuradse in 1932 proposed that this corresponds to a power law correlation for the fluid velocity profile. Mishra and Gupta in 1979 proposed
Darcy friction factor formulae
Darcy_friction_factor_formulae
Dimensionless number; ratio of a fluid's flow inertia to the external field
Navier–Stokes momentum equation is a Cauchy momentum equation with the Pascal law and Stokes's law being the stress constitutive relations: σ = p I + μ ( ∇ u +
Froude_number
Calculation of strain energy release rate
The strain energy release rate can also be computed from J for pure power-law hardening plastic materials that undergo small-scale yielding at the crack
J-integral
Property of materials with both viscous and elastic characteristics under deformation
and ε is the strain that occurs under the given stress, similar to Hooke's law. The viscous components can be modeled as dashpots such that the stress–strain
Viscoelasticity
Branch of physics which studies the behavior of materials modeled as continuous media
equations that describe the behavior of such matter according to physical laws, such as mass conservation, momentum conservation, and energy conservation
Continuum_mechanics
Study of propagation of cracks in materials
Bernoulli's principle Navier–Stokes equations Poiseuille equation · Pascal's law Viscosity (Newtonian · non-Newtonian) Buoyancy · Mixing · Pressure Liquids
Fracture_mechanics
Hydraulic fluid used for braking applications
Tributyl phosphate Brake fluid pressure sensor Hydropneumatic suspension Pascal's law "Chapter 7 : Basic Hydraulic System Theory" (PDF). Peterverdone.com.
Brake_fluid
Pseudovector field describing the local rotation of a continuum near some point
Vortex tube Vortex stretching Horseshoe vortex Wingtip vortices Biot–Savart law Circulation Vorticity equations Vorticity confinement Kutta–Joukowski theorem
Vorticity
Process of mechanically stirring a heterogeneous mixture to homogenize it
Bernoulli's principle Navier–Stokes equations Poiseuille equation · Pascal's law Viscosity (Newtonian · non-Newtonian) Buoyancy · Mixing · Pressure Liquids
Mixing_(process_engineering)
Material designed to manipulate sound waves
Bernoulli's principle Navier–Stokes equations Poiseuille equation · Pascal's law Viscosity (Newtonian · non-Newtonian) Buoyancy · Mixing · Pressure Liquids
Acoustic_metamaterial
Fluid whose properties can be changed by applying an electric or magnetic field
Bernoulli's principle Navier–Stokes equations Poiseuille equation · Pascal's law Viscosity (Newtonian · non-Newtonian) Buoyancy · Mixing · Pressure Liquids
Smart_fluid
Non-reversible deformation of a solid material in response to applied forces
critical resolved shear stress for single crystals is defined by Schmid’s law τCRSS=σy/m, where σy is the yield strength of the single crystal and m is
Plasticity_(physics)
Study of the deformation of solids that touch each other
Subsequently, Derjaguin and his collaborators by applying Bradley's surface force law to an elastic half space, confirmed that as the Tabor parameter increases
Contact_mechanics
Scientific instrument used to measure fluid flow (rheology)
Bernoulli's principle Navier–Stokes equations Poiseuille equation · Pascal's law Viscosity (Newtonian · non-Newtonian) Buoyancy · Mixing · Pressure Liquids
Rheometer
Legal and philosophical theory that there are values inherent in nature
Natural law (Latin: ius naturale, lex naturalis) is a philosophical and legal theory that posits the existence of inherent laws derived from nature and
Natural_law
sound energy value in comparison to the reference level of 1 pPa (= 10−12 pascals). It is a logarithmic measure of the ratio of two sound energy densities
Sound_energy_density
Hyperelastic material model
Bernoulli's principle Navier–Stokes equations Poiseuille equation · Pascal's law Viscosity (Newtonian · non-Newtonian) Buoyancy · Mixing · Pressure Liquids
Mooney–Rivlin_solid
scientific laws named after people (eponymous laws). For other lists of eponyms, see eponym. Eponym Fields of science Glossary of sound laws in the Indo-European
List of scientific laws named after people
List_of_scientific_laws_named_after_people
Process by which gases diffuse through a biological membrane
that no energy is required to power the transport, and it follows Fick's law: [citation needed] J = − D d φ d x {\displaystyle J=-D{\frac {d\varphi }{dx}}}
Gas_exchange
Law of electrical current and voltage
field; this leads to Ohm's law. A hydraulic analogy is sometimes used to describe Ohm's law. Water pressure, measured by pascals (or PSI), is the analog
Ohm's_law
Concept in physics
Bernoulli's principle Navier–Stokes equations Poiseuille equation · Pascal's law Viscosity (Newtonian · non-Newtonian) Buoyancy · Mixing · Pressure Liquids
Drucker–Prager yield criterion
Drucker–Prager_yield_criterion
Model of rubber elasticity
Bernoulli's principle Navier–Stokes equations Poiseuille equation · Pascal's law Viscosity (Newtonian · non-Newtonian) Buoyancy · Mixing · Pressure Liquids
Gent_hyperelastic_model
Mechanical power source
Positive displacement pumps of various types all work on the principle of Pascal's law of fluid-pressure transmission. Non-positive displacement pumps, also
Hydraulic_pump
2001 disappearance of a 5-year-old boy in Saarbrücken, Germany
ISSN 2195-1349. Retrieved 2025-03-22. Schmidt, Silvia (2004-11-12). "Pascals Quäler". B.Z. – Die Stimme Berlins (in German). Dahlkamp, Jürgen; Röbel
Disappearance of Pascal Zimmer
Disappearance_of_Pascal_Zimmer
Perpendicular-axis marine propulsion system
Bernoulli's principle Navier–Stokes equations Poiseuille equation · Pascal's law Viscosity (Newtonian · non-Newtonian) Buoyancy · Mixing · Pressure Liquids
Cyclorotor
Type of chemical suspension
Triboelectricity Magnetostatics Magnetic field Ampère's law Ampère's force law Biot–Savart law Gauss's law for magnetism Magnetic dipole Magnetic flux Magnetic
Electrorheological_fluid
Materials engineered to have properties that have not yet been found in nature
energy away from the source using either array theory or generalized Snell's law. This has led to aerodynamically favorable shapes for the targets with the
Metamaterial
Classic science experiment demonstrating the Archimedes' principle and the ideal gas law
Therefore, the diver floats at the water's surface. As a result of Pascal's law, squeezing the airtight container increases the pressure of the air,
Cartesian_diver
Mathematical model in materials science
the tables below. 3-D elasticity Hoek–Brown failure criterion Byerlee's law Lateral earth pressure von Mises stress Yield (engineering) Drucker Prager
Mohr–Coulomb_theory
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