Incompressible flow, the Glossary

Table of Contents

1. 31 relations: Atmosphere of Earth, Atmospheric science, Bernoulli's principle, Chain rule, Compressibility, Compressible flow, Conservation of mass, Conservative vector field, Continuum mechanics, Control volume, Curl (mathematics), Density, Divergence, Divergence theorem, Euler equations (fluid dynamics), Flow velocity, Fluid dynamics, Fluid mechanics, Fluid parcel, Infinitesimal, Isochoric process, Laplacian vector field, Mach number, Material derivative, Navier–Stokes equations, Projection method (fluid dynamics), Solenoidal vector field, Surface integral, Total derivative, Vector calculus identities, Volume integral.

Atmosphere of Earth

The atmosphere of Earth is composed of a layer of gas mixture that surrounds the Earth's planetary surface (both lands and oceans), known collectively as air, with variable quantities of suspended aerosols and particulates (which create weather features such as clouds and hazes), all retained by Earth's gravity.

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Atmospheric science

Atmospheric science is the study of the Earth's atmosphere and its various inner-working physical processes.

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Bernoulli's principle

Bernoulli's principle is a key concept in fluid dynamics that relates pressure, speed and height.

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Chain rule

In calculus, the chain rule is a formula that expresses the derivative of the composition of two differentiable functions and in terms of the derivatives of and.

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Compressibility

In thermodynamics and fluid mechanics, the compressibility (also known as the coefficient of compressibility or, if the temperature is held constant, the isothermal compressibility) is a measure of the instantaneous relative volume change of a fluid or solid as a response to a pressure (or mean stress) change.

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Compressible flow

Compressible flow (or gas dynamics) is the branch of fluid mechanics that deals with flows having significant changes in fluid density. Incompressible flow and Compressible flow are fluid mechanics.

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Conservation of mass

In physics and chemistry, the law of conservation of mass or principle of mass conservation states that for any system closed to all transfers of matter and energy, the mass of the system must remain constant over time, as the system's mass cannot change, so the quantity can neither be added nor be removed.

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Conservative vector field

In vector calculus, a conservative vector field is a vector field that is the gradient of some function.

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Continuum mechanics

Continuum mechanics is a branch of mechanics that deals with the deformation of and transmission of forces through materials modeled as a continuous medium (also called a continuum) rather than as discrete particles.

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Control volume

In continuum mechanics and thermodynamics, a control volume (CV) is a mathematical abstraction employed in the process of creating mathematical models of physical processes.

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Curl (mathematics)

In vector calculus, the curl, also known as rotor, is a vector operator that describes the infinitesimal circulation of a vector field in three-dimensional Euclidean space.

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Density

Density (volumetric mass density or specific mass) is a substance's mass per unit of volume.

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Divergence

In vector calculus, divergence is a vector operator that operates on a vector field, producing a scalar field giving the quantity of the vector field's source at each point.

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Divergence theorem

In vector calculus, the divergence theorem, also known as Gauss's theorem or Ostrogradsky's theorem, reprinted in is a theorem relating the flux of a vector field through a closed surface to the divergence of the field in the volume enclosed.

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Euler equations (fluid dynamics)

In fluid dynamics, the Euler equations are a set of partial differential equations governing adiabatic and inviscid flow.

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Flow velocity

In continuum mechanics the flow velocity in fluid dynamics, also macroscopic velocity in statistical mechanics, or drift velocity in electromagnetism, is a vector field used to mathematically describe the motion of a continuum.

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Fluid dynamics

In physics, physical chemistry and engineering, fluid dynamics is a subdiscipline of fluid mechanics that describes the flow of fluids—liquids and gases. Incompressible flow and fluid dynamics are fluid mechanics.

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Fluid mechanics

Fluid mechanics is the branch of physics concerned with the mechanics of fluids (liquids, gases, and plasmas) and the forces on them.

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Fluid parcel

In fluid dynamics, a fluid parcel, also known as a fluid element or material element, is an infinitesimal volume of fluid, identifiable throughout its dynamic history while moving with the fluid flow.

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Infinitesimal

In mathematics, an infinitesimal number is a non-zero quantity that is closer to 0 than any non-zero real number is.

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Isochoric process

In thermodynamics, an isochoric process, also called a constant-volume process, an isovolumetric process, or an isometric process, is a thermodynamic process during which the volume of the closed system undergoing such a process remains constant.

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Laplacian vector field

In vector calculus, a Laplacian vector field is a vector field which is both irrotational and incompressible.

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Mach number

The Mach number (M or Ma), often only Mach, is a dimensionless quantity in fluid dynamics representing the ratio of flow velocity past a boundary to the local speed of sound.

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Material derivative

In continuum mechanics, the material derivative describes the time rate of change of some physical quantity (like heat or momentum) of a material element that is subjected to a space-and-time-dependent macroscopic velocity field.

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Navier–Stokes equations

The Navier–Stokes equations are partial differential equations which describe the motion of viscous fluid substances.

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Projection method (fluid dynamics)

In computational fluid dynamics, the projection method, also called Chorin's projection method, is an effective means of numerically solving time-dependent incompressible fluid-flow problems.

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Solenoidal vector field

In vector calculus a solenoidal vector field (also known as an incompressible vector field, a divergence-free vector field, or a '''transverse vector field''') is a vector field v with divergence zero at all points in the field: \nabla \cdot \mathbf.

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Surface integral

In mathematics, particularly multivariable calculus, a surface integral is a generalization of multiple integrals to integration over surfaces.

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Total derivative

In mathematics, the total derivative of a function at a point is the best linear approximation near this point of the function with respect to its arguments.

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Vector calculus identities

The following are important identities involving derivatives and integrals in vector calculus.

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Volume integral

In mathematics (particularly multivariable calculus), a volume integral (∭) is an integral over a 3-dimensional domain; that is, it is a special case of multiple integrals.

See Incompressible flow and Volume integral

References

[1] https://en.wikipedia.org/wiki/Incompressible_flow

Also known as Incompressible, Incompressible Fluid, Incompressible fluid flow, Numerical methods for incompressible flow.