Fluid Numbers

Fluid Numbers

Dimensieloze Navier-Stokes

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Froude

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“For a ship, the Froude number is defined as:

where v is the velocity of the ship, g is the acceleration due to gravity, and L is the length of the ship at the water line level, or Lwl in some notations. It is an important parameter with respect to the ship's drag, or resistance, including the wave making resistance. Note that the Froude number used for ships, by convention, is the square root of the Froude number as defined above.”

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Euler

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” Reynolds

“Reynolds number can be defined for a number of different situations where a fluid is in relative motion to a surface. These definitions generally include the fluid properties of density and viscosity, plus a velocity and a characteristic length or characteristic dimension. This dimension is a matter of convention – for example a radius or diameter are equally valid for spheres or circles, but one is chosen by convention. For aircraft or ships, the length or width can be used. For flow in a pipe or a sphere moving in a fluid the internal diameter is generally used today. Other shapes such as rectangular pipes or non-spherical objects have an equivalent diameter defined. For fluids of variable density such as compressible gases or fluids of variable viscosity such as non-Newtonian fluids, special rules apply. The velocity may also be a matter of convention in some circumstances, notably stirred vessels. The inertial forces, which characterize how much a particular fluid resists any change in motion are not to be confused with inertial forces defined in the classical way.”

Invloed van de stromingstoestand:  Stroming in leiding onder druk  Stroming met vrij oppervlak  Stroming rond een lichaam

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Weber

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” “The Weber number is a dimensionless number in fluid mechanics that is often useful in analysing fluid flows where there is an interface between two different fluids, especially for multiphase flows with strongly curved surfaces. It can be thought of as a measure of the relative importance of the fluid's inertia compared to its surface tension. The quantity is useful in analyzing thin film flows and the formation of droplets and bubbles.

It is named after Moritz Weber (1871–1951) and may be written as:”

Mach

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Strouhal

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Rossby

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Prandtl

“The Prandtl number Pr is a dimensionless number; the ratio of momentum diffusivity (kinematic viscosity) to thermal diffusivity. It is named after the German physicist Ludwig Prandtl. It is defined as:”

Eigenschap van het fluïdum.

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Nusselt

“In heat transfer at a boundary (surface) within a fluid, the Nusselt number is the ratio of convective to conductive heat transfer across (normal to) the boundary. In this context, convection includes both advection and conduction. Named after Wilhelm Nusselt, it is a dimensionless number. The conductive component is measured under the same conditions as the heat convection but with a (hypothetically) stagnant (or motionless) fluid. A Nusselt number close to one, namely convection and conduction of similar magnitude, is characteristic of "slug flow" or laminar flow. A larger Nusselt number corresponds to more active convection, with turbulent flow typically in the 100–1000 range. The convection and conduction heat flows are parallel to each other and to the surface normal of the boundary surface, and are all perpendicular to the mean fluid flow in the simple case.”

Dimensieloze convectiecoëfficiënt.

Stanton

“The Stanton number, St or CH, is a dimensionless number that measures the ratio of heat transferred into a fluid to the thermal capacity of fluid. It is used to characterize heat transfer in forced convection flows.

It can also be represented in terms of the fluid's Nusselt, Reynolds, and Prandtl numbers:

The Stanton number arises in the consideration of the geometric similarity of the momentum boundary layer and the thermal boundary layer, where it can be used to express a relationship between the shear force at the wall (due to viscous drag) and the total heat transfer at the wall (due to thermal diffusivity).”

Dimensieloze convectiecoëfficiënt.

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Péclet

“The Péclet number is a dimensionless number relevant in the study of transport phenomena in fluid flows. It is named after the French physicist Jean Claude Eugène Péclet. It is defined to be the ratio of the rate of advection of a physical quantity by the flow to the rate of diffusion of the same quantity driven by an appropriate gradient. In the context of the transport of heat, the Peclet number is equivalent to the

product of the Reynolds number and the Prandtl number. In the context of species or mass dispersion, the Peclet number is the product of the Reynolds number and the Schmidt number.

For diffusion of heat (thermal diffusion), the Péclet number is defined as:

For diffusion of particles (mass diffusion), it is defined as:

where L is the characteristic length, U the velocity, D the mass diffusion coefficient, and α the thermal diffusivity,

where k is the thermal conductivity, ρ the density, and the heat capacity. In engineering applications the Péclet number is often very large. In such situations, the dependency of the flow upon downstream locations is diminished, and variables in the flow tend to become 'one-way' properties. Thus, when modelling certain situations with high Péclet numbers, simpler computational models can be adopted.[1] A flow will often have different Péclet numbers for heat and mass. This can lead to the phenomenon of double diffusive convection.”

Grashof

“The Grashof number Gr is a dimensionless number in fluid dynamics and heat transfer which approximates the ratio of the buoyancy to viscous force acting on a

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fluid. It frequently arises in the study of situations involving natural convection. It is named after the German engineer Franz Grashof.

for vertical flat plates

for pipes

for bluff bodies where the L and D subscripts indicates the length scale basis for the Grashof Number. The transition to turbulent flow occurs in the range for natural convection from vertical flat plates. At higher Grashof numbers, the boundary layer is turbulent; at lower Grashof numbers, the boundary layer is laminar. The product of the Grashof number and the Prandtl number gives the Rayleigh number, a dimensionless number that characterizes convection problems in heat transfer. There is an analogous form of the Grashof number used in cases of natural convection mass transfer problems.”

where

Invloed van stromingstoestand.

Rayleigh

“In fluid mechanics, the Rayleigh number for a fluid is a dimensionless number associated with buoyancy driven flow (also known as free convection or natural convection). When the Rayleigh number is below the critical value for that fluid, heat transfer is primarily in the form of conduction; when it exceeds the critical value, heat transfer is primarily in the form of convection. The Rayleigh number is named after Lord Rayleigh and is defined as the product of the Grashof number, which describes the relationship between buoyancy and viscosity within a fluid, and the Prandtl number, which describes the relationship between momentum diffusivity and thermal diffusivity. Hence the Rayleigh number

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itself may also be viewed as the ratio of buoyancy and viscosity forces times the ratio of momentum and thermal diffusivities. For free convection near a vertical wall, the Rayleigh number is defined as”

Invloed van stromingstoestand.

Sherwood

“The Sherwood number, Sh (also called the mass transfer Nusselt number) is a dimensionless number used in mass-transfer operation. It represents the ratio of convective to diffusive mass transport, and is named in honor of Thomas Kilgore Sherwood. It is defined as follows”

Analogon van het Nusselt getal.. Schmidt

“Schmidt number is a dimensionless number defined as the ratio of momentum diffusivity (viscosity) and mass diffusivity, and is used to characterize fluid flows in which there are simultaneous momentum and mass diffusion convection processes. It was named after the German engineer Ernst Heinrich Wilhelm Schmidt (1892-1975). Schmidt number is the ratio of the shear component for diffusivity viscosity/density to the diffusivity for mass transfer D. It physically relates the relative thickness of the hydrodynamic layer and mass-transfer boundary layer. It is defined as:

The heat transfer analog of the Schmidt number is the Prandtl number.” Analogon van het Prandtl getal.

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Referenties

[1] Wikipedia, datum en auteur van publicatie onbekend, Froude number, wetenschappelijk artikel, URL: http://en.wikipedia.org/wiki/Froude_number, geraadpleegd op 13 december 2012. [2] Wikipedia, datum en auteur van publicatie onbekend, Euler number, wetenschappelijk artikel, URL: http://en.wikipedia.org/wiki/Euler_number_(physics), geraadpleegd op 13 december 2012. [3] Wikipedia, datum en auteur van publicatie onbekend, Reynolds number, wetenschappelijk artikel, URL: http://en.wikipedia.org/wiki/Weber_number, geraadpleegd op 13 december 2012. [4] Wikipedia, datum en auteur van publicatie onbekend, Weber number, wetenschappelijk artikel, URL: http://en.wikipedia.org/wiki/Reynolds_number, geraadpleegd op 13 december 2012. [5] Wikipedia, datum en auteur van publicatie onbekend, Prandtl number, wetenschappelijk artikel, URL: http://en.wikipedia.org/wiki/Prandtl_number, geraadpleegd op 13 december 2012. [6] Wikipedia, datum en auteur van publicatie onbekend, Nusselt number, wetenschappelijk artikel, URL: http://en.wikipedia.org/wiki/Nusselt_number, geraadpleegd op 13 december 2012. [7] Wikipedia, datum en auteur van publicatie onbekend, Stanton number, wetenschappelijk artikel, URL: http://en.wikipedia.org/wiki/Stanton_number, geraadpleegd op 13 december 2012. [8] Wikipedia, datum en auteur van publicatie onbekend, Péclet number, wetenschappelijk artikel, URL: http://en.wikipedia.org/wiki/P%C3%A9clet_number, geraadpleegd op 13 december 2012. [9] Wikipedia, datum en auteur van publicatie onbekend, Grashof number, wetenschappelijk artikel, URL: http://en.wikipedia.org/wiki/Grashof_number, geraadpleegd op 13 december 2012. [10] Wikipedia, datum en auteur van publicatie onbekend, Raayleigh number, wetenschappelijk artikel, URL: http://en.wikipedia.org/wiki/Rayleigh_number, geraadpleegd op 13 december 2012. [11] Wikipedia, datum en auteur van publicatie onbekend, Sherwood number, wetenschappelijk artikel, URL: http://en.wikipedia.org/wiki/Sherwood_number, geraadpleegd op 13 december 2012. [12] Wikipedia, datum en auteur van publicatie onbekend, Schmidt number, wetenschappelijk atikel, URL: http://en.wikipedia.org/wiki/Schmidt_number, geraadpleegd op 13 december 2012.

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[13] Universiteit Gent, Prof. Dr. Ir. J. Vierendeels & Prof. Dr. Ir. P. Verdonck, Cursus: 2e Bachelor Burgerlijk Ingenieur Bouwkunde: Transportverschijnselen, Documentnaam: Hoofdstuk_11_TransVersch_2012_2013_v1.pdf, Slides: 7-8-10-12-19-20-21- 22, geraadpleegd op 13 december 2012.

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