Euler Number definition of Euler Number in the Free Online Encyclopedia.

Euler Number

a similarity criterion used in the study of the motion of liquids or gases.

The Euler number Eu characterizes the relation between the pressure forces acting on an elementary volume of a liquid or gas and the inertia forces. It is defined by the formula

(sometimes 2p/ρv²), where p₂ and p₁ are the pressures at two characteristic points of the flow (or of a body moving in it), ρv²/2 is the velocity head, ρ is the density of the liquid or gas, and v is the fluid velocity (or the velocity of the body).

In the case of liquid flows with cavitation, the analogous criterion is called the cavitation number κ = 2(p₀ – p_s)/ρv², where p₀ is the characteristic pressure and p_s is the saturation vapor pressure of the liquid.

For compressible gas flows the relation between the Euler number in the form Eu = 2p/ρv² and two other similarity criteria—the Mach number M and the ratio of the specific heats of the medium γ—is given by the equation Eu = 2/γM², where γ = c_p/c_v (c_p is the specific heat at constant pressure, and c_v is the specific heat at constant volume).

It should be noted that in the American literature two Euler numbers are often used. Euler number 1 equals the friction head divided by two times the velocity head, and Euler number 2 is equal to two times the Fanning friction factor.

The Euler number is named for L. Euler.

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No references found	On the one hand, they include the widely used volume V, surface area S, and Euler number [chi]. Miles formulae for Boolean models observed on lattices by Ohser, Joachim; Nagel, Werner; Schladitz, Katja / Image Analysis and Stereology Descartes discovered that there is a connection between the total defect, T, and the Euler number V - E + F, where V, E, F denote the number of vertices, edges and faces of the given polyhedron. Angle defect and Descartes' theorem by Scott, Paul / Australian Mathematics Teacher An important insight is that, in 3D, complementarity according to a consistency relation for the Euler number differs from the complementarity as conventionally defined by the discrete Jordan-Brouwer theorem. Labeling of N-dimensional images with choosable adjacency of the ... by Sandfort, Kai; Ohser, Joachim / Image Analysis and Stereology	Euglenophyceae Euglenophyta euglobulin Eugregarinida euhedral euhemerism Euhemerus Eukaryotae Eukaryote Eukman, Christiaan EULA Eulamellibranchia Eulenburg's disease Eulenburg, Philipp, Fürst zu Eulenspiegel, Till Euler Euler Angles Euler Characteristic Euler characteristic of a topological space X Euler diagram Euler equation Euler equations of motion Euler force Euler formula for long columns Euler method Euler Number Euler number 1 Euler number 2 Euler Numbers Euler Phi-Function Euler Substitutions Euler transformation Euler's Constant Euler's criterion Euler's Equation Euler's Equations Euler's equations of motion Euler's expansion Euler's Formula Euler's Integral Euler's numbers Euler's phi function Euler's spiral Euler's theorem Euler, Leonhard Euler, Ulf Svante Von Euler-Chelpin Euler-Chelpin, Hans Karl August Simon Von Euler-Fourier Formulas Euler-Lagrange equation Euler-Maclaurin formula	Euler diagram Euler diagrams Euler equation Euler equation of motion Euler equations of motion Euler force Euler formula Euler formula for long columns Euler formula in complex analysis Euler formulas Euler forward method Euler graph Euler Hermes Servicii Financiare Euler Hermes Trade Credit Euler homogeneous function theorem Euler Institute for Discrete Mathematics and its Applications Euler integration Euler International Mathematical Institute Euler lagrange Euler lagrange equations Euler Leonhard Euler Maclaurin Euler maclaurin formula Euler method Euler Number Euler number (physics) Euler number (topology) Euler number 1 Euler number 2 Euler Number/Tissue Volume Euler numbers Euler path Euler phi-function Euler polyhedron theorem Euler quadratic residue theorem Euler rotation Euler Substitutions Euler summation formula Euler theorem Euler theorem on homogeneous functions Euler totient rule Euler totient theorem Euler tour Euler trail Euler transformation Euler Venn diagram Euler walk Euler wenn diagram Euler zeta function

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On the one hand, they include the widely used volume V, surface area S, and Euler number [chi].

Miles formulae for Boolean models observed on lattices by Ohser, Joachim; Nagel, Werner; Schladitz, Katja / Image Analysis and Stereology

Descartes discovered that there is a connection between the total defect, T, and the Euler number V - E + F, where V, E, F denote the number of vertices, edges and faces of the given polyhedron.

Angle defect and Descartes' theorem by Scott, Paul / Australian Mathematics Teacher

An important insight is that, in 3D, complementarity according to a consistency relation for the Euler number differs from the complementarity as conventionally defined by the discrete Jordan-Brouwer theorem.

Labeling of N-dimensional images with choosable adjacency of the ... by Sandfort, Kai; Ohser, Joachim / Image Analysis and Stereology