Euler numbers

The dimensionless quantities in brackets are, respectively, the reciprocal of the Froude number, the Euler number, and the reciprocal of the Reynolds number for the system. 

The result is a modified Euler number. You can prove to yourself that the pressure drop over the particle can be obtained by accounting for the projected area of the particle through particle size, S, in the denominator. Thus, by application of dimensional analysis to the force balance expression, a relationship between the dimensionless complexes of the Euler and Reynolds numbers, we obtain ... 

Figure 2.12 Packed bed pressure loss Euler number versus particle Reynolds number (Ergun, 1952)...

At a given Weber number, condition (8.71) may be satisfied at some values of the Euler number, which play the role of eigenvalues. 

The effect of wall heat flux on the length of the heating and evaporation regions, vapor velocity, temperature and pressure in the outlet cross-section is shown in Figs. 8.13, 8.14, and 8.15. These data illustrate some important features of capillary flow at large Euler numbers. 

Euler number Froud number Nusselt number Peclet number Weber number... 

At large Euler numbers when AP < 1, the vapor essure may be calculated by the Clausius-Clapeyron equation. In this case Ps and ft in Eq. (9.38) correspond to the saturation parameters. 

Velocity of the evaporating front in the system of coordinates associated with the fluid flow Euler number... 

The Euler number (Eu) is defined as the ratio of the pressure force to the inertial force, as in the form... 

Group N6 (or some multiple thereof) is also known as a friction factor (/), because the driving force (AP) is required to overcome friction (i.e., the energy dissipated) in the pipeline (assuming it to be horizontal), and N3 is known as the Reynolds number (N e). There are various definitions of the pipe friction factor, each of which is some multiple of N6 e.g., the Fanning friction factor is N6/2, and the Darcy friction factor is 2N6. The group N4 is also known as the Euler number. 

Euler number Neu. . A P Neu PV2 AP = pressure drop in pipe (Pressure energy)/ (kinetic energy) Flow in closed conduits... 

Remark 2.3.12. The Euler numbers of the Hilbert schemes can be expressend in terms of modular forms let q = e2,rlT for r in the upper half plane... 

Table of the Euler numbers (A abelian surface, S geometrically ruled surface over an elliptic curve) ... 

Let G be a finite group acting on a compact differentiable manifold X. Then there exists the well known formula for the Euler number of the quotient... 

This formula we will call the orbifold Euler number formula. In the case that the group G is abelian this conjecture has been proved in [Roan (1)] under certain additional hypotheses. In [Hirzebruch-Hofer (1)] some examples of this formula are studied. First they give a reformulation ... 

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