Number, defined

The ability to assign a group of resonance states, as required for mode-specific decomposition, implies that the complete Hamiltonian for these states is well approxmiated by a zero-order Hamiltonian with eigenfunctions [M]. The ( ). are product fiinctions of a zero-order orthogonal basis for the reactant molecule and the quantity m. represents the quantum numbers defining ( ).. The wavefimctions / for the compound state resonances are given by... 

The degree of conditioning of a matrix is detennined by the "condition number defined as (Fox and Mayei s, 1977)... 

Column Efficiency. Under ideal conditions the profile of a solute band resembles that given by a Gaussian distribution curve (Fig. 11.1). The efficiency of a chromatographic system is expressed by the effective plate number defined from the chromatogram of a single band. 

The decay constant is the key to the mixing rate number defined for Re > lO" by N/ D/TY = 0.5 for a disk flat blade turbine (DFBT), and N/ (D/TY = 0.9 for the propeUer. Therefore, power required to achieve any degree of uniformity in a fixed time is proportional to D and D for DFBT and propeUer, respectively. 

TurbulentPremixedFlames. Combustion processes and flow phenomena are closely coimected and the fluid mechanics of a burning mixture play an important role in forming the stmcture of the flame. Laminar combusting flows can occur only at low Reynolds numbers, defined as... 

For banks of staggered tubes, the friction factor for isothermal flow is obtained from Fig. (6-42). Each fence (group of parametric curves) represents a particular Reynolds number defined as... 

Impeller Reynolds Number The presence or absence of turbulence in an impeller-stirred vessel can be correlated with an impeller Reynolds number defined... 

The comparison of the magnitude of the two resistances clearly indicates whether tire metal or the slag mass transfer is rate-determining. A value for the ratio of the boundary layer thicknesses can be obtained from the Sherwood number, which is related to the Reynolds number and the Schmidt number, defined by... 

This expression can be represented graphically in dimensionless form to simplify its use. It is generally expressed as the so-called filtration number , defined as follows E, = /iR, / 2APT3 jr x . The filtration number, E, is dimensionless and varies from zero at Rf = 0 to a large value when there is an increase in the viscosity of the sludge and Rf or a decrease in pressure drop, auxiliary time, specific cake resistance and the ratio of cake volume to filtrate volume. It may be assumed in practice that F(, = 0 to 10. If washing and drying times are constant and independent of filtration time, they may be added directly to the auxiliary time. In... 

The LHS of this expression contains a dimensionless group known as the Galileo number, defined as Ga = gdVv. ... 

The theoretical analysis could also be valid for nonisothermal jets assuming that the buoyancy is negligible. Grimitlyn, as reported by Hagstrom, suggests a local Archimedes number defined as ... 

The arrangement of electrons in an atom is described by means of four quantum numbers which determine the spatial distribution, energy, and other properties, see Appendix 1 (p. 1285). The principal quantum number n defines the general energy level or shell to which the electron belongs. Electrons with n = 1.2, 3, 4., are sometimes referred to as K, L, M, N,. .., electrons. The orbital quantum number / defines both the shape of the electron charge distribution and its orbital angular... 

Since the Reynolds number is greater than 104, therefore the flow is turbulent. Based on a power number defined in the turbulent regime, the power number is defined as about 6 (from Figure 6.6). 

Naturally, there are two more Peclet numbers defined for the transverse direction dispersions. In these ranges of Reynolds number, the Peclet number for transverse mass transfer is 11, but the Peclet number for transverse heat transfer is not well agreed upon (121, 122). None of these dispersions numbers is known in the metal screen bed. A special problem is created in the monolith where transverse dispersion of mass must be zero, and the parallel dispersion of mass can be estimated by the Taylor axial dispersion theory (123). The dispersion of heat would depend principally on the properties of the monolith substrate. Often, these Peclet numbers for individual pellets are replaced by the Bodenstein numbers for the entire bed... 

A sample of polyester (ca. 1 g, exactly weighed) is dissolved in 20 mL toluene-ethanol mixture (1/1 vol.) and titrated by a solution of KOH in ethanol (0.05 mol/L) using a potentiometric titrator. A blank titration must be performed under the same conditions. Hardly soluble polyesters (e.g., PET) must be dissolved in an o-cresol-chloroform mixture or in hot benzyl alcohol.417 The result (acid content) is normally expressed in mmol COOH/g polyester but may also be given as the acid number, defined as the number of milligrams of KOH required to neutralize 1 g of polyester. [Acid number = (number of mmol COOH/g polyester) x 56.106.]... 

For the study of flow stability in a heated capillary tube it is expedient to present the parameters P and q as a function of the Peclet number defined as Pe = (uLd) /ocl. We notice that the Peclet number in capillary flow, which results from liquid evaporation, is an unknown parameter, and is determined by solving the stationary problem (Yarin et al. 2002). Employing the Peclet number as a generalized parameter of the problem allows one to estimate the effect of physical properties of phases, micro-channel geometry, as well as wall heat flux, on the characteristics of the flow, in particular, its stability. 

The secondary flows from natural convection can become larger than the primary flow, so it seems likely that the secondary flows might become turbulent or nonsteady. Shown in Tables 1 and 2 are the dimensionless groups at the inlet and outlet, based on cup-average quantities, as well as the Reynolds numbers for the primary and secondary flows (Reynolds numbers defined in terms of the respective total mass flowrate, the viscosity and the ratio of tube perimeter to tube area). 

The principle quantity determining the flow regime of gases and deviations from the standard continuum description is the Knudsen number, defined as... 

The term Lu / D is known as the Peclet number, Pe, and its inverse as the dispersion number. The magnitude of the Peclet number defines the degree of axial mixing in the reactor. 

GrL Grashof number = gli Ap/pv2 Gr Grashof number defined by Eq. (40) Gr Grashof number defined by Eq. (37) GrJ Grashof number defined by Eq. (39) / Ionic strength = c( z2 (moles liter"1)... 

Ra Rayleigh number defined by Eq. A Difference of an electrolyte property... 

The Peclet number defined for this case is unique to Regime II flows, due to the definition of kn eff given in Eq. (23). Therefore, Peu must be correlated with experimental data from Regime II flows. 

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