Characteristic parameters

We analyze the dimensionless form of the governing equations to obtain important characteristic similarity parameters. This can facilitate subsequent analysis over restricted ranges of parameters. 

For steady, incompressible, and constant density fluid flow case, we write the mass conservation equation as 

For incompressible case, — = 0. If we assume the viscous dissipation to be negligible compared to the average energy level, the above equation simplifies to 

The subscripts 0 represent the free stream condition and w represent the value at a wall or surface. Introducing the above dimensionless variables, in equations (4.33)-(4.35) and (4.37), we have 

The Strouhal number is a measure of unsteadiness of flow motion. The Froude number is important for free surface flow  

---

Here is described the verification of one particular characteristic parameter of one flaw detector, i.e. vertical linearity. The system of verification VERAPUS is connected to peripheral equipment as indicated in figure 2. The dialogue boxes show the operator how to adjust the R.F. signals that are sent by the arbitrary generator to the flaw detector. 

Verify each characteristic parameter according to a standardised methodology. 

Assuming that concentration effects have been eliminated by extrapolating Kc2/Rg to C2 = 0 (subscript c = 0), we see that Eq. (10.89) is the equation of a straight line if (Kc2/Rg)(,=o plotted against sin (0/2). The characteristic parameters of the line have the following significance ... 

The structure formation in an ER fluid was simulated [99]. The characteristic parameter is the ratio of the Brownian force to the dipolar force. Over a wide range of this ratio there is rapid chain formation followed by aggregation of chains into thick columns with a body-centered tetragonal structure observed. Above a threshold of the intensity of an external ahgn-ing field, condensation of the particles happens [100]. This effect has also been studied for MR fluids [101]. The rheological behavior of ER fluids [102] depends on the structure formed chainlike, shear-string, or liquid. Coexistence in dipolar fluids in a field [103], for a Stockmayer fluid in an applied field [104], and the structure of soft-sphere dipolar fluids were investigated [105], and ferroelectric phases were found [106]. An island of vapor-liquid coexistence was found for dipolar hard spherocylinders [107]. It exists between a phase where the particles form chains of dipoles in a nose-to-tail... 

Then, in this two-term unfolding model remains to define this exponent 2q, since all other quantities and especially the r-radius are either given, or evaluated from the thermodynamic equilibrium relations. Then, in this model the 2q-exponent is the characteristic parameter defining the quality of adhesion and therefore it may be called the adhesion coefficient. This exponent depends solely on the ratios of the main-phase moduli (Ef/Em), as well as on the ratio of the radii of the fiber and the mesophase. 

Table 1. The values of the characteristic parameters of a series of iron-epoxy particulates for various filler volume contents of... 

As one would expect, the rate of orientational relaxation in the jump model is activated, and the higher the libration barrier U0, the lower the rate. However, the Hubbard relation obtained as a result of Eq. (1.123) used in Eq. (2.96) does not involve this characteristic parameter of the solid-like model ... 

The quasi-classical description of the Q-branch becomes valid as soon as its rotational structure is washed out. There is no doubt that at this point its contour is close to a static one, and, consequently, asymmetric to a large extent. It is also established [136] that after narrowing of the contour its shape in the liquid is Lorentzian even in the far wings where the intensity is four orders less than in the centre (see Fig. 3.3). In this case it is more convenient to compare observed contours with calculated ones by their characteristic parameters. These are the half width at half height Aa)i/2 and the shift of the spectrum maximum ftW—< > = 5a>+A, which is usually assumed to be a sum of the rotational shift 5larger scale A determined by vibrational dephasing. 

With formulae (3.58), (3.59) and (3.66) Q-branch contours are calculated for CARS spectra of spherical rotators at various pressures and for various magnitudes of parameter y (Fig. 3.14). For comparison with experimental data, obtained in [162], the characteristic parameters of the spectra were extracted from these contours half-widths and shifts of the maximum subject to the density. They are plotted in Fig. 3.15 and Fig. 3.16. The corresponding experimental dependences for methane were plotted by one-parameter fitting. As a result, the cross-section for rotational energy relaxation oe is found ... 

It is shown that an increase in the heat flux is accompanied by an increase in the liquid and vapor velocities, the meniscus displacement towards the outlet cross-section, as well as growth of vapor to liquid forces ratio and heat losses. When is large enough, the difference between the intensity of heat transfer and heat losses are limited by some final value, which determines the maximum rate of vaporization. Accordingly, when is large all characteristic parameters are practically invariable. 

First we estimate the values of the coefficients a, ft, c and r/ for realistic physical values of the characteristic parameters (Table 11.1). 

The form of the solution of the dispersion equation (11.61) depends on the sign of the determinant D = q + Pl, i.e., on the values of the characteristic parameters g and P. The latter are determined by the physical properties of the liquid and its vapor, as well as the values of the Peclet number. This allows us to use g and P as some general characteristics of the problem considered here. 

Equation (8) is a corresponding-states expression and therefore can be used for mixtures as well as for pure components. For mixtures, the characteristic parameters are given by (3)... 

At a definite value of the electrode potential E, the charge of the electrode s surface and hence the value of drop to zero. This potential is called the point of zero charge (PZC). The metal surface is positively charged at potentials more positive than the PZC and is negatively charged at potentials more negative than the PZC. The point of zero charge is a characteristic parameter for any electrode-electrolyte interface. The concept of PZC is of exceptional importance in electrochemistry. 

Characteristic parameters of each wave are the valne of the half-wave potential i/2> which is dehned by Eq. (6.26), and the wave height [the valne of the limiting diffusion cnrrent, determined by the llkovic eqnation (23.1) for c j = 0]. The... 

In the transient voltammetric methods, one measures the characteristic parameters on transient polarization curves after some potential or current perturbation has been... 

APPROXIMATE VALUES OF CHARACTERISTIC PARAMETERS IMPORTANT IN PREDICTING BAND BROADENING... 

NMR interpretation has made significant advances with diffusion-editing pulse sequences and two-dimensional inversion of diffusivity and T2 relaxation [7,40-44]. The 2D inversion can also be used to compare Tj and T2 relaxation with each other [42]. Distributions of these two characteristic parameters can now be displayed on a 2D map and the relationship between them more easily visually interpreted. The 2D distribution map can be interpreted by comparing the measured distribution with the line for the bulk diffusivity of water and the correlation lines for the hydrocarbon components in crude oils, shown in Figure 3.6.10 as dashed lines [40-46]. Figure... 

A characteristic parameter of the process is the ratio of the overall rate of erosion relative to the overall rate of rupture given by... 

---