Equation fitting the

Figure 15 shows results for a difficult type I system methanol-n-heptane-benzene. In this example, the two-phase region is extremely small. The dashed line (a) shows predictions using the original UNIQUAC equation with q = q. This form of the UNIQUAC equation does not adequately fit the binary vapor-liquid equilibrium data for the methanol-benzene system and therefore the ternary predictions are grossly in error. The ternary prediction is much improved with the modified UNIQUAC equation (b) since this equation fits the methanol-benzene system much better. Further improvement (c) is obtained when a few ternary data are used to fix the binary parameters. 

How well the developed equation fits the data is given by the coiielation coefficient, y (0.0 = poor fit, 1.0 = excellent fit), which is the square root of the... 

Development of the Nomograph. Tw o main sources of data were used to develop the nomograph McAuliffe and Price. The hydrocarbons were divided into 14 homologous series as listed in Table 1. Solubilities at 25°C were then regressed with the carbon numbers of the hydrocarbons in order to obtain the best fit for each homologous series. A second order polynomial equation fits the data very well ... 

Their data, which were obtained using a small annulus, are somewhat below those given by equation 9.95 for values of deG jfi less than 10,000, although this may be because the flow was not fully turbulent with an index on the Reynolds group of 0.9, the equation fitted the data much better. There is little to choose between these two equations, but they both give rather high values for h. 

This equation fits the experimental values (the observed dipole moment divided by the electronic charge and the bond length) quite well. Somewhat more accurate equations have been formulated by Nethercot.56... 

Perrin model and the Johansson and Elvingston model fall above the experimental data. Also shown in this figure is the prediction from the Stokes-Einstein-Smoluchowski expression, whereby the Stokes-Einstein expression is modified with the inclusion of the Ein-stein-Smoluchowski expression for the effect of solute on viscosity. Penke et al. [290] found that the Mackie-Meares equation fit the water diffusion data however, upon consideration of water interactions with the polymer gel, through measurements of longitudinal relaxation, adsorption interactions incorporated within the volume averaging theory also well described the experimental results. The volume averaging theory had the advantage that it could describe the effect of Bis on the relaxation within the same framework as the description of the diffusion coefficient. 

Does the rate equation fit the observed reaction rates ... 

The ICRP (1994b, 1995) developed a Human Respiratory Tract Model for Radiological Protection, which contains respiratory tract deposition and clearance compartmental models for inhalation exposure that may be applied to particulate aerosols of americium compounds. The ICRP (1986, 1989) has a biokinetic model for human oral exposure that applies to americium. The National Council on Radiation Protection and Measurement (NCRP) has also developed a respiratory tract model for inhaled radionuclides (NCRP 1997). At this time, the NCRP recommends the use of the ICRP model for calculating exposures for radiation workers and the general public. Readers interested in this topic are referred to NCRP Report No. 125 Deposition, Retention and Dosimetry of Inhaled Radioactive Substances (NCRP 1997). In the appendix to the report, NCRP provides the animal testing clearance data and equations fitting the data that supported the development of the human mode for americium. 

What power law rate equation fits the data ... 

By comparing with experiment, we see that this equation fits the three reported facts ... 

Multiple regression programs also calculate auxiliary statistics, designed to help decide how well the calibration fits the data, and how well it can be expected to predict future samples. For example, two of these statistics are the standard error of calibration (SEC) and the multiple correlation coefficient (R). The SEC (also called standard error of estimate, or residual standard deviation) and the multiple correlation coefficient indicate how well the calibration equation fits the data. Their formulas are given in Table 3. 

This equation fits the titration curve of all weak acids and enables us to deduce a number of important quantitative relationships. For example, it shows why the pKa of a weak acid is equal to the pH of the solution at the midpoint of its titration. At that point, [HA] equals [A-], and... 

Validity Range is range of the pressure (in MPa) over which the equations apply Equations are based on limited data beyond about 130MPa, and should be used with caution Shock wave is not exponential, but has a hump the similitude equation fits the portion of the wave beyond the hump. 

Equation 3 was verified experimentally (3) over wide ranges of temperature and equilibrium pressure for the adsorption of various vapors on active carbons with different parameters for the microporous structure. For adsorption on zeolites, this equation fitted the experimental results well only in the range of high values of 0 (4, 5, 6, 7). Among other equations proposed for the characteristic curve (4, 5, 8, 9, 10) we chose to use the Cohen (4) and Kisarov s (10) equation, which starts from the following adsorption isotherm equation ... 

Equation B-75 was developed from data which have a temperature range of 86.5 to 167°F and pressures to 14,000 psia.27 The equation fits the data to within four percent for pressures below 10,000 psia and seven percent at pressures between 10,000 and 14,000 psia. Pressure is in psia. 

Isothermal curves derived from this equation are shown in Fig. 2.19. It is clear that this equation fits the experimental data. A comparison of the kinetic equation (2.48) and the Avrami equation shows93 that any experimental data described by the Avrami equation can be approximated by Eq. (2.48) for any arbitrary set of constants. The divergence of the curves does not exceed 1% in the range 0.2 experimental data (in the isothermal case) can be analyzed by both equations with practically the same reliability. Thus the choice of approximating equation depends on the goal of this procedure if we are interested in physi-... 

This equation is first order in T with respect to t. A first order mixing pattern has been assumed/ and a first order pattern is exhibited by most "we 11-mixed" vessels that do not have baffles or flow directing nozzles. How closely this first order equation fits the actual process will be determined later. 

When these values of a and b are used, the van der Waals equation fits the critical point and the slope and curvature of the critical isotherm. By continuity, the equation should also be a good fit to experimental data at temperatures slightly above the critical point. Other values of the constants may provide a better fit to data at conditions far from the critical point. Because it is an analytical function, the van der Waals equation cannot reproduce the discontinuities characteristic of vaporization shown at the two-phase regions in Figs. 7-9. Equation (21) (as well as other two-parameter equations, such as those of Berthelot, and Redlich and... 

Experiments on ILs have generally shown a highly non-Arrhenius behavior that is well described by the VFT equation. Xu et al. [149] report the temperature-dependent viscosity of a series of covalently stable ILs, and note that the VFT equation fits the temperature dependence of the fluidity quite well. A series of studies by Watanabe and co-workers [167-169] on a range of different ILs shows that the VFT provides a good fit to diffusion constants, molar conductivity and viscosity. 

The three equations fit the experimental data well within the limits of experimental error. Moreover, the values obtained for the absolute enthalpy of hydration of the proton do not appear to be very dependent on the model chosen. Results for the quadrupole of the water molecule 0 in the direction of the ja axis obtained from the three equations are, respectively, 0.70, 0.58 and 0.81 Xl0-26 e.s.u. these magnitudes correspond more closely than the analogous values of Halliwell and Nyburg to a result of quantum mechanical calculation, namely 0 0.43 X 10-2a... 

Final infiltration rates on both types of runs, however, became appreciably the same. The general equation fitting the infiltration data obtained by Free et al was found by these investigators to be... 

Figure 3 shows that the Gordon-Taylor equation fits the quenched data for the PVC/PCL blends quite well. The thermograms for the blends of 25, 35, and 50% PVC display PCL heats of fusion, and conse-... 

Different values of the constant and exponent r were used for different system geometries and operating conditions. Thus, for the turbine agitators at a Reynolds number less than 7400, was 0.00058 and r was 1.4. For the turbine agitators at a Reynolds number above 7400, was 0.62 and r was 0.62. For the propellers, over a range of Reynolds numbers from 3300 to 330,000, was 0.0043, and r was 1.0. In every case, the Schmidt number exponent s was 0.5. Although these equations fit the data fairly well, there is a scatter of the individual points. Hence, for any particular solid-liquid combination at constant temperature in a... 

This equation fitted the experimental data within experimental error. 

If the plotted points fall on a straight line, the equation fits the data. Choose two points on the line—(pi./i) and (p2, fz)—and calculate a and b as outlined in the previous section. 

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