Curve-fit equation

Curve-fitting of the storage modulus master curve. All individual G (toa ) master curves were smoothed out and digitized equidistantly (d log(ua>p) 0.2). The data so obtained were analyzed with the following curve-fitting equations ... 

All expressions are given in equation form, and it is not necessary to read and interpolate any plots to solve the problems (i.e., the empirical data are represented analytically by curve-fitting equations). 

I derived this curve-fit equation from datasheets and data provided by Chemicon. For the cases included at least, I could confirm that the above equation was accurate to within 6% for all capacitor outer diameters in the range of 10mm to 76mm. And for diameters greater than 40mm, the error from the use of this formula was less than 1%. 

Various integrals are found with the curve fit equation. 

The next lines of the program, to line number 2480, establish curve-fitted equations. Refer to code lines 2420 through 2490. (See the program code listing in Table 1.7.) Note that linear equations between each of the given ASTM data points are made, giving an overall ASTM... 

This critical pressure Pc method is a curve fit of the API Fig. 4D4.1 [17]. Rather than just one curve-fit equation, however, the reader will soon realize there are seven curve-fit equations, code lines 4520 through 4580. Also, please realize that the mean average boiling point of each pseudocomponent is first calculated in code lines 3370 through... 

Values of Dv greater than 0.17 lb/ft3, the following curve-fit equations apply ... 

The following curve-fitted equations for sieve tray loading refer to Fig. 18-10 in the Chemical Engineer s Handbook [10,11]. 

Using these calculated ratios, AHAA and THDIA, a hole discharge coefficient factor CFCV is calculated from a curve-fitted equation in Fig. 18-14 in the Chemical Engineer s Handbook [14], CFCV is a factor in Eq. (3.112) for calculating the sieve tray dry pressure drop. 

CRE is the Boucher [3] Reynolds number calculation to derive a drag coefficient, CD. The CD factor is calculated in the program by a curve-fit equation as shown. The velocity, called the terminal droplet velocity, is calculated as the variable VT, also called the dropout velocity or the settling velocity. All three terms refer to this same variable. 

You may use this curve-fit equation to find Jh, or you may use the figure it was taken from, Fig. 28 in Kern [4], which is provided in App. A as Fig. A.2. Using Kern s figure is recommended as more accurate however, the figure and the curve-fit equation given here have equal accuracies in regard to the final exchanger hL or h0 calculation [2],... 

The preceding J factor calculations are curve-fitted equations from the GPS A. Engineering Data Book [15], Sec. 10, Fig. 10-15. 

It should also be noted that while the nomograph program reported here uses the WLF equation to calculate the shift factor, the data reduction scheme is not limited to the WLF equation. That is, any curve fitting equation that results in the calculation of a temperature shift factor can easily be added to the program and used for the generation of the master curve in the nomograph... 

The retention time tRjin and the second moment for the Gaussian profile (Eq. 6.61) have been replaced by variables indexed with g . These parameters tg and og must be optimized by curve fitting. Equation 6.143 is only suitable for symmetric peaks. Analytical solutions of, for example, the transport dispersive model (which describes asymmetric band broadening only for a very low number of stages) are not suited to describing the asymmetry often encountered in practical chromatograms. Thus, many different, mostly empirical functions have been developed for peak modeling. A recent extensive review by Marco and Bombi (2001) lists over 90 of them. 

Until recently, most mathematical models that were used to describe proton binding by humic substances were far too simple, and, consequently, served only as empirical curve-fitting equations. More recently, several authors have used mathematical models that treat humic substances as having... 

An example of a curve-fitted equation of state is shown in Figure 4 for the nonionic Ci2E6 while Figure 8 shows the fit for the surface pressure—log concentration curve for the same compound. A second- and third-order negative ( repulsion ) term and a fourth-order positive ( attraction ) term in the series expansion for In /is provide a good description of the experiments. 

A large number of equations have been proposed to describe the relationship between pressure and volume reduction during the compaction process. Many of these have an empirical basis and may relate to a particular material or range of pressures, while others attempt to define the complete process of densification. The equation that has been most widely used to describe the compaction of pharmaceutical powders is the Heckel equation (Heckel 1961). This equation, originally used to describe the densification of ceramics, is essentially a curve-fitting equation that provides reasonable correlation with the observed facts over a wide range of pressures. 

Northwest Pipeline Corporation, Internal Company memo correlating IGT Bulletin 8 with Least Squares Curve Fit equation. 

Of the three equations available to interpret adsorption isotherms, the Langmuir and BET equations are based on general models of adsorption and are not derived from concepts of porosity. They could be described as curve-fitting equations. The Langmuir and BET equations, initially, were derived to interpret adsorption isotherms of non-porous carbons. Here, the concept of a surface area has a physical interpretation. Later, the equations were applied to isotherms derived from microporous materials and appeared to work, and values for monolayer coverage could be derived. However, the meaning of monolayer coverage in a microporous solid is an issue which has not been resolved to this day. 

---