Graphic method

A graphical method, proposed by Zimm (thus tenned the Zinnn plot), can be used to perfomi this double extrapolation to detemiine the molecular weight, the radius of gyration and the second virial coefficient. An example of a Zinnn plot is shown in figure Bl.9.6 where the light scattering data from a solution of poly... 

Derive this relationship and explain the graphical method it suggests for evaluating and p. The critical temperatures for precipitation for the data shown in Fig. 8.3b are the following ... 

Use the graphical method outlined above to evaluate and and, from these, X for polyisobutylene in diisobutylketone. 

As can be seen from Figure 11, the graphical method does provide a good visual means for analysing life data and is easUy understood and explained. If used with discretion, graphical analysis can provide a useful means for data analysis. 

Gas-phase temperatures have been obtained by an extension of the graphical method illustrated (22). When equation 30 is divided by equation 34, the result is... 

This equation relates the (instantaneous) copolymer composition with the monomer feed of M and M2. Values for and are usually determined by graphical methods (9,10). Today, with the prevalence of powerful desktop computers, numerical minimisa tion methods are often used (11—14). 

W. C. Marshall, Graphical Methods for Schools, Colleges, Statisticians, Engineers and Executives, McGraw-HiU Book Co., Inc., New York, 1921, pp. 

Note that use of the Lee-Kesler fit [Eq. (2-78)] would give a slightly more accurate answer than the graphical method, and this fit is used for any computer applications. 

Values of Z and of (3Z/3T)p come from experimental PVT data, and the integrals in Eqs. (4-158), (4-159), and (4-161) may be evaluated by numerical or graphical methods. Alternatively, the integrals are expressed analytically when Z is given by an equation of state. Residual properties are therefore evaluated from PVT data or from an appropriate equation of state. 

Various numerical and graphical methods are used for unsteady-state conduction problems, in particular the Schmidt graphical method (Foppls Festschrift, Springer-Verlag, Berhn, 1924). These methods are very useful because any form of initial temperature distribution may be used. 

Typical methods are those of F. C. Zevnik and R. L. Buchanan [Chem. Eng. Progi , 59, 70-77 (Feb. 1963)] and J. H. Taylor Eng. 6-Proc. Econ., 2, 259-267, 1977). The former is mainly a graphical method of estimating the cost per functional unit (Cp) based on the capacity, the maximum pressure, the maximum temperature, and the materials of construction. The Taylor method requires the determination of the costliness index, which is dependent on the complexity of the process. A simpler method was suggested by S. R. Timms (M.Phil. thesis, Aston University, England, 1980) to give the battery hmits cost for gas phase processes only in U.S. dollars with a Marshall and Swift index of 1000. The simple equation is... 

A. Pikiilik and H. E. Diaz [Chem. Eng., 84, 106-122 (Oct. 10, 1977)] presented a graphical method for estimating the fabricated cost of distillation cohimns and pressnre vessels, storage tanks, fired heaters, pnmps and drivers, compressors and drivers, and vacnnm eqnipment. 

A useful method for a binary mixture employs an analysis based on the McCabe-Thiele graphical method. In addition to the usual assumptions of adiabatic column and equimolal overflow on the trays, the following procedure assumes neghgible holdup of hquid on the trays, in the column, and in the condenser. 

Figure 14-6 illustrates the graphical method for a three-theoretical-plate system. Note that in gas absorption the operating line is above the equihbrium curve, whereas in distillation this does not happen. In gas stripping, the operating line will be below the equihbrium curve. 

FIG. 14-6 Graphical method for a three-theoretical-plate gas-ahsorption tower with inlet-liquor composition and inlet-gas composition y. ... 

For the first time through a liqmd-liquid extrac tion problem, the right-triangular graphical method may be preferred because it is completely rigorous for a ternary system and reasonably easy to understand. However, the shortcut methods with the Bancroft coordinates and the Kremser equations become valuable time-savers for repetitive calculations and for data reduction from experimental runs. The calculation of pseudo inlet compositions and the use of the McCabe-Thiele type of stage calculations lend themselves readily to programmable calculator or computer routines with a simple correlation of equilibrium data. 

Graphical methods of evaluating efficiency, using sieve analyses, are also employed and are recommended when serious research on screening is done. 

It therefore appears that other hydrocarbons than medrane take part, but to a lesser extent. The other species which were considered in this calculation were SiCl, SiH4, CH3CI, SiHs, H, Si, Sia, Cl and CI2, all of which are gaseous at this temperature. It is difficult to predict before dris calculation what will be the major species, and attempts to limit die number of compounds which are included is to some extent subjective, but this can be conected by using the graphical method as a preliminaty. 

MT McMahon, E Oldfield. Determination of order parameters and correlation times m proteins A comparison between Bayesian, Monte Carlo and simple graphical methods. I Biomol NMR 13 133-137, 1999. 

Solution Constructed McCabe-Thiele diagram. Pinch found. (See Section 3 Fractionators Graphical Methods.)... 

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