Integrated Graphics

These are software packages that have the ability to perform computations using several computational techniques. Most also have an integrated graphic user interface. 

To solve the right side of the Raleigh-like equation, integrate graphically by plotting ... 

Thus, from Figure 14.9, the McCabe-Thiele diagram can be used to determine the reflux ratio for a given xa,b-This allows Equation 14.19 to be integrated graphically, as shown in Figure 14.10. 

Table 11,1.1 contains a workup of the data in terms of the above analysis. In the more general case one should be sure to use appropriate averaging techniques or graphical integration to determine both F(t) and T. When there is an abundance of data, plot it, draw a smooth curve, and integrate graphically instead of using the strictly numerical procedure employed above. 

Momentum Dissipation of a Gas-Solid Two-Phase Jet. Gas velocity profiles in a gas-solid two-phase jet inside a fluidized bed were determined at five different horizontal planes perpendicular to jet direction using a pitot tube (Yang and Keaims, 1980). The velocity profiles were integrated graphically, and gas entrainment into a jet was found to occur primarily at the base of the jet. 

Using these values to evaluate the integral graphically,... 

The needed ll-r js, versus data are determined in Table E18.5 and are plotted in Fig. E18.5. Integrating graphically then gives... 

If Vj. is to be found and the exit conditions are known, then the procedure is direct. Pick a number of values and integrate graphically. 

To evaluate this integral graphically, we need to plot ... 

To evaluate the integral graphically, it is best to replot our data as 1/(HS - H) versus T. Table 5.5 summarizes these data, and Figure 5.15 shows the plot. We can now evaluate the area under the curve between the inlet and exit water temperatures by counting squares in the shaded region. From this the solution is... 

Related Calculation. When the equilibrium and/or operating lines are curved, Eqs. (11.27) and (11.28) do not apply exactly. In this case, it is necessary to base the design on the individual number of transfer units for the liquid resistance and integrate graphically to determine Nt. This is illustrated in the following example. 

The behavior of metal redox electrodes in general will now be discussed in connection with Eq. (5). For this purpose the distribution functions for free and occupied electron levels are plotted on the same scale in parallel and are integrated graphically over the products of these functions for equilibrium conditions (Fig. 7). For simplicity it is assumed that K should be approximately constant. The scales axe related to one another by Eq. (6). ft can be shown that the energy level equivalent to AF0 must be between the peaks of Wox and Wre( in Fig. 6, It is further assumed that the concentrations cox and cred 3X6 equal. 

One way would of course be to plot Cp versus 7, draw a curve by visual inspection through the points at which Cp is known, and estimate the integral graphically as the area under the curve from 7j to T2. This is a cumbersome procedure, however, even if you have access to a planimeter, a device that can calculate the area under a traced-out curve. 

This is the general form of the Rayleigh equation. When the relationship between y and x is known, the equation may be integrated graphically or numerically. 

Equation (18.75) is known as the Rayleigh equation. The function dx/ y — x) can be integrated graphically or numerically using tabulated equilibrium data or an equilibrium curve. 

However, the appreciation of the role of computers in science is developing rapidly. For example, the introduction of more powerful computers with integral graphics facilities have led to significant applications in chemistry (see a number of general articles which have appeared on the use of mini- and microcomputers as workstations in chemical laboratories [3-5]). 

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