Plotting curves

Figure 6.30 shows the grand composite curve plotted from the problem table cascade in Fig. 6.186. The starting point for the flue gas is an actual temperature of 1800 C, which corresponds to a shifl ed temperature of (1800 — 25) = mS C on the grand composite curve. The flue gas profile is not restricted above the pinch and can be cooled to pinch temperature corresponding to a shifted temperature of 145 C before venting to the atmosphere. The actual stack temperature is thus 145 + 25= 170°C. This is just above the acid dew point of 160 C. Now calculate the fuel consumption ...

Figure 16.19 shows the grand composite curve plotted from the problem table cascade. The two levels of steam generation are shown. 

It is possible for some projects to reach a stage at which repairs, replacements, etc., can exceed net earnings in a particular year. In this case the cumulative-discounted-cash-flow or net-present-value curve plotted against time has a genuine maximum. 

FIG. 20-1 Particle -size distribution curve plotted on linear axes,... 

Measurement versus Equipment Performance Pumps that are in reasonable condition typically operate within 5 percent of their pump curve. Consequently, pressures and flows that are inconsistent with the pump curve imply that the indicated flow and/or pressure are incorrecl . Figure 30-16 shows a single impeller curve plotted as head versus flow. The point shown is inconsistent with the pump operation. Therefore, that pair of flow and pressure measurements is not validated and should not be used in the subsequent steps. 

Figures 12 and 13 illustrate two of the more commonly used methods for displaying societal risk results (1) an F-N curve and (2) a risk profile. The F-N curve plots the cumulative frequencies of events causing N or more impacts, with the number of impacts (N) shown on the horizontal axis. With the F-N curve you can easily see the expected frequency of accidents that could harm greater than a specified number of people. F-N curve plots are almost always presented on logarithmic scales because of...

Systems for curve plotting, documentation, and reporting Data Inputs... 

If a confined fluid is thermodynamically open to a bulk reservoir, its exposure to a shear strain generally gives rise to an apparent multiplicity of microstates all compatible with a unique macrostate of the fluid. To illustrate the associated problem, consider the normal stress which can be computed for various substrate separations in grand canonical ensemble Monte Carlo simulations. A typical curve, plotted in Fig. 16, shows the oscillatory decay discussed in Sec. IV A 2. Suppose that instead... 

Consecutive reactions involving one first-order reaction and one second-order reaction, or two second-order reactions, are very difficult problems. Chien has obtained closed-form integral solutions for many of the possible kinetic schemes, but the results are too complex for straightforward application of the equations. Chien recommends that the kineticist follow the concentration of the initial reactant A, and from this information rate constant k, can be estimated. Then families of curves plotted for the various kinetic schemes, making use of an abscissa scale that is a function of c kit, are compared with concentration-time data for an intermediate or product, seeking a match that will identify the kinetic scheme and possibly lead to additional rate constant estimates. 

Kurven-schar, /. group or system of curves, -schreiber, m. curve tracer, -zacke, /. iag (sharp change in direction) in a curve, -zeichnen, n. curve plotting. -zug, m. curve. 

The behavior of the failure rate as a function of time can be gaged from a hazard plot. If data are plotted on exponential hazard paper, the derivative of the cumulative hazard function at some time is the instantaneous failure rate at that time. Since time to failure is plotted as a function of the cumulative hazard, the instantaneous failure rate is actually the reciprocal of the slope of the plotted data, and the slope of the plotted data corresponds to the instantaneous mean time to failure. For the data that are plotted on one of the other hazard papers and that give a curved plot, one can determine from examining the changing slope of the plot whether the tme failure rate is increasing or decreasing relative to the failure rate of the theoretical distribution for the paper. Such information on the behavior of the failure rate cannot be obtained from probability plots. 

A clean first-order process may erroneously appear to be a biphasic one, and vice versa. If the distortion to the property-time curve is not so evident as in the example, there might be a smooth rise or fall from reactant to product. The linearity of the plot of In (Y, - Kcc) versus time depends on the end point reading Yr.. One must be cautious, however, in ascribing a mildly curved plot of In Y, - W) versus time to a biphasic pattern. Were the observed value of Yx off by a small amount, a simple adjustment could give a straight-line plot indicative of first-order kinetics. Of course, if Tec is adjusted to force linearity, one must surely ask whether the revised value of Yx represents a reasonable extrapolation of the data, lest the proper but more complex reaction pattern be concealed. 

As an example of the problem that arises when the mechanism changes, consider the data presented in Figure 10-3. Part (a) depicts the apparent rate constants for semi-carbazone formation measured at an intermediate pH of 3.9. The rate-controlling step is not clearly defined under such conditions, and a curved plot is obtained. 

Fig. 23—A schematic force curve plotted as a function of sliding velocity. A viscous friction forms the background of the force curve upon which the frictions from superharmonic and parametric resonance are superposed.

Figure 1.30. A histogram of raw weights from Figure 1.29 and the distribution of residuals that resulted after subtraction of a shifted box-car average are superimposed. The CP-curve, plotted with the (NPS) option in HISTO, is for the raw weights the corresponding curve for the residuals would be about twice as steep. The asymmetry of the raw-weight distribution is evident both in the histogram and the lack of linearity of the CP-curve it is due to many subpopulations of product being lumped into one batch. Every time a mechanic makes an adjustment on a knife, a new subpopulation is created. The residuals appear to be normally distributed, however.

In the Dynamic method a flow of He is passed over the sample at 77 K. A small amount of N2 is introduced into the He stream. The gas stream coming from the sample is monitored using mass spectroscopy. N2 is only detected after a monolayer is formed. The N2 supply is then switched off and the desorption curve plotted. Integration of this curve gives the information required for the BET equation. 

In experimental practice, we usually ignore the temperature dependence of the prefactor and extract the activation energy by making an Arrhenius plot, as discussed in Chapter 2. The consequence of collision theory, however, is that a curved plot, rather than a straight line, will result if the activation energy is of the same order of k T. 

For the amino-borane dehydrocoupling using [Rh(l,5-cod)(p-Cl)]2 as starting catalyst, an induction period and a sigmoid-shaped kinetic curve (plot of substrate conversion versus time) were also observed, consistent with metal-particle formation. But, for Ph2PH BH3... 

Polymers in solution or as melts exhibit a shear rate dependent viscosity above a critical shear rate, ycrit. The region in which the viscosity is a decreasing function of shear rate is called the non-Newtonian or power-law region. As the concentration increases, for constant molar mass, the value of ycrit is shifted to lower shear rates. Below ycrit the solution viscosity is independent of shear rate and is called the zero-shear viscosity, q0. Flow curves (plots of log q vs. log y) for a very high molar mass polystyrene in toluene at various concentrations are presented in Fig. 9. The transition from the shear-rate independent to the shear-rate dependent viscosity occurs over a relatively small region due to the narrow molar mass distribution of the PS sample. 

Note, too, the convergence at low agonist concentrations of the curves plotted in Figure 1.27. The antagonist becomes less active when the response is small, because there are fewer receptors in the AR form available to combine with C. Again, in contrast to the other kinds of antagonism that have been described, there is no initial parallel displacement of the curves (even if many spare receptors are present), and the Schild equation is never obeyed. 

B) Corresponding sum intensity decay curves plotted on a semilogarithmic scale. From Ref. 86 with permission. 

Figure 5. Logarithm of the retractive force at 49% strain (lower curve) and sample temperature (upper curve) plotted against logarithm of time reduced to 263 K. Cross-links are introduced at log t/aT is 3 in the glassy state where the spike on the force curve is due to thermal contraction upon cooling below the glass transition temperature. Equilibrium force at 263 K after cross-linking is feQ. (Reproduced, with permission, from Ref. 27. Copyright 1981, Journal of Chemical Physics.)...

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