Dimensionless cumulative distributions

Fir) Cumulative distribution function expressed in terms of tube radius for monotonic velocity profile Dimensionless 15.29... 

In the first instance, when the results were analyzed by simple mean and standard deviation analysis, Amico et al. [16-18] got large relative standard deviatiOTi, indicating limitatimi of this method for the proper characterizatiOTi of the diameter. Then, they used Weibull probability density and cumulative distribution functions [20,56,58] to estimate two parameters, the characteristic life and a dimensionless positive pure number, which were supposed to determine the shape and scale of the distribution curve. For this, they adopted two methods, the maximum likelihood technique, which requires the solution of two nonlinear equations, and the analytical method using the probability plot as mentioned earlier for coir fibers. 

F Cumulative residence time distribution Dimensionless Dimensionless... 

The cumulative residence-time distribution function F(t) is defined as the fraction of exit stream that is of age 0 to t (i.e., of age t) it is also the probability that a fluid element that entered at t = 0 has left at or by time t. Since it is defined as a fraction, it is dimensionless. Furthermore, since F(O) = 0, that is, no fluid (of age 0) leaves the vessel before time 0 and F( ) = 1, that is, all fluid leaving the vessel is of age 0 to or all fluid entering at time 0 has left by time then... 

FIGURE 4.8 Cumulative size distribution of grovind material after various dimensionless times in a continuous open-circuit ball mill, size selectivity Sbc) = kxfi, /3 = 0. Taken from AIME [22] and Randolph and Larson [23],... 

FIGURE 7.15 Cumulative weight distribution versus dimensionless size for a cascade of reactors with nucleation only in the first tank or for a dispersed plug flow reactor with nucleation only at the entrance to the reactor. Data from Abegg and Balaktishnan [331. 

We now move to the consideration of reactors with an assigned residence time distribution (RTD)y(O. where t is the dimensionless residence time (i.e., the dimensional one times the average frequency factor in the feed). In this section, we indicate with curly braces integrals over t ranging from 0 to < . Then [/(t) = 1 and T = [tj t). We also make use of the complementary cumulative RTD, F(t), which is defined as... 

The filaments formed are, of course, still quite polydisperse in length. Figure 6.9 shows the time evolution of the polydispersity index (p.i.). The p.i. is a dimensionless parameter calculated from a cumulant s analysis of the measured intensity autocorrelation function. It is used to characterize the relative shape of the cluster-size distributions. For the electrolyte-free sample (0 mM), aggregation... 

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