Distance-time diagram

A root velocity can be defined as the rate of advance of a given value of an H function root. For any given composition, roots with lower index numbers have lower velocities. An arbitrary initial noncoherent boundary involving variations of all roots thus is resolved, upon undisturbed development, into separate variations of the roots. This is shown by schematic trajectories of root values in a distance-time diagram in Figure 6. After resolution, each trajectory bundle involves variation of... 

Figure 9.8 The distance-time diagram illustrating the progressive formation of an isotachic train for a binary mixture. H.-K. Rhee and N. R. Amundson, AICHE J, 28 (1982) 423 (Fig. 2). Reproduced by permission of the American Institute of Chemical Engineers. 19S2 AIChE. All rights reserved.

As an example. Figure 9.8 illustrates the development of a displacement train for a binary mixture. It provides a distance-time diagram indicating the boimdaries of the different domains defined in the previous theoretical discussions. 

Once the values of tOi for the different states involved have been identified and calculated, all the wave interactions can be analyzed in detail [15]. The same approach can be applied to multicomponent samples [10]. As mentioned earlier, the /z-transform and the ra-transform give the same results. Distance-time diagrams, such as the one just discussed and shown in Figure 9.8, can be constructed using the fz-transform as well [9,11,12,14]. 

Even in an ideal coltunn, the reorganization of the distribution of the component concentrations between the injection and the formation of the isotachic train requires a certain time, i.e., it cannot be achieved in less than a minimum migration distance. This distance can be derived from the distance-time diagram. 

Distance Time diagram In displacement chromatography, diagram indicating the trajectory of the concentration shocks and the regions where diffuse boimd-aries appear. 

The remaining calculations of for this example were done with a short computer program. Cols. 2 and 3 of Table 5.27 contain pairs of coordinates on the distance/time diagram that... 

The path of the rear of the polymer frcmt and the saturation paths in the drive water can be determined with the method presented in Sec. 5.7.2, Program PREAR in Appendix Cwas used to determine the values of S, ., xp, and tp when the saturation interval between 1 —Sgr and 5 3 was divided into 100 increments. Fig. 5.62 presents Ae distance/time diagram for 0[Pg.41]

Fig. 5.63 is the distance/time diagram for the displacement process. After the polymer slug is overtaken by the drive water, the oil bank is eroded continually by the drive water until the drive-water saturation at the rear of the oil bank decreases to. The... 

In Appendix I, Lutzky stated that it is instructive to display the Taylor Wave in the form of a space-time diagram (See Fig 1). Since all of the dependent variables are functions only of the quantity r/t, as was shown by Taylor (where r is distance and t is time), constant values of these variables are propagated along straight lines in the (r-t) plane, fanning out from the origin. 

Fignre 4.9 shows the head-on collision of two waves. Local collisions at several distances d from the wave origin at the central cap are analyzed in the space-time diagram. 

In consequence, one finds, for any component Ai for which exactly two of the parameters differ from zero as the distance between the extrema and the point of inflection within a concentration-time diagram in general. 

Figure 2-1 Breakdown of velocity-time diagram into sub-sections By adding up the different squares we get the distance travelled.

Since accurate means of measuring distance, time, and velocity were not available, a scheme was adopted where distances on a geometrical diagram are proportional to all three of these quantities. This procedure is described in passage 281 of the Galileo text in terms of Fig. 110. 

Stmctures that form as a function of temperature and time on cooling for a steel of a given composition are usually represented graphically by continuous-cooling and isothermal-transformation diagrams. Another constituent that sometimes forms at temperatures below that for peadite is bainite, which consists of ferrite and Fe C, but in a less well-defined arrangement than peadite. There is not sufficient temperature and time for carbon atoms to diffuse long distances, and a rather poody defined acicular or feathery stmcture results. 

Figure 2.10. (a) An Eulerian x-t diagram of a shock wave propagating into a material in motion. The fluid particle travels a distance ut, and the shock travels a distance Uti in time ti. (b) A Lagrangian h-t diagram of the same sequence. The shock travels a distance Cti in this system. 

The properties required of a material in order for it to support a stable shock wave were listed and discussed. Rarefaction, or release waves were defined and their behavior was described. The useful tool of plotting shocks, rarefactions, and boundaries in the time-distance plane (the x-t diagram) was introduced. The Lagrangian coordinate system was defined and contrasted to the more familiar Eulerian coordinate system. The Lagrangian system was then used to derive conservation equations for continuous flow in one dimension. 

Figure 6.7 shows a Lagrangian time-distance diagram of a symmetric impact by a driver plate with the target backed by a spall plate. The symmetry... 

Figure 6.7. Lagrangian time-distance diagram of a symmetric impact shock.

Figure S-IS. Representation of a reaction coordinate diagram by straight line trajectories determined by the condition of minimum time or distance. The reaction coordinate is specibed as the bond order of a bond formed in the reaction.

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