Elapsed time

Fig. IV-3. Velocity profiles for particles suspended in water with elapsed time, due to spreading of oleic acid. Time after onset of spreading O, 5 sec, , 5 sec. (From Ref. 31.)...

In a study of tarnishing the parabolic law, Eq. VII-30, is obeyed, with kj = 0. The film thickness y, measured after a given constant elapsed time, is determined in a... 

Titrations may be automated using a pump to deliver the titrant at a constant flow rate, and a solenoid valve to control the flow (Figure 9.5). The volume of titrant delivered is determined by multiplying the flow rate by the elapsed time. Automated titrations offer the additional advantage of using a microcomputer for data storage and analysis. 

A chromatographic peak may be characterized in many ways, two of which are shown in Figure 12.7. The retention time, is the elapsed time from the introduction of the solute to the peak maximum. The retention time also can be measured indirectly as the volume of mobile phase eluting between the solute s introduction and the appearance of the solute s peak maximum. This is known as the retention volume, Vr. Dividing the retention volume by the mobile phase s flow rate, u, gives the retention time. 

An alternative to a fixed-time method is a variable-time method, in which we measure the time required for a reaction to proceed by a fixed amount. In this case the analyte s initial concentration is determined by the elapsed time, Af, with a higher concentration of analyte producing a smaller Af. For this reason variabletime integral methods are appropriate when the relationship between the detector s response and the concentration of analyte is not linear or is unknown. In the one-point variable-time integral method, the time needed to cause a desired change in concentration is measured from the start of the reaction. With the two-point variable-time integral method, the time required to effect a change in concentration is measured. 

One important application of the variable-time integral method is the quantitative analysis of catalysts, which is based on the catalyst s ability to increase the rate of a reaction. As the initial concentration of catalyst is increased, the time needed to reach the desired extent of reaction decreases. For many catalytic systems the relationship between the elapsed time, Af, and the initial concentration of analyte is... 

The reduction of the yellow-colored Mo(VI) complex to the blue-colored Mo(V) complex is a slow reaction. In the standard spectrophotometric method, it is difficult to reprodudbly control the amount of time that reagents are allowed to react before measuring the absorbance. To achieve good precision, therefore, the reaction is allowed sufficient time to proceed to completion before measuring the absorbance. In the FIA method, the flow rate and the dimensions of the reaction coil determine the elapsed time between sample introduction and the measurement of absorbance (about 30 s in this configuration). Since this time is precisely controlled, the reaction time is the same for all standards and samples. 

Suppose we define the rate of radial growth of the crystalline disks as r. Then disks originating from all nuclei within a distance rt of an arbitrary point, say, point X in Fig. 4.6a, will reach that point in an elapsed time t. If the average concentration of nuclei in the plane is N (per unit area), then the average number of fronts F which converge on x in tliis time interval is... 

Figure 4.6 The growth of disk-shaped crystals, (a) All crystals have been nucleated simultaneously. All crystals have the same radius rt after an elapsed time t. (b) Nucleation is sporadic. Crystal A has had enough time to reach point X, while B has not, although both originate in the same ring a distance r from x.

Real-time clocks (RTCs). Real-time systems are required to respond to events, as they occur, in a timely manner. This is especially crucial in process control systems where control actions applied at the wrong time may amplify process deviations or destabilize the processes. The nodes in the systems are interrupted periodically by the real-time clocks to maintain the ac tual elapsed times. 

Inflation (DCFRR) and Payback Period More insight into the effect of inflation on (DCFRR) calculations can be gained dv considering the payback period (PBP), which is defined as the elapsed time necessary for the positive aftertax cash flows from the project to... 

Figure 9-31 shows that the elapsed time necessary to reach a nominal (DCFRR) for a given project decreases sharply with inflation. This figure, hke Fig. 9-29, shows that the effect of inflation is to make a projec t seem more profitable than it ac tuaUy is. 

Data expressing moisture content in terms of elapsed time should be obtained and the results plotted as shown in Fig. 12-42. For purposes of analysis, the moisture-time curve must be differentiated... 

When a flocculated feed is added to a filter tank, there is a definite time lag before this material reaches the surface of the filter medium. Since this lag time is not known at the time of testing, a lag time of 8 to 10 minutes should be allowed before starting the first leaf test on a flocculated shiny. Two, or perhaps three, tests can be run before the elapsed time exceeds the probable retention time in the full-scale filter tank. With knowledge of the elapsed time after flocculation and data relating to the rate of degradation, the rates obtained on the leaf test runs can be adjusted to some constant lag time consistent with the anticipated full-sc e design. 

Refers to the elapsed time after an adhesive is applied until pressure effects curing. Intermediate-stage reaction step for various thermosetting resins. During this stage the material swells when in contact with certain liquids and... 

Assembly time Refers to the elapsed time after an adhesive is applied... 

This equation is the basis of linear viscoelasticity and simply indicates that, in a tensile test for example, for a fixed value of elapsed time, the stress will be directly proportional to the strain. The different types of response described are shown schematically in Fig. 2.1. 

Elapsed Time in Thousands of Reactor Years Fig. 2.7-1 ERMA simulation of a low pressure coolant injection system. The absence of oscillations in the convergence is evidence of voter statistics Reprinted with permission of EPRI. USA... 

The sound speed c, m s , is the velocity of propagation of the pressure variations. This depends on the physical properties of the medium and increases with the density of the medium. In air, for example, it is. 344 m s, while in water, 1410 m s and in concrete, 3000 m s . The elapsed time between successive compressions is called the period time T. 

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