Time Zero at Start-up

Example 8 Cumulative Cash Position Table (Time Zero at Start-up) A specialty chemical company is considering the manufacture of an additive for use in the plastics industry. The following is a list of production, sales, and cash operating expenses. 

Cumulative Cash Position Plot A pictorial representation of the cumulative cash flows as a function of time is the cumulative cash position plot. All expenditures for capital as well as revenue from sales are plotted as a function of time. Figure 9-11 is such an idealized plot showing time zero at start-up in part a and time zero when the first funds are expended in part b. It should be understood that the plots have been idealized for illustration purposes. Expenditures are usually stepwise, and accumulated cash flow from sales is seldom a straightline but more likely a curve with respect to time. 

Example 8 Cumulative Cash Position Table (Time Zero at Start-up). 9-28... 

An input pulse of fairly arbitrary shape is put into the process. This pulse starts and ends at the same value and is often Just a square pulse (i.e., a step up at time zero and a step back to the original value at a later lime t ). See Fig. 14.3. The response of the output is recorded. It typically returns eventually to its original steadystate value, If C(,j and m, are perturbations from steadystate, they start and end at zero. The situation where the output does not return to zero will be discussed in Sec. 14.3.4,... 

Set RAMPTIME = lOnSec in the. OPTIONS statement, if available. This statement ramps all independent sources up from zero at the beginning of the transient analysis. The statement is beneficial if the transient analysis will not start. Take care to allow enough time for sources to ramp up, otherwise this statement could do more harm than good. 

The buildup of the H2 concentration, for any given depth x, starts with all its time derivatives zero at t = 0, increases gradually, and after a depth-dependent induction time becomes linear in t. The unbounded growth can be truncated by allowing the molecules either to dissociate or to diffuse. Dissociation will of course modify the development of the H° distribution molecular diffusion will not. As regards dissociation, there are to date no time-dependent solutions for this problem available presumably if the molecules are immobile, they would show an approach to a flat thermal-equilibrium distribution, which would extend to deeper depths at longer times. The case of diffusion without dissociation will be taken up in the paragraphs to follow. 

Figure 6 shows in a cylindrical coordinate (radial/thm-plane) how H2 depletes and N2 pressure builds up with time. At the center of the H2-starved region, the N2 pressure becomes higher than 80 kPaabs after 1 s. The radius of this N2 bubble grows to 7 mm after 10 s and covers 80% of the liquid-water-blocked region at 100 s (near steady-state). The H2 pressure drops quickly to zero at the edge of the N2 bubble, within which the cathode potential rises sharply, and the carbon corrosion rate starts to increase, as shown in Fig. 7. Conventional DM has a value of permeability ranging from 1 to 10 Darcy. There is no impact of DM permeability within its realistic range.14 N2 crossover through the membrane results in N2 pressure build-up in the H2-starved anode region. As a result, convective...

First, let us consider a situation in which the concentration starts at zero and goes up to a steady-state value. An example is a clean lake in which someone starts dumping some pollutant at a constant rate (perhaps the green dye mentioned above). Because the dumping just started, the flow of the pollutant into the lake is greater than its flow out of the lake, and the flow into the lake is constant. We know that the concentration at time = 0 is... 

Above result is of central importance for the study of harmonic excitation of a shear layer with the excitation having a finite start-up time. Usage of the above, allows one to distinguish between the transient and asymptotic part of the receptivity solution of a shear layer to a harmonic excitation starting at a finite time. This was used in Sengupta et al. (1994) to study the receptivity of zero pressure gradient shear layer to harmonic excitation. 

The exponential term in the conversion equation arises from the assumed start-up condition of a reactor filled only with degased water and then fed at time zero with a stream having monomer concentration [Mp],... 

Figure 3.2 Trouton ratio, Tr, of uniaxial extensional viscosity to zero-shear viscosity jq after start-up of steady uniaxial extension at a rate of 1 sec i for a Boger fluid consisting of a 0.185 wt% solution of flexible polyisobutylene (Mu, = 2.11 x 10 ) in a solvent composed mostly of viscous polybutene with some added kerosene (solid line). The dashed line is a fit of a multimode FENE dumbbell model, where each mode is represented by a FENE dumbbell model, with a spring law given by Eq. (3-56), without preaveraging, as described in Section 3.6.2.2.I. The relaxation times were obtained by fitting the linear viscoelastic data, G (co) and G"(cu). The slowest mode, with ri = 5 sec, dominates the behavior at large strains the best fit is obtained by choosing for it an extensibility parameter of = 40,000. The value of S — = 3(0.82) n/C(x, predicted from the...

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