The Calculation Procedure

As the feed composition approaches a plait point, the rate of convergence of the calculation procedure is markedly reduced. Typically, 10 to 20 iterations are required, as shown in Cases 2 and 6 for ternary type-I systems. Very near a plait point, convergence can be extremely slow, requiring 50 iterations or more. ELIPS checks for these situations, terminates without a solution, and returns an error flag (ERR=7) to avoid unwarranted computational effort. This is not a significant disadvantage since liquid-liquid separations are not intentionally conducted near plait points. 

The calculational procedure employed in BLIPS, when used with the particular initial phase-composition estimated included in the subroutine, has converged satisfactorily for all systems we have encountered (except very near plait points as noted). 

Let us consider the calculation of sensitivity threshold in the case when the cracks are revealing by PT method. Constant distance H between crack s walls along the whole defect s depth is assumed for the simplicity. The calculation procedure depends on the dispersity of dry developer s powder [1]. Simple formula has to be used in the case when developer s effective radius of pores IC, which depends mainly on average particle s size, is smaller than crack s width H. One can use formula (1) when Re is small enough being less than the value corresponding maximum sensitivity (0,25 - 1 pm). For example. Re = 0,25 pm in the case when fine-dispersed magnesia oxide powder is used as the developer. In this case minimum crack s width H that can be detected at prescribed depth lo is calculated as... 

Computer codes are used for the calculational procedures which provide highly detailed data, eg, the Ruby code (70). Rapid, short-form methods yielding very good first approximations, such as the Kamlet equations, are also available (71—74). Both modeling approaches show good agreement with experimental data obtained ia measures of performance. A comparison of calculated and experimental explosive detonation velocities is shown ia Table 5. 

Figure 1 A stepwise view of the Verlet integration algorithm and its variants, (a) The basic Verlet method, (b) Leap-frog integration, (c) Velocity Verlet integration. At each algorithm dark and light gray cells indicate the initial and calculating variables, respectively. The numbers in the cells represent the orders m the calculation procedures. The arrows point from the data that are used in the calculation of the variable that is being calculated at each step.

The calculation procedure for temperature correction factors won t work for a temperature cross in a single shell pass, but this is an undesirable situation anyway. 

Once all computations are completed, SCREEN summarizes the maximum concentrations for each of the calculation procedures examined. Before execution terminates, whether it is after complex terrain calculations are completed or at the end of the simple terrain calculations, you are given the option of printing a hardcopy of the results. 

Burning Pit Flare Sizing - The burning-pit area is sized to provide sufficient surface to vaporize and bum liquid at a rate equal to the maximum incoming liquid rate. The calculation procedure is as follows ... 

Application of this procedure to inadvertently ignited safety valve discharges can involve a special problem. Certain combinations of pressure ratio and length of safety valve riser can result in choked flow, with a pressure discontinuity at the exit. The pressure of the jet then adjusts to atmospheric pressure in a system of shock waves or expansion waves over a distance of a few pipe diameters. These waves can affect the local mixing of the jet with the crosswind. Since the calculation procedure incorporates correlations for subsonic jets, it cannot be expected to be entirely accurate in this case. Nevertheless, since the wave system... 

The calculation procedures just described are methods for predicting shortterm GLC s for single stack cases. In the calculation of short-term GLC s it is as sinned that meteorological conditions are constant throughout the measuring time period. Short-term time periods are usually considered to be 1 hour or less. The averaging times for the various methods discussed are as follows ... 

Calculations were performed for two different venting rates, namely 3 and 5 minutes. Note that the calculation procedure predicts short-term GLC s for the single stack. This means that meteorological conditions are assumed to be... 

The stopwatch technique for determining emission volume flow rate is based on measuring with a stopwatch the elapsed time for fume to rise between two known levels (e.g., Zj, Z,). For this test procedure to be valid, the test must be carried out in a region where the rising fume clearly exhibits buoyancy-dominated plume behavior. The calculation procedure depends on a good estimate of the location of the virtual origin of the plume and the heat release for the process. 

There is more than one solution to the SCF equations for the system, and the calculation procedure converges to a solution which is not the minimum (often a saddle point in wavefunction space). This indicates an RHF-to-RHF or UHF-to-UHF instability, depending on the wavefunction type. 

The calculation procedure for single-stage noncondensing general-purpose turbine is as follows ... 

When tested in accordance with the methods given in Table 20.1 the properties of the commercial butane and commercial propane shall be in accordance with the limiting requirements given in that table. For gauge vapor pressure, either the direct measurements method described in BS 3324 or the calculation procedure described in Appendix C of this standard shall be used. 

We have entered into some details of the method of Poincar6 because it opened an entirely new approach to nonlinear problems encountered in applications. Moreover, the method is very general, since by taking more terms in the series solution (6-65), one can obtain approximations of higher order. However, the drawback of the method is its complexity, which resulted in efforts being directed toward a simplification of the calculating procedure. 

At the end of 24 hours of continuous process the system was shut down. The knowledge of flowed buffer volumes and of the optical densities inside and downstream each ultrafiltration stage allowed to estimate product distribution (see appendix for mass-balance equations and the calculation procedure). The content of each cell was recovered and ffeeze-dried in order to be stored and used for subsequent kinetic experiments. A schematic flow-sheet of the whole procedure is illustrated in figure 1. 

Of the gas holdup tine are obtained by regression procedures after testing the linearity of the hoaologous series plot and selecting an appropriate nuadser of standards to give the required statistical accuracy In the calculation procedure (353,354. ... 

In this chapter the calculation procedures used in flow-sheeting have for convenience been divided into manual calculation procedures and computer-aided procedures. 

Only the thermal design will be carried out, to illustrate the calculation procedure for an exchanger with a divided shell. 

This method uses simple, unsophisticated, methods to estimate the two-phase pressure drop through the exchanger and piping, and the convective boiling heat transfer coefficient. The calculation procedure is set out below and illustrated in Example 12.11... 

This equation, of course, contains information regarding stability, and as it is written, implies that one may match properties on the LHS with the point (-1,0) on the complex plane. The form in (7-2a) also imphes that in the process of analyzing the closed-loop stability property, the calculation procedures (or computer programs) only require the open-loop transfer functions. For complex problems, this fact eliminates unnecessary algebra. We just state the Nyquist stability criterion here.1... 

The calculation procedures can be extended to multicomponent systems using shortcut or rigorous simulation of the column as the batch progresses6. 

As a simplified initial approach to the problem, we chose a polymethylene chain with a single spin residing at every other carbon center, to allow sufficient flexibility between spins. The calculational procedure is based on that of Flory and Mark (16), with conformer parameters taken from Abe, et al. (17) and Yoon, et al. (18, 19) The elongation and field directions were col I inear. 

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