Procedural errors

Equation (9-54) may be solved for i either graphically or by an iterative trial-and-error procedure. The value of i given by Eq. (9-54) is known as the discounted-cash-flow rate of return (DCFRR). It is also known as the profitability index, true rate of return, investor s rate of return, and interest rate of return. 

A trial-and-error procedure is required with any K-value correlation that takes into account the effect of composition. One cannot calculate K values until phase compositions are known, and those cannot be known until the K values are available to calculate them. For K as a function of T and P only, the DePriester charts provide good starting values for the iteration. These nomographs are shown in Fig. 13-14/7 andZ . SI versions of these charts have been developed by Dadyburjor [Chem. Eng. Prog., 74(4), 85 (1978)]. 

The problem is different from typical heat transfer problems. The heat balance is not straightforward because the outlet temperatures are unknown. A trial-and-error procedure is therefore required. 

Determination of friction factors for some fluid flow applications can involves a trial-and-error procedure because the friction factor is not a simple function of the Reynolds number. Process engineers, therefore, refer to a Moody chart that has been developed using the following relationships ... 

By trial and error procedure, determine the amount of liquid which flashes by an isoenthalpic (constant enthalpy) expansion to the critical flow pressure (or actual pressure if greater than critical) for the flashed vapor. 

The number of neurons to be used in the input/output layer are based on the number of input/output variables to be considered in the model. However, no algorithms are available for selecting a network structure or the number of hidden nodes. Zurada [16] has discussed several heuristic based techniques for this purpose. One hidden layer is more than sufficient for most problems. The number of neurons in the hidden layer neuron was selected by a trial-and-error procedure by monitoring the sum-of-squared error progression of the validation data set used during training. Details about this proce-... 

The minimum stripping medium (steam or gas) lean oil ratio is estimated by a trial and error procedure based on key component ... 

A trial-and-error procedure is needed to solve the cubic equation in T. ... 

A double trial-and-error procedure is needed to determine uq and Tq. If done only once, this is probably best done by hand. This is the approach used in the sample program. Simultaneous satisfaction of the boundary conditions for concentration and temperature was aided by using an output response that combined the two errors. If repeated evaluations are necessary, a two-dimensional Newton s method can be used. Dehne... 

Eqs. (IS) and (16) should be solved simultaneously by a trial and error procedure to obtain the optimum temperature and time. 

Eq. (18) is now a function of temperature only. It can be solved by any trial and error procedure such as successive substitution or regula falsi (Gerald (1978)). Having obtained the optimum temperature from Eq. (18), the corresponding minimum time can be calculated from Eq. (17). 

Following the first preliminary comparison, a next step could be to find a set of parameters, that give the best or optimal fit to the experimental data. This can be done by a manual, trial-and-error procedure or by using a more sophisticated mathematical technique which is aimed at finding those values for the system parameters that minimise the difference between values given by the model and those obtained by experiment. Such techniques are general, but are illustrated here with special reference to the dynamic behaviour of chemical reactors. 

One additional important reason why nonbonded parameters from quantum chemistry cannot be used directly, even if they could be calculated accurately, is that they have to implicitly account for everything that has been neglected three-body terms, polarization, etc. (One should add that this applies to experimental parameters as well A set of parameters describing a water dimer in vacuum will, in general, not give the correct properties of bulk liquid water.) Hence, in practice, it is much more useful to tune these parameters to reproduce thermodynamic or dynamical properties of bulk systems (fluids, polymers, etc.) [51-53], Recently, it has been shown, how the cumbersome trial-and-error procedure can be automated [54-56A],... 

Where the calculation of the net present value was straightforward, die determination of the rate of return requires a trial-and-error procedure. An interest rate is chosen and then the net present value is determined. If it is not zero, another interest rate is chosen and the net present value is recalculated. This is continued until a zero net present value is obtained. 

The general integral technique for the determination of reaction rate functions consists of the following trial-and-error procedure. 

Obviously this approach is not easily extended to cascades containing more than three reactors and, in those cases, an alternative trial and error procedure is preferable. One chooses a reactor volume and then determines the overall fraction conversion that would be obtained in a cascade of N reactors. When one s choice of individual reactor size meets the specified overall degree of conversion, the choice may be regarded as the desired solution. This latter approach is readily amenable to iterative programming techniques using a digital computer. 

This equation can be solved for T using a trial and error procedure. This gives T = 410 °K. Thus... 

A variation on the second approach involves a somewhat different manner of combining the equations used in the trial and error procedure. From equation 12.3.11,... 

The trial and error procedure outlined in Section 12.3.1.1 is quite general if appropriate modification is made for the use of 0S values and effective diffusivities. Thus we will start by assuming that rj = 0.20. From Figure 12.6, we find that s = 13.4. 

For isothermal systems, it is occasionally possible to eliminate the external surface concentrations between equations 12.6.1 and 12.6.2 and arrive at a global rate expression involving only bulk fluid compositions (e.g., equation 12.4.28 was derived in this manlier). In general, however, closed form solutions cannot be achieved and an iterative trial and error procedure must be employed to determine thq global rate. One possible approach is summarized below. 

However, solution of the difference equations requires a knowledge of the temperature at the end of the conversion increment. Consequently, a trial and error procedure is indicated. One assumes a value for the temperature at the end of the increment, computes Az from equation A, and checks the temperature assumption using equation B. Under normal circumstances, the... 

The mass velocity (G) is the unknown, which is equivalent to the mass flow rate because the pipe diameter is known. This requires a trial and error procedure, because neither the Reynolds nor Mach numbers can be calculated a priori. 

The procedure for an unknown diameter involves a trial-and-error procedure similar to the one for the unknown flow rate. 

The procedure of Lifson and Warshel leads to so-called consistent force fields (OFF) and operates as follows First a set of reliable experimental data, as many as possible (or feasible), is collected from a large set of molecules which belong to a family of molecules of interest. These data comprise, for instance, vibrational properties (Section 3.3.), structural quantities, thermochemical measurements, and crystal properties (heats of sublimation, lattice constants, lattice vibrations). We restrict our discussion to the first three kinds of experimental observation. All data used for the optimisation process are calculated and the differences between observed and calculated quantities evaluated. Subsequently the sum of the squares of these differences is minimised in an iterative process under variation of the potential constants. The ultimately resulting values for the potential constants are the best possible within the data set and analytical form of the chosen force field. Starting values of the potential constants for the least-squares process can be derived from the same sources as mentioned in connection with trial-and-error procedures. 

An alternative to this trial and error procedure for two pumps in parallel is to calculate QT from equation 4.32 for various values of the total head from known values of Q and Q2 at these total heads. The operating point for stable operation is at the intersection of the AhT against QT curve with the A/ts against Qs curve. 

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