Variable design

Traffic volume is expressed in ESALs. The conversion of mixed axial loads to ESAL is conducted with the use of equivalency coefficients related to the terminal serviceability value, pt, and the structural number, SN, of the pavement. For the design of new flexible pavements, it is suggested that equivalency coefficients corresponding to p, = 2.5 and SN = 5 be used (see Table 12.3). 

To calculate the cumulative number of ESALs over a design period of n years, the equations given in Section 13.5.1 are used. 

For the determination of traffic in the design lane (design traffic), if the cumula- 

The directional distribution factor, D, is usually 0.5 (50%). However, there are instances where more traffic is moving in one direction than the other. If this is the case, the pavement is designed with a greater number of ESAL. 

As for the lane distribution factor, Dl, if no other information is available, the methodology proposes to use values ranging between 100%, for sections with one lane in each direction, and 50%, for sections with four lanes in each direction. 

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If distillation is the choice of separator, then some preliminary selection of the major design variables must be made to allow the design to proceed. The first decision is operating pressure. As pressure is raised,... 

The last design variable which needs to be fixed before the design can proceed, but which is of lesser importance, is feed condition. Subcooled feed (i.e., below bubble point)... 

Computer solutions entail setting up component equiUbrium and component mass and enthalpy balances around each theoretical stage and specifying the required design variables as well as solving the large number of simultaneous equations required. The expHcit solution to these equations remains too complex for present methods. Studies to solve the mathematical problem by algorithm or iterational methods have been successflil and, with a few exceptions, the most complex distillation problems can be solved. 

Optimization. Optimi2ation of the design variables is an important yet often neglected step in the design of extractive distillation sequences. The cost of the solvent recovery (qv) step affects the optimi2ation and thus must also be included. Optimi2ation not only yields the most efficient extractive distillation design, it is also a prerequisite for vaUd comparisons with other separation sequences and methods. 

Extensive design and optimization studies have been carried out for this sequence (108). The principal optimization variables, ie, the design variables that have the largest impact on the economics of the process, are the redux ratio in the azeo-column the position of the tie-line for the mixture in the decanter, determined by the temperature and overall composition of the mixture in the decanter the position of the decanter composition on the decanter tie-line (see Reference 104 for a discussion of the importance of these variables) and the distillate composition from the entrainer recovery column. 

It is important to recognize that the effects of temperature on the liquid-phase diffusion coefficients and viscosities can be veiy large and therefore must be carefully accounted for when using /cl or data. For liquids the mass-transfer coefficient /cl is correlated in terms of design variables by relations of the form... 

The existing data indicate that fcja is proportional to the square root of the solute-diffusion coefficient, and since the interfacial area a does not depend on Dl, it follows that /cl is proportional to Dl. An analysis of the design variables involved indicates that /cl should be proportional to Nsc when the Reynolds number is held constant. 

Design Methods for Spray Dryers Design variables must be... 

N, Number of design variables Minimum number of Mole fraction in feed ... 

An element is defined as part of a more complex unit. The unit may be all or only part of an operation or the entire process. Our strategy will be to analyze all elements that appear in a separation process and determine the number of design variables associated with each. The appropriate elements can then be quickly combined to form the desired units and the various units combined to form the entire process. Allowance must of course be made for the connecting streams (interstreams) whose variables are counted twice when elements or units are joined. 

Specification of the feed stream L (C + 2 variables), the ratio L i i/D, the heat leak q, and the pressure of either stream leaving the divider utilizes these design variables and defines one unique operation of the divider. 

In Table 13-6, the number of design variables is summarized for several distillation-type separation operations, most of which are shown in Fig. 13-7. For columns not shown in Figs. 13-1 or 13-7 that... 

Example 3 Calculation of TG Method The TG method will he demonstrated hy using the same example problem that was used above for the approximate methods. The example column was analyzed previously and found to have C -I- 2N + 9 design variables. The specifications to be used in this example were also hstedat that time and included the total number of stages (N = 10), the feed-plate location (M = 5), the reflux temperature (corresponding to saturated liquid), the distillate rate (D = 48.9), and the top vapor rate (V = 175). As before, the pressure is uniform at 827 kPa (120 psia), but a pressure gradient could be easily handled if desired. 

For these three applications, Eq. (14-190) gives good prediction of drop size when the design variables are used to c culate E, as illustrated by Eqs. (14-198) and (14-201). 

When macro-scale variables are involved, every geometric design variable can affect the role of shear stresses. They can include such items as power, impeller speed, impeller diameter, impeller blade shape, impeller blade width or height, thickness of the material used to make the impeller, number of blades, impeller location, baffle location, and number of impellers. 

The varianee equation provides a valuable tool with whieh to draw sensitivity inferenees to give the eontribution of eaeh variable to the overall variability of the problem. Through its use, probabilistie methods provide a more effeetive way to determine key design parameters for an optimal solution (Comer and Kjerengtroen, 1996). From this and other information in Pareto Chart form, the designer ean quiekly foeus on the dominant variables. See Appendix XI for a worked example of sensitivity analysis in determining the varianee eontribution of eaeh of the design variables in a stress analysis problem. 

Three different methods ean be used to solve the varianee equation as previously shown. The varianee equation is also a valuable tool with whieh to draw sensitivity inferenees, providing the eontribution of eaeh variable to the overall variability and so determining the key design variables. 

Figure 3 Pareto chart showing the variance contribution of each design variable in the tension bar problem...

Cruse, T. A. 1997b Mechanical Reliability Design Variables and Models. In Cruse, T. A. (ed.), Reliability-Based Mechanical Design. NY Marcel Dekker. 

The packing factor (F) is an important design variable in determining the capacity of any packing design from a flooding, or pressure drop standpoint. This-factor was first described by Sherwood in 1938. The empirical correlation is ... 

From the slope and intereept of the heat absorption line, it is possible to manipulate Equation 6-117 by ehanging operating variables sueh as u, Tq, and T or design variables sueh as the dimensionless heat transfer group UA/puCp. It is also possible to alter the magnitude of the reaetion exotherm by ehanging the inlet reaetant eoneentrations. Any of tliese manipulations ean be used to vary tlie number of loeations of the possible steady states. 

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