Magnitude estimation

These terms are analogous to those on p. 265 of [7], It will be noted that the symbol c has been reinstated as in Section VI.F, so as to facilitate the order of magnitude estimation in the nearly nonrelativistic limit. We now proceed based on Eq. (168) as it stands, since the transformation of Eq. (168) to modulus and phase variables and functional derivation gives rather involved expressions and will not be set out here. 

In spite of the three methods of estimating open question that needs to be investigated further in the future. The above expressions are order of magnitude estimates and not exact formulas. 

The capillary retention forces in the pores of the filter cake are affected by the size and size range of the particles forming the cake, and by the way the particles have been deposited when the cake was formed. There is no fundamental relation to allow the prediction of cake permeabiUty but, for the sake of the order-of-magnitude estimates, the pore size in the cake may be taken loosely as though it were a cylinder which would just pass between three touching, monosized spheres. If dis the diameter of the spherical particles, the cylinder radius would be 0.0825 d. The capillary pressure of 100 kPa (1 bar) corresponds to d of 17.6 pm, given that the surface tension of water at 20°C is 12.1 b mN /m (= dyn/cm). 

Order-of-Magnitude Estimates. Unit capital cost data (dollars per aimual ton of product) are occasionally reported for chemical plants. These data can be multiphed by a selected plant capacity to estimate a capital cost. This is, however, feasible only if the reference process, conditions, and capacity are similar. 

Order-of-magnitude estimate (ratio estimate). Rule-of-thumb method based on cost data for previous similar types of plant probable error within 10 to 50 percent. 

Step Count Methods These methods, used for order-of-magnitude estimates, are based on the definition of the functional units required to carry out the process. A functional unit is a signifi-... 

Complete Plant Costs It is difficult to compare costs of domestic and overseas plants owing to the wide variation in types of plants and sizes and the rapid changes in technology. Useful data are scarce, and the following comparisons must be used with caution and then only for order-of-magnitude estimates of fixed-capital costs. 

Application The theoretical considerations that have been expounded should be used only for order-of-magnitude estimates, since a number of extraneous factors may enter into actual performance. In actual instaUations rectified alternating current is em-... 

A simplified form of event tree analysis using selected accident scenarios and order-of-magnitude estimates to determine whether additional protection is needed... 

This chapter provides a compendium of short engineering calculation methods and formulas for select process operations and equipment. The formulas and procedures provided in this chapter offer simple, rapid estimates of key parameters important to specifying and obtaining various engineering parameters. The information is derived from the open literature, and is believed to be accurate for obtaining better than an order of magnitude estimate for each calculation. 

A key aspect in most cost estimation studies is the evalutUion of the cost of individual pieces of equipment. In addition to quotations from equipment manufacturers, there are several methods for developing cost estimates. For a typical conceptual design, it is normally acceptable to develop an order of magnitude or preliminary estimate whose accuracy is within -h/— 25 to 50%. The following methods may be employed to develop order of magnitude estimates ... 

QRA is generally resource intensive. FEIR, is much less although it uses the framework of QRA for screening and ranking systems by relative risk using order-of-magnitude estimates of the frequencies and consequences of events. It incorporates plant experience and industry data to estimate the potential for future losses. 

A simple order of magnitude estimate of the rate constants for reaction with ethylene can be made for the high intensity ions in the 5-torr spectrum. Since the average reaction time, limited by neutralization or removal from the ion source is a few milliseconds (see section dealing with sampling conditions and section on ethylene in xenon) we can take 1 msec, as the half-life of these ions in 5-torr ethylene. This leads to k = 10-14 to 10-15 cc. molecule-1 sec.-1 as a rate constant for further reaction with ethylene. The value for 5a found by the kinetic treatment above was 8 X 10 -14. 

Mixing times in mechanically agitated vessels typically range from a few seconds in laboratory glassware to a few minutes in large industrial reactors. The classic correlation by Norwood and Metzner for turbine impellers in baffled vessels can be used for order of magnitude estimates of... 

The theory of nonisothermal effectiveness is sufficiently well advanced to allow order-of-magnitude estimates for rj. The analysis requires simultaneous... 

However, even with the most advanced measuring and simulation tools, the most efficient methods are simple calculations that give an order-of-magnitude estimation of the influence of a phenomenon. Time constants for diffusion, heat conduction, and acceleration are very useful. For example, the time constant for diffusion Td = f/D is the time it takes to fill a cube of size I by diffusion, and the time for a particle to accelerate from zero velocity to approximately two-third of the velocity of the surrounding fluids is 118/j, where p[Pg.331]

Step counting estimating methods provide a way of making a quick, order of magnitude, estimate of the capital cost of a proposed project. 

We are only seeking an approximate theory since a more precise simple analytical result is not possible. We only seek an order of magnitude estimation and insight into the important variables. With this approximation the energy equation for CV[ is... 

The constant 3 is an order of magnitude estimate which depends on the approximate analysis for the model of Figure (4.10). In addition, the burning rate m " and the properties a and cp should be evaluated at some appropriate mean temperature. For example, in Equation (4.34), the more correct expression for is... 

Now let us consider the mixing time, t. This will be estimated by an order of magnitude estimate for diffusion to occur across the boundary layer thickness, <5Bl- If we have turbulent natural conditions, it is common to represent the heat transfer in terms of the Nusselt number for a vertical plate of height, , as... 

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