Analysis rigorous

Many processes involved ultimately make the analysis rigorous and unnecessarily sluggish. 

To supplement the SVD analysis, rigorous d mamic simulations under closed loop operation were carried out. For the closed-loop analysis, several issues must be defined first, such as the control loops for each system, the type of process controller to be used, and the values of the controller parameters. 

One should realize that these calculations are based on an expression for Vr which corresponds to potential flow past a stationary nonde-formable bubble, as seen by an observer in a stationary reference frame. However, this analysis rigorously requires the radial velocity profile for potential flow in the Uquid phase as a nondeformable bubble rises through an incompressible liquid that is stationary far from the bubble. When submerged objects are in motion, it is important to use liquid-phase velocity components that are referenced to the motion of the interface for boundary layer mass transfer analysis. This is accomplished best by solving the flow problem in a body-fixed reference frame which translates and, if necessary, rotates with the bubble such that the center of the bubble and the origin of the coordinate system are coincident. Now the problem is equivalent to one where an ideal fluid impinges on a stationary nondeformable gas bubble of radius R. As illustrated above, results for the latter problem have been employed to estimate the maximum error associated with the neglect of curvature in the radial term of the equation of continuity. 

In any series of measurements, one or more results may appear to be very different from all the others. Such spurious results occur In all methods of analysis and there Is a tendency to simply ignore the seemingly odd results. However a simple inspection of all the results is not sufficiently rigorous for making a decision on when to reject or retain any one result. 

The development of precise and reproducible methods of sensory analysis is prerequisite to the determination of what causes flavor, or the study of flavor chemistry. Knowing what chemical compounds are responsible for flavor allows the development of analytical techniques using chemistry rather than human subjects to characterize flavor (38,39). Routine analysis in most food production for the quaUty control of flavor is rare (40). Once standards for each flavor quaUty have been synthesized or isolated, they can also be used to train people to do more rigorous descriptive analyses. 

Partially Plastic Thick-Walled Cylinders. As the internal pressure is increased above the yield pressure, P, plastic deformation penetrates the wad of the cylinder so that the inner layers are stressed plasticady while the outer ones remain elastic. A rigorous analysis of the stresses and strains in a partiady plastic thick-waded cylinder made of a material which work hardens is very compHcated. However, if it is assumed that the material yields at a constant value of the yield shear stress (Fig. 4a), that the elastic—plastic boundary is cylindrical and concentric with the bore of the cylinder (Fig. 4b), and that the axial stress is the mean of the tangential and radial stresses, then it may be shown (10) that the internal pressure, needed to take the boundary to any radius r such that is given by... 

Theoretically based correlations (or semitheoretical extensions of them), rooted in thermodynamics or other fundamentals are ordinarily preferred. However, rigorous theoretical understanding of real systems is far from complete, and purely empirical correlations typically have strict limits on apphcabihty. Many correlations result from curve-fitting the desired parameter to an appropriate independent variable. Some fitting exercises are rooted in theory, eg, Antoine s equation for vapor pressure others can be described as being semitheoretical. These distinctions usually do not refer to adherence to the observations of natural systems, but rather to the agreement in form to mathematical models of idealized systems. The advent of readily available computers has revolutionized the development and use of correlation techniques (see Chemometrics Computer technology Dimensional analysis). 

The first five methods are apphcable only after rigorous circuit analysis and when piping layouts and isometric drawings or scale models are available for quantity takeoff (e.g., pipe size, length, and specification, flanges and valve count, etc.). 

Visual inspection techniques are stressed as the most important tools used to study failures. This text is not a substitute for rigorous failure analysis conducted by experts, but it will help the reader identify and eliminate many cooling water system problems. Still, on occasion, the experienced, skilled, failure analyst using sophisticated analytical techniques and specialized equipment may be required to solve complex or unusual problems. Common sense, appropriate experience, and systematic investigation are, however, often superior to the more elaborate, but less effective, techniques used by some. 

For FCC applications, a rigorous analysis typically involves transient evaluations of expander coupling failures, generator load drops, compressor and surge system operation, and control valve malfunctions. The results of these evaluations permit optimum selection of control valves and control strategies. 

Many of the better known shortcut equipment design methods have been derived by informed assumptions and mathematical analysis. Testing in the laboratory or field was classically used to validate these methods but computers now help by providing easy access to rigorous design calculations. 

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