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Dimensional analysis concept

Other dimensional systems have been developed for special appHcations which can be found in the technical Hterature. In fact, to increase the power of dimensional analysis, it is advantageous to differentiate between the lengths in radial and tangential directions (13). In doing so, ambiguities for the concepts of energy and torque, as well as for normal stress and shear stress, are eliminated (see Ref. 13). [Pg.104]

These scale-up methods will necessarily at times include fundamental concepts, dimensional analysis, empirical correlations, test data, and experience [32]. [Pg.312]

Dimensional Analysis. In the design of rather simple devices or systems, dimensional analysis can be used in conjunction with physical model experimental investigations to gain insight into the performance of a particular design concept. It is usually possible to define the performance of a simple device or system with a certain number of well chosen geometric and performance related variables that describe the device or system. Once these variables have been selected, dimensional analysis can be used to ... [Pg.371]

In reviewing the pH-partition hypothesis, it is apparent that it is an oversimplification of a very complex process. It does not consider one of the critical physicochemical factors, solubility. Low aqueous solubility is often the cause of the low bioavailability. To address this issue, Dressman et al. [28] developed an absorption potential concept that takes into account not only the partition coefficient but also solubility and dose. Using a dimensional analysis approach, the following simple equation was proposed ... [Pg.394]

An alternative system proved to be both simpler and more user friendly (Unger et al., 2004 Machtejevas et al., 2006). Thus far we have used this configuration to analyze human plasma, sputum, urine, cerebrospinal fluid, and rat plasma. For each particular analysis we set up an analytical system based on a simple but specific strategy (Figure 9.5). The analysis concept is based on an online sample preparation and a two-dimensional LC system preseparating the majority of the matrix components from the analytes that are retained on a RAM-SCX column followed by a solvent switch and transfer of the trapped peptides. The SCX elution used five salt steps created by mixing 20 mM phosphate buffer (pH 2.5) (eluent Al) and 20 mM phosphate buffer with 1.5 M sodium chloride (eluent Bl) in the following proportions 85/15 70/30 65/45 45/55 0/100 with at the constant 0.1 mL/min flow rate. Desorption of the... [Pg.214]

A related concept to dimensional analysis is quantity calculus, a method we find particularly useful when it comes to setting out table header rows and graph axes. Quantity calculus is the handling of physical quantities and their units using the normal rules of algebra. A physical quantity is defined by a numerical value and a unit ... [Pg.13]

Keeping pace with the increased influence of PAT in the pharmaceutical industry, this completely updated reference spans the latest research and regulations, technologies, and expert solutions for every significant aspect of pharmaceutical process scale-up—clearly introducing readers to the theoretical concept of dimensional analysis to quantify similar processes on varying scales. [Pg.539]

Along with the methods of similarity theory, Ya.B. extensively used and enriched the important concept of self-similarity. Ya.B. discovered the property of self-similarity in many problems which he studied, beginning with his hydrodynamic papers in 1937 and his first papers on nitrogen oxidation (25, 26). Let us mention his joint work with A. S. Kompaneets [7] on selfsimilar solutions of nonlinear thermal conduction problems. A remarkable property of strong thermal waves before whose front the thermal conduction is zero was discovered here for the first time their finite propagation velocity. Independently, but somewhat later, similar results were obtained by G. I. Barenblatt in another physical problem, the filtration of gas and underground water. But these were classical self-similarities the exponents in the self-similar variables were obtained in these problems from dimensional analysis and the conservation laws. [Pg.13]

It should be mentioned that, as is often the case in a first draft, the author based his treatment of the turbulent convection on certain assumptions which in fact were not necessary, in particular the semi-empirical concept of L. Prandtl. Moreover, even in the analysis of laminar convection, the author [cf., for example the transition from equation (9) to equation (10)], to derive the asymptotic laws, resorts to simplifications of the equations which are really not necessary. Actually, it is possible to manage without these assumptions so that Zeldovich s asymptotic laws (8), (8a), (11), and (11a) may be obtained by simple dimensional analysis under the most general assumptions. [Pg.85]

Astarita6 presents a brief history of the concept of dimensions and dimensional analysis from Euclid to the present day. [Pg.172]

This characteristic of pi-representation represents the basis of the concept of similarity based on dimensional analysis Processes which are described by the same pi-relationship are considered similar to each other if they correspond to the same point in the pi-framework. From the standpoint of dimensional analysis it is there-... [Pg.22]

Naturally, the results of dimensional analysis discussed above and their consequences were not known to the ship builders of the 19th century. Since the time of Rankine, the total drag resistance of a ship has been divided into three parts the surface friction, the stern vortex and the bow wave. However, the concept of Newtonian mechanical similarity, known at that time, only stated that for mechanically similar processes the forces vary as F p l2 v2. Scale-up was not considered for assessing the effect of gravity. [Pg.38]

Fig. 3. (a) Hierarchy of deterministic, continuum models. Dimensional analysis and symmetry are powerful concepts in reducing the dimensionality of complex models, (b) Hierarchy of stochastic models for chemically reacting well-mixed systems. [Pg.7]

One of the goals of the experimental research is to analyze the systems in order to make them as widely applicable as possible. To achieve this, the concept of similitude is often used. For example, the measurements taken on one system (for example in a laboratory unit) could be used to describe the behaviour of other similar systems (e.g. industrial units). The laboratory systems are usually thought of as models and are used to study the phenomenon of interest under carefully controlled conditions. Empirical formulations can be developed, or specific predictions of one or more characteristics of some other similar systems can be made from the study of these models. The establishment of systematic and well-defined relationships between the laboratory model and the other systems is necessary to succeed with this approach. The correlation of experimental data based on dimensional analysis and similitude produces models, which have the same qualities as the transfer based, stochastic or statistical models described in the previous chapters. However, dimensional analysis and similitude do not have a theoretical basis, as is the case for the models studied previously. [Pg.461]

ShelUe, R. Marriot, P. Morrison, P. Concepts and preliminary observations on the triple-dimensional analysis of complex volatile samples by using GC x GC-TOFMS. Anal. Chem. 2001, 73, 1336-1344. [Pg.658]

Dimensional analysis is emphasized throughout to give you a better feel for the proper setting up of problems. SI units or symbols (e.g., L, mL, mol, and s) are used throughout. The concept of normality and equivalents is introduced, but emphasis remains on the use of molarity and moles. The presentation of normality is done in a way that allows it to be ignored if your instructor chooses not to assign it. [Pg.836]

Explain the concept and importance of dimensional analysis in correlating experimental data on convective mass-transfer coefficients. [Pg.97]

Dimensional analysis was introduced by Fourier in 1822. He stressed the importance of dimensional homogeneity and also the concept of a dimensional formula. In any physical (and chemical) equation, the quantity on the left-hand side must have the same physical dimension as the quantity on the right-hand side. This is the only way that retains the validity if the units used are changed, say for example from cm to inch, etc. The basic principle is best explained in an example. [Pg.325]

Conversions of mass to moles and of moles to mass are frequently encountered in calculations using the mole concept. These calculations are simplified using dimensional analysis, as shown in Sample Exercises 3.10 and 3.11. [Pg.90]


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