In fluid mechanics

Macroscopic and Microscopic Balances Three postulates, regarded as laws of physics, are fundamental in fluid mechanics. These are conservation of mass, conservation of momentum, and con-servation of energy. In addition, two other postulates, conservation of moment of momentum (angular momentum) and the entropy inequality (second law of thermodynamics) have occasional use. The conservation principles may be applied either to material systems or to control volumes in space. Most often, control volumes are used. The control volumes may be either of finite or differential size, resulting in either algebraic or differential consei vation equations, respectively. These are often called macroscopic and microscopic balance equations. 

For purposes of data correlation, model studies, and scale-up, it is useful to arrange variables into dimensionless groups. Table 6-7 lists many of the dimensionless groups commonly founa in fluid mechanics problems, along with their physical interpretations and areas of application. More extensive tabulations may oe found in Catchpole and Fulford (Ind. Eng. Chem., 58[3], 46-60 [1966]) and Fulford and Catchpole (Ind. Eng. Chem., 60[3], 71-78 [1968]). 

Quite a few years ago, Dr. Azbel and I analyzed the operational requirements for these machines and developed some design formulae. You can find this analysis on pages 646 through 665 in Fluid Mechanics and Unit Operations, David S. Azbel and Nicholas P. Cheremisinoff, Ann Arbor Science Publishers, 1983. There are some sample calculations and sizing criteria that you can follow for some practical exercises in this publication. 

D. Anderson, G. McFadden, A. Wheeler. Diffuse-interface methods in fluid mechanics. Ann Rev Fluid Mech 20 130, 1998. 

In fluid mechanics the principles of conservation of mass, conservation of momentum, the first and second laws of thermodynamics, and empirically developed correlations are used to predict the behavior of gases and liquids at rest or in motion. The field is generally divided into fluid statics and fluid dynamics and further subdivided on the basis of compressibility. Liquids can usually be considered as incompressible, while gases are usually assumed to be compressible. 

Dimensional analysis techniques are especially useful for manufacturers that make families of products that vary in size and performance specifications. Often it is not economic to make full-scale prototypes of a final product (e.g., dams, bridges, communication antennas, etc.). Thus, the solution to many of these design problems is to create small scale physical models that can be tested in similar operational environments. The dimensional analysis terms combined with results of physical modeling form the basis for interpreting data and development of full-scale prototype devices or systems. Use of dimensional analysis in fluid mechanics is given in the following example. 

DE Nevers. N. Fluid Mechanics for Chemical Engineers, 2nd edn (McGraw-Hill, New York, 1970). Douglas, J. F. Solution of Problems in Fluid Mechanics (Pitman, London. 1971). 

Paterson, A. R. A First Course in Fluid Mechanics (Cambridge University Press, Cambridge 1985). Streeter, V. L. and Wylie, E. B. Fluid Mechanics, 8th edn (McGraw-Hill, New York, 1985). 

The issues of selection of the spatial wavelength and the deterministic character of the fine scale features of the microstructure are closely related to similar questions in nonlinear transitions in a host of other physical systems, such as macroscopic models of immiscible displacement in porous media - - the Hele Shaw Problem (15) - and flow transitions in fluid mechanical systems (16). 

L. G. Leal, Challenges and Opportunities in Fluid Mechanics and Transport Phenomena William B. Russel, Fluid Mechanics and Transport Research in Chemical Engineering J. R. A. Pearson, Fluid Mechanics and Transport Phenomena... 

Deviation variables are analogous to perturbation variables used in chemical kinetics or in fluid mechanics (linear hydrodynamic stability). We can consider deviation variable as a measure of how far it is from steady state. 

In fluid mechanics, it is customary to express the torque requirement in terms of a turning moment coefficient CM defined as... 

Robert A. Brown is Warren K. Lewis Professor of Chemical Engineering and Provost at the Massachusetts Institute of Technology. He received his B.S. (1973) and M.S. (1975) from the University of Texas, Austin, and his Ph.D. from the University of Minnesota in 1979. His research area is chemical engineering with specialization in fluid mechanics and transport phenomena, crystal growth from the melt, microdefect formation in semiconductors and viscoelastic fluids, bifurcation theory applied to transitions in flow problems, and finite element methods for nonlinear transport problems. He is a member of the National Academy of Engineering, the National Academy of Sciences, and the American Academy of Arts and Sciences. 

A control volume is a volume specified in transacting the solution to a problem typically involving the transfer of matter across the volume s surface. In the study of thermodynamics it is often referred to as an open system, and is essential to the solution of problems in fluid mechanics. Since the conservation laws of physics are defined for (fixed mass) systems, we need a way to transform these expressions to the domain of the control volume. A system has a fixed mass whereas the mass within a control volume can change with time. 

An important concept in fluid mechanics is the hydrodynamic boundary layer (also known as Prandtl layer) or region where the effective disturbance... 

To understand the difference in stagnation pressure losses between subsonic and supersonic combustion one must consider sonic conditions in isoergic and isentropic flows that is, one must deal with, as is done in fluid mechanics, the Fanno and Rayleigh lines. Following an early NACA report for these conditions, since the mass flow rate (puA) must remain constant, then for a constant area duct the momentum equation takes the form... 

On the other hand, the proposed approach has structure of low pass filter see Eq.(8). Thus, we can expect that the closed-loop response is not sensitive to high frequency signals (as, for example, by noisy measurements or fluctuations in fluids mechanics by agitation). Although Figure 3 depicts the frequency... 

VI. Van Dyke, M. D., Perturbation Methods in Fluid Mechanics. Academic Press, New York, 1964. 

This may not seem like much help, because we have expanded three terms into six. However, if the flow is assumed to be incompressible, a derivation given in fluid mechanics texts (the continuity equation) is... 

Fluid Flow A First Course in Fluid Mechanics , Macmillan, NY (1964), 393pp 2) B. Adler, S. Fembach M. Rotenberg, Fundamental Methods in Hydrodynamics,... 

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