Basic Principles of Fluid Mechanics

The energy consumption in agitation depends on the basic principles of fluid mechanics however, the flow patterns in a mixing vessel are much too complex for their rigorous application. Therefore, empirical relationships based on dimensionless groups are used. Here, because most fluid foods are non-Newtonian in nature, the... 

According to the Cubic Law, fracture is formed by the smooth, flat, infinite long parallel plates without filling medium, and the water flow between the plates is viscous incompressible flow which is permanent laminar flow. Thus, according to the basic principle of fluid mechanics, the discharge per unit width through the crack surface i.e. q can be calculated by the follow formula ... 

Materials are usually transferred between different parts of a chemical plant in the fluid state. Large quantities of gases, liquids and fluidized solids may be easily and economically transported by pumping along a network of pipes. In process design and analysis it is necessary to determine pump duties, pipe sizes, pressure drops, flowrates etc. This section reviews the basic principles of fluid mechanics on which such calculations depend. 

Once the continuum hypothesis has been adopted, the usual macroscopic laws of classical continuum physics are invoked to provide a mathematical description of fluid motion and/or heat transfer in nonisothermal systems - namely, conservation of mass, conservation of linear and angular momentum (the basic principles of Newtonian mechanics), and conservation of energy (the first law of thermodynamics). Although the second law of thermodynamics does not contribute directly to the derivation of the governing equations, we shall see that it does provide constraints on the allowable forms for the so-called constitutive models that relate the velocity gradients in the fluid to the short-range forces that act across surfaces within the fluid. 

The basic principle of a diffusion pump can be explained with a simple single-stage mercury diffusion pump (see Fig. 7.21). On the system side of the pump (at about 10 2 to 10 3 torr, or better), gas molecules wander around, limited by their mean free path and collisions with other molecules. The lowest section of this diffusion pump is an electric heater that brings the diffusion pump liquid up to its vapor pressure temperature. The vapors of the diffusion pump liquid are vented up a central chimney where, at the top, they are expelled out of vapor jets at supersonic speeds (up to 1000 ft/sec). Below these jets is a constant rain of the pumping fluid (mercury or low vapor-pressure oil) on the gases within the vacuum system. Using momentum transfer/ gas molecules are physically knocked to the bottom of the pump, where they are trapped by the vapor jets from above. Finally, they are collected in a sufficient quantity to be drawn out by the auxiliary (mechanical) pump. 

So far, we have seen that the basic macroscopic principles of continuum mechanics lead to a set of five scalar DEs sometimes called the field equations of continuum mechanics -namely, (2 5) or (2 20), (2 32), and (2-51) or (2 52). On the other hand, we have identified many more unknown variables, u, T, 9,p, and q, plus various fluid or material properties such as p, Cp (or Cv), (dp/d())p, [or (dp/d0)p], which generally require additional equations of state to be determined from p and 9 if the latter are adopted as the thermodynamic state variables. Let us focus just on the independent variables u, T,9, p, and q. Taking account of the symmetry of T, these comprise 14 unknown scalar variables for which we have so far obtained only the five independent field equations that were just listed. It is evident that we require additional equations relating the various unknown variables if we are to achieve a well-posed problem from a mathematical point of view. Where are these equations to come from Why is it that the fundamental macroscopic principles of continuum physics do not, in themselves, lead to a mathematical problem with a closed set of equations ... 

To describe the theoretical dynamical and thermal behavior of the atmosphere, the fundamental equations of fluid mechanics must be employed. In this section these equations are presented in a relatively simple form. A more conceptual view will be presented in Section 3.6. The circulation of the Earth s atmosphere is governed by three basic principles Newton s laws of motion, the conservation of energy, and the conservation of mass. Newton s second law describes the response of a fluid to external forces. In a frame of reference which rotates with the Earth, the first fundamental equation, called the momentum equation, is given by ... 

The field of solid-phase synthesis instrumentation is continually advancing. Improvements in synthesis reagents, reaction monitoring, and instrument hardware and software will extend the limits of the instrumentation. As synthesizer capabilities improve, there is the potential that more and more control will be taken from the user until the instrument becomes a black box. It is important, however, to maintain an understanding of the principles of instrument operation and the chemistry that is being performed. The instrument is secondary to the chemistry but is an essential tool to help carry out the synthesis efficiently. The best instrument cannot improve ineffective chemistry and, conversely, a poorly designed instrument can compromise a very efficient chemical process. As long as the basic principles of reaction kinetics, fluid mechanics, and instrument safety are sustained, a solid-phase synthesizer can be used to its maximum potential and benefits. 

The first eight chapters form the core of the book. The remaining nine are intended as extra reading which will introduce the student to further topics in fluid mechanics. No nbw principles are introduced in these last chapters, but special topics and techniques in fluid mechanics are discussed. These chapters show the reader the connections between the basic material in Chaps. 1 to 8 and the sometimes special terminology and special ideas in other areas of fluid mechanics., ... 

This chapter provides a bridge between the formal theories of liquids and various modelistic approaches devised for the study of aqueous fluids. Such a bridge is needed for the comfortable accommodation, in a single book, of both a fundamental theory, based on first principles of statistical mechanics, and various, basically heuristic, approaches. 

In the preceding sections we have discussed the basic principles of RESS and shown how to carry out simplified calculations of the fluid dynamics of a rapid expansion. We now apply these calculations to the two limiting types of expansion devices the plain orifice and the long capillary. For the plain orifice, L/D for the cylindrical section is typically of the order of unity. We picked L/D = 5 as a value typical of many investigations, with the holes being short enough to be drilled either mechanically (23) or with the use of a laser (e.g., 12,20). For the capillary, we chose L/D = 5000 as a typical aspect ratio, which can be either an individual tube or part of a microchannel that leads through a porous frit plate (37). 

For the student, this is a basic text for a first-level course in process engineering fluid mechanics, which emphasizes the systematic application of fundamental principles (e.g., macroscopic mass, energy, and momentum balances and economics) to the analysis of a variety of fluid problems of a practical nature. Methods of analysis of many of these operations have been taken from the recent technical literature, and have not previously been available in textbooks. This book includes numerous problems that illustrate these applications at the end of each chapter. 

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