Physical law

Non-Newtonian flow processes play a key role in many types of polymer engineering operations. Hence, formulation of mathematical models for these processes can be based on the equations of non-Newtonian fluid mechanics. The general equations of non-Newtonian fluid mechanics provide expressions in terms of velocity, pressure, stress, rate of strain and temperature in a flow domain. These equations are derived on the basis of physical laws and... 

The Schrodinger equation contains the essence of all chemistry. To quote Dirac The underlying physical laws necessary for the mathematical theory of a large part of physics and the whole of chemistry are thus completely known. [P.A.M. Dirac, Proc. Roy. Soc. (London) 123, 714 (1929)]. The Schrodinger equation is... 

Although ion transmission guides and ion traps both use the same universal physical laws to achieve control over ion behavior, the ways in which the laws are used are different, as are the objectives. The guides do not retain ions to gain control over their velocities and are used simply to transmit both slow and fast ions over a very wide range of gas pressures. Ion traps retain ions over a relatively long period of time so as to adjust their kinetic energies and thereby improve mass resolution. The so-called bath gas is used at carefully controlled pressures. 

Spray characteristics are those fluid dynamic parameters that can be observed or measured during Hquid breakup and dispersal. They are used to identify and quantify the features of sprays for the purpose of evaluating atomizer and system performance, for estabHshing practical correlations, and for verifying computer model predictions. Spray characteristics provide information that is of value in understanding the fundamental physical laws that govern Hquid atomization. 

Molecular Connectivity Indexes and Graph Theory. Perhaps the chief obstacle to developing a general theory for quantification of physical properties is not so much in the understanding of the underlying physical laws, but rather the inabiUty to solve the requisite equations. The plethora of assumptions and simplifications in the statistical mechanics and group contribution sections of this article provide examples of this. Computational procedures are simplified when the number of parameters used to describe the saUent features of a problem is reduced. Because many properties of molecules correlate well with stmctures, parameters have been developed which grossly quantify molecular stmctural characteristics. These parameters, or coimectivity indexes, are usually based on the numbers and orientations of atoms and bonds in the molecule. 

Formulation. The expression of the problem in mathematical language. That translation is based on the appropriate physical laws governing the process. 

The formulation step may result in algebraic equations, difference equations, differential equations, integr equations, or combinations of these. In any event these mathematical models usually arise from statements of physical laws such as the laws of mass and energy conservation in the form. 

When the basic physical laws are expressed in this form, the formulation is greatly facilitated. These expressions are quite often given the names, material balance, energy balance, and so forth. To be a little more specific, one could write the law of conservation of energy in the steady state as... 

Development of Process (Matfiematical) Models Constraints in optimization problems arise from physical bounds on the variables, empirical relations, physical laws, and so on. The mathematical relations describing the process also comprise constraints. Two general categories of models exist ... 

Chemistry is the science of chemicals which studies the laws governing their formation, combination and behaviour under various conditions. Some of the key physical laws as they influence chemical safety are discussed in Chapter 4. 

Purely physical laws mainly control the behaviour of very large particles. Further down the particle size range, however, specific surface area, i.e. surface area per unit mass, increases rapidly. Chemical effects then become important, as in the nucleation and growth of crystals. Thus, a study of particulate systems within this size range of interest has become very much within the ambit of chemical engineering, physical chemistry and materials science. 

Most equipment failures occur under abnonnal conditions, especially elevated pressures and temperatures. The design of equipment presents internal and external constraints. External limits may arise from physical laws, while internal limits may depend on tlie process and materials. In any case, if these limits are exceeded, tlie chance of an accident is greatly increased. 

The physical laws of thermodynamics, which define their efficiency and system dynamics, govern compressed-air systems and compressors. This section discusses both the first and second laws of thermodynamics, which apply to all compressors and compressed-air systems. Also applying to these systems are the ideal gas law and the concepts of pressure and compression. 

Three properties of gases must be well understood in order to gain an understanding of pneumatic power systems. These are its temperature, pressure, and volume. Physical laws that define their efficiency and system dynamics govern compressed air systems and compressors. These laws include ... 

Toffoli Applied cellular automata directly to modeling physical laws... 

In any particular situation, it is usually possible to give a variety of reasons why the observed quantity behaves in an erratic manner. The observed quantity may be critically dependent on certain parameters and the observed fluctuations attributed to slight variations of these parameters. The implication here is that the observed fluctuations appear erratic only because we have not taken the trouble to make a sufficiently precise analysis of the situation to disclose the pattern the observations are following. It is also possible, in some situations, to adopt the viewpoint that certain aspects of the phenomenon being studied are inherently unknowable and that the best physical laws we can devise to explain the phenomenon will have some form of randomness or unpredictability built into them. Such is the case, for example, with thermal noise voltages, which are believed to be governed by the probabilistic laws of quantum physics. 

This is by no means a self-evident truth it is a physical law based on experience, and depends on the property of temperature equilibrium. 

It will be observed that the definition of intrinsic energy by means of the equation (c) implies in itself no physical law, since the value of (U2—Ui) can always be chosen so as to make the values of 2Q and 2A satisfy the equation. We shall now show that the value of (U2 — Ui) is uniquely so defined, and is quite independent of the way in which the process is executed. This is a physical law, which we shall call the Principle of Conservation of Energy. 

Since the physical properties of a system are interconnected by a series of mechanical and physical laws, it is convenient to regard certain quantities as basic and other quantities as derived. The choice of basic dimensions varies from one system to another although it is usual to take length and time as fundamental. These quantities are denoted by L and T. The dimensions of velocity, which is a rate of increase of distance with time, may be written as LT , and those of acceleration, the rate of increase of velocity, are LT-2. An area has dimensions L2 and a volume has the dimensions L3. 

If, however, some other physical law were to be introduced so that, for instance, the attractive force between two bodies would be proportional to the product of their masses, then this relation between F and M would no longer hold. It should be noted that mass has essentially two connotations. First, it is a measure of the amount of material and appears in this role when the density of a fluid or solid is considered. Second, it is a measure of the inertia of the material when used, for example, in equations 1.1-1.3. Although mass is taken normally taken as the third fundamental quantity, as already mentioned, in some engineering systems force is used in place of mass which then becomes a derived unit. 

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