Compressive effects

Flows are typically considered compressible when the density varies by more than 5 to 10 percent. In practice compressible flows are normally limited to gases, supercritical fluids, and multiphase flows containing gases. Liquid flows are normally considerea incompressible, except for certain calculations involved in hydraulie transient analysis (see following) where compressibility effects are important even for nearly incompressible hquids with extremely small density variations. Textbooks on compressible gas flow include Shapiro Dynamics and Thermodynamics of Compre.ssible Fluid Flow, vol. 1 and 11, Ronald Press, New York [1953]) and Zucrow and Hofmann (G .s Dynamics, vol. 1 and 11, Wiley, New York [1976]). 

Most often, the Mach number is calculated using the speed of sound evaluated at the local pressure and temperature. When M = 1, the flow is critical or sonic and the velocity equals the local speed of sound. For subsonic flowM < 1 while supersonic flows have M > 1. Compressibility effects are important when the Mach number exceeds 0.1 to 0.2. A common error is to assume that compressibihty effects are always negligible when the Mach number is small. The proper assessment of whether compressibihty is important should be based on relative density changes, not on Mach number. 

Some wave phenomena, familiar to many people from the human senses, include the easy undulation of water waves from a dropped stone or the sharp shock of the sonic boom from high-speed aircraft. The great power and energy of shock events is apparent to the human observer as he stands on the rim of the Meteor Crater of Arizona. Human senses provide little insight into the transition from these directly sensed phenomena to the high-pressure, shock-compression effects in solids. This transition must come from development of the science of shock compression, based on the usual methods of scientific experimentation, theoretical modeling, and numerical simulation. 

The efficiency of the compression effect is high and its quantity large, favored by high pressure. However, it would not have the opportunity to act to this degree in the absence of the turboexpander. 

In equation (4.30), the rate of change of chamber volume is due to the piston movement, i.e. dVldt. The rate of change of oil volume is due to compressibility effects, i.e. ... 

The expansion factor e takes into account the compressibility effects of the fluid. It is close to unity in most industrial ventilation applications. 

The preceding section described the state of transition expected in a deflagration process when the mixture in front of the flame is sufficiently preconditioned by a combination of compression effects and local quenching by turbulent mixing. However, additional factors determine whether the onset of detonation can actually occur and whether the onset of detonation will be followed by a self-sustaining detonation wave. 

J. C. Giddings, Plate height of nonuniform cliromatographic columns. Gas compression effects, coupled columns and analogous systems . Anal. Chem. 35 353-356 (1963). 

Le Chatelier s principle A relation stating that when a system at equilibrium is disturbed it responds in such a way as to partially counteract that change, 337-338 buffers and, 385 compression effects, 339-340 expansion effects, 339-340 precipitation equilibrium, 442 reaction conditions, 348q temperature changes, 340 Lead, 2,501 Leclanch cell, 500 Leucine, 622t... 

As observed with cyclohexanones, the diastereoselectivity of the addition reaction of trimeth-ylaluminum to 2-methylcyclopentanone depends on the stoichiometry of the reactants. Thus, addition of one equivalent of trimcthylaluminum proceeds via preferential tram attack whereas, due to the "compression effect , addition of an excess of the reagent leads to the formation of the equatorial alcohol via predominant attack from the cis side (Table 3)6. In contrast to the addition reactions with trimethylaluniinum, no reversal of the diastereoselectivity upon change of reagent stoichiometry was observed in the addition of triphenylaluminum to 2-methylcyclopentanone6. Even with an excess of the aluminum reagent trans attack predominates. However, the diastereoselectivity is lower than with the use of an equimolar amount of the reactants. 

Celata GP, Cumo M, McPhail SJ, Tesfagabir L, Zummo G (2005) Experimental study on compressibility effects in micro-tubes, in Proceedings of the XXIII UIT Italian National Coference, 2005 53-60... 

On the assumption that compressibility effects are negligible, the effect of pressure on the rate constant of the reaction... 

The flow phenomena described by the Navier-Stokes equation fall into two classes discriminated by the nature of the compressibility effects to be taken into account. For compressible flow, the Navier-Stokes equation [Eq. (1)] has to be solved in com-... 

As will be outlined below, the computation of compressible flow is significantly more challenging than the corresponding problem for incompressible flow. In order to reduce the computational effort, within a CED model a fluid medium should be treated as incompressible whenever possible. A rule of thumb often found in the literature and used as a criterion for the incompressibility assumption to be valid is based on the Mach number of the flow. The Mach number is defined as the ratio of the local flow velocity and the speed of sound. The rule states that if the Mach number is below 0.3 in the whole flow domain, the flow may be treated as incompressible [84], In practice, this rule has to be supplemented by a few additional criteria [3], Especially for micro flows it is important to consider also the total pressure drop as a criterion for incompressibility. In a long micro channel the Mach number may be well below 0.3, but owing to the small hydraulic diameter of the channel a large pressure drop may be obtained. A pressure drop of a few atmospheres for a gas flow clearly indicates that compressibility effects should be taken into account. 

Lagutchev A, Patterson JE, Huang W, Dlott DD. 2005. Ultrafast dynamics of self-assembled monolayers under shock compression Effects of molecular and substrate structiue. J Phys ChemB 109 5033-5044. 

The method is better suited to dilute, rather than concentrated suspensions, since the data can be obtained in a short time (a few minutes at most) and only thin filter cakes are formed. With higher concentrations, much longer filtration times are needed and the thicker filter cakes are more likely to show compressibility effects and non-linear behaviour. 

Star-branched butyl rubber, 4 437-438 copolymers, 4 445-446 Starch(es), 4 703-704, 20 452-453 as blood substitute, 4 111-112 cationic, 18 114-115 in cereal grains, 26 271-274 in cocoa shell from roasted beans, 6 357t compression effects in centrifuges, 5 513 depolymerization, 4 712 in ethanol fermentation, 10 534—535 etherified, 20 563 as a flocculant, 11 627 high-amylose, 26 288 Mark-Houwink parameters for, 20 558t modified and unmodified, 12 52-53 in paper manufacture, 18 122-123 performance criteria in cosmetic use, 7 860t... 

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