Important Variables

The fluid velocity vector is one of the most important variables in fluid dynamics. A vector can be described as a quantity that has magnitude and direction. 

A more sophisticated description identifies a vector as a mathematical entity that associates a scalar with each coordinate direction in a particular coordinate system. Hence, there are three scalar velocity components that constitute the velocity vector, and they are typically written in the following manner in three different coordinate systems  

Each flow problem is solved in only one coordinate system (i.e., the coordinate system that best exploits the symmetry of the macroscopic boundaries). 

Viscous stress is an extremely important variable, and this quantity is identified by the Greek letter r. Viscous stress represents molecular transport of momentum, analogous to heat conduction and diffusion. All molecular transport mechanisms correspond to irreversible processes that generate entropy under realistic conditions. When fluids obey Newton s law of viscosity, there is a linear relation between viscous stress and velocity gradients. All fluids do not obey Newton s law of viscosity, but almost aU gases and low-molecular-weight liquids are Newtonian. 

Fluid pressure is the third important variable, and it is designated by the letter p. Force balances contain fluid pressure because pressure forces are exerted across surfaces, and there are, at most, six surfaces that enclose fluid completely within a control volume. Pressure forces are operative under hydrodynamic and hydrostatic conditions. Force balances in this chapter typically apply to fluids in motion—hence, the naint fluid dynamics. However, these balances are generic enough to describe the situation when fluids are at rest. In other words, the force balances will be applicable to describe hydrostatics when the velocity vector and r vanish. 

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The most common alternative to distillation for the separation of low-molecular-weight materials is absorption. In absorption, a gas mixture is contacted with a liquid solvent which preferentially dissolves one or more components of the gas. Absorption processes often require an extraneous material to be introduced into the process to act as liquid solvent. If it is possible to use the materials already in the process, this should be done in preference to introducing an extraneous material for reasons already discussed. Liquid flow rate, temperature, and pressure are important variables to be set. 

The most common alternative to distillation for the separation of low-molecular-weight materials is absorption. Liquid flow rate, temperature, and pressure are important variables to be set, but no attempts should be made to carry out any optimization at this stage. 

Apart from chemical composition, an important variable in the description of emulsions is the volume fraction, outer phase. For spherical droplets, of radius a, the volume fraction is given by the number density, n, times the spherical volume, 0 = Ava nl2>. It is easy to show that the maximum packing fraction of spheres is 0 = 0.74 (see Problem XIV-2). Many physical properties of emulsions can be characterized by their volume fraction. The viscosity of a dilute suspension of rigid spheres is an example where the Einstein limiting law is [2]... 

Temperature is an important variable in the discussion of viscoelasticity. For reasons of pedagogy, most consideration of this variable is deferred to the next chapter. This does not mean that temperature is unimportant to the present discussion, only that the agenda is full enough without it. 

Density. Density is the most important variable in determining mechanical properties of a foamed plastic of given composition. Its effect has been recognized since foamed plastics were first made and has been extensively studied. 

Compressive Behavior. The most kiformative data ki characterising the compressive behavior of a flexible foam are derived from the entire load-deflection curve of 0—75% deflection and its return to 0% deflection at the speed experienced ki the anticipated appHcation. Various methods have been reported (3,161,169—172) for relating the properties of flexible foams to desked behavior ki comfort cushioning. Other methods to characterize package cushioning have been reported. The most important variables affecting compressive behavior are polymer composition, density, and cell stmcture and size. 

The decomposition rate of NaBH solutions in water is convenientiy estimated from equation 23 which expresses half-life in terms of the two most important variables, pH and temperature when is in minutes and Tis in K (23). 

In what may be an example of tme cluster catalysis, [HRU3 (CO) ] shows good catalytic activity and high regioselectivity using propylene as substrate (24,25). Solvent, CO partial pressure, and temperature are important variables. In monoglyme, at 80°C and starting partial pressures for C H, ... 

Floor poHshes typically are evaluated for gloss, appHcation and leveling properties, discoloration, sHp resistance, scratch resistance, heel-mark resistance, scuff resistance, damp-mopping and detergent resistance, repairabiHty, lack of sediment, and removabiHty (3). RecoatabiHty and formula stabiHty are also important. A review of test methods is available (35). More than 20 ASTM test methods for floor poHshes exist. From the standpoint of product safety, sHp resistance is a particularly important variable and many test methods are available (39). 

The choice of the strain of microorganism is one of the important variables in the process. The strains to be used in manufacture are mutants of the original producer, which are chosen as the result of a planned program of mutant selection. Sometimes a spontaneous mutation occurs usually, it is induced by mutagenic agents or irradiation of various sorts. The choice of the best strain depends on its abiUty to produce large amounts of the proper antibiotic in a reasonable time from ingredients that are economically feasible (73). 

Temperature is the most important variable and preheating is generally necessary to 200—230°C. After air has been introduced, there is a gradual temperature rise because of the exothermic reaction, until some means is appHed to hold the temperature such as a water or steam spray on the asphalt surface to maintain a temperature of approximately 260°C. The end point can be predicted by periodic testing of the softening point. 

The most important variables affecting nucleation rate are shown by equations 10 and 11 to be iaterfacial eaergy, temperature, and supersaturation. 

Preliminary Estimates of Repeatability. Initial estimates of repeatabihty should be obtained before embarking on any significant test program. Such information may be available from previous testing if it is not, vaUd preliminary mns should be conducted at different times under supposedly identical conditions. If these mns result in large variabiUty in performance, the important variables that affect the results have not been identified, and further research may be needed before the proposed experiment can commence. 

The reproducibility of test results between labs using the neutral salt spray tests has not been consistent, but the repeatability, within one lab, is better, and the test has value in comparing variations in coating systems. Correlation of hours of exposure in the salt spray test to actual performance of the plated part in service, even in marine atmospheres, is not consistent and usually avoided. A classic example is that cadmium deposits outlast zinc deposits on steel in salt spray tests and clean marine atmospheres, yet zinc outlasts cadmium when exposed to real, industrial atmospheres, because of the presence of sulfur-bearing corrodents in industrial environments. An important variable in salt spray testing is the position of the surface to be tested. Whereas the surface of test panels is specified to be 15—30° from the vertical (40), when salt spray testing chromated zinc-plated specimens, this range has appeared excessive (41). 

Important variables which must be fixed before design of a commer-ciaT diyer are the following ... 

Measuring process parameters on full-scale plants is notoriously difficult, but is needea for control. Usually few of the important variables are accessible to measurement. Recycle of material makes it difficult to isolate the effects of changes to individual process units in the circuit. Newer plants have more instrumentation, including on-line viscosimeters [Kawatra and Eisele, International ]. Mineral Processing, 22, 251-259 (1988)], mineral composition by on-line X-ray fluorescence, belt feeder weighers, etc., but the information is always incomplete. Therefore it is helpful to have models to predict quantities that cannot be measured while measuring those that can. 

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