Principal drags

The principal drags of some nonspherical bodies are given in [179] and below. 

Let us calculate the average drag for a thin disk of radius a. To this end, we substitute the principal drags (2.6.23) into (2.6.36). As a result, we obtain... 

In summary, the principal sources of drag on a body moving through a fluid are skin friction drag. 

In Spite of the existence of numerous experimental and theoretical investigations, a number of principal problems related to micro-fluid hydrodynamics are not well-studied. There are contradictory data on the drag in micro-channels, transition from laminar to turbulent flow, etc. That leads to difficulties in understanding the essence of this phenomenon and is a basis for questionable discoveries of special microeffects (Duncan and Peterson 1994 Ho and Tai 1998 Plam 2000 Herwig 2000 Herwig and Hausner 2003 Gad-el-Hak 2003). The latter were revealed by comparison of experimental data with predictions of a conventional theory based on the Navier-Stokes equations. The discrepancy between these data was interpreted as a display of new effects of flow in micro-channels. It should be noted that actual conditions of several experiments were often not identical to conditions that were used in the theoretical models. For this reason, the analysis of sources of disparity between the theory and experiment is of significance. 

In the case of a high-intensity wet magnetic separation process, the principal force acting to resist particles from being captured in the matrix is the fluid drag force, FD, which is given by the expression ... 

Two mid-term objectives are closely related to the principal goal of RP. The first of them has to do with encouraging price competition, as it provides an incentive for companies to bring their prices close to the reference level. This is precisely one of the reasons why the European Commission5 recommends RP. The second mid-term objective concerns incentives, as it takes into account the cost-effectiveness ratio of prescription drags by increasing the financial responsibility of patients, which in turn may influence prescriber decisions. It is important to note that, unlike in traditional co-payment, under this system the patient s share of the cost of the product is avoidable if the patient and/or doctor select a product with a price that does not exceed the reference price. 

On the other hand, inter-individual differences in a drug s effects may also be observed in the presence of appropriate concentrations of the intended compound at the intended site of action, i.e., be due to differential pharmacodynamics. Here, two conceptually quite different conceptual scenarios may be distinguished that relate to the two principal mechanisms by which drags act etiology-specific and palliative. 

Thus the drag resulting from any translation can be determined if the two principal resistances are known. The principal resistances of common axisymmetric shapes are given in subsequent sections. 

The principal resistances may be obtained from the drag ratios as... 

For an orthotropic particle in steady translation through an unbounded viscous fluid, the total drag is given by Eq. (4-5). In principle, it is possible to follow a development similar to that given in Section IT.B.l for axisymmetric particles, to deduce the general behavior of orthotropic bodies in free fall. This is of limited interest, since no analytic results are available for the principal resistances of orthotropic particles which are not bodies of revolution. General conclusions from the analysis were given in TLA. 

The only orthotropic particles for which comprehensive experimental results are available are square bars, rectangular parallelepipeds with one pair of square faces. Symmetry then shows that the two principal resistances corresponding to translation with square faces parallel to the direction of motion are equal. These resistances will be denoted by c 2, while the resistance for translation normal to the square faces will be called cy. Consider such a particle in arbitrary translation at velocity U. Figure 4.11 shows a section of the particle parallel to the square faces (72 is the component of U in this plane, and the angle between U2 and principal axis 2 is 0. From Eq. (4-5), the drag components are as shown in Fig. 4.11. Hence the drag component parallel to U2 is... 

For a particle which is spherically isotropic (see Chapter 2), the three principal resistances to translation are all equal. It may then be shown (H3) that the net drag is — judJ regardless of orientation. Hence a spherically isotropic particle settling through a fluid in creeping flow falls vertically with its velocity independent of orientation. 

Principally, investigations have been conducted of suitable linear velocities and power requirements. Slurries of 40-50 vol% solids can be handled satisfactorily, with particle sizes less than 24-48 mesh or so (0.7-0.3 mm). At low line velocities, particles settle out and impede the flow of the slurry, and at high velocities the frictional drag likewise increases. An intermediate condition exists at which the pressure drop per unit distance is a minimum. The velocity at this condition is called a critical velocity of which one correlation is... 

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