Inertial effect

Equation 16 is a form of the generalized Ohm s law. Ion mobiUty, electron pressure gradients, and inertial effects have been neglected. The latter two phenomena are generally of no concern in MHO generator flows, but ion mobiUty is sometimes significant. Ohm s law including ion mobiUty, stated here without proof, is... 

Particulates Procedures for testing a particulate source are more detailed than those used for sampling gases. Because particulates exhibit inertial effects and are not uniformly distributed within a stack, sampling to obtain a representative sample is more complex than for gaseous pollutants. EPA Method 5 (as shown in Fig. 25-32) is the most widely used procedure for determination of particulate emissions from a stationary source. In-stack samphng guidehnes are presented in EPA Method 17. 

These inertial effects become less important for particles with diameters less than 5 /rm and for low wind velocities, but for samplers attempting to collect particles above 5 p.m, the inlet design and flow rates become important parameters. In addition, the wind speed has a much greater impact on sampling errors associated with particles more than 5 fim in diameter (4). 

Gases, vapors, and fumes usually do not exhibit significant inertial effects. In addition, some fine dusts, 5 to 10 micrometers or less in diameter, will not exhibit significant inertial effects. These contaminants will be transported with the surrounding air motion such as thermal air current, motion of machinery, movement of operators, and/or other room air currents. In such cases, the exterior hood needs to generate an airflow pattern and capture velocity sufficient to control the motion of the contaminants. However, as the airflow pattern created around a suction opening is not effective over a large distance, it is very difficult to control contaminants emitted from a source located at a di,stance from the exhaust outlet. In such a case, a low-momentum airflow is supplied across the contaminant source and toward the exhaust hood. The... 

Inertial effects The force due to inertia equal in magnitude but opposite in direction to the accelerating force. 

Although long-time Debye relaxation proceeds exponentially, short-time deviations are detectable which represent inertial effects (free rotation between collisions) as well as interparticle interaction during collisions. In Debye s limit the spectra have already collapsed and their Lorentzian centre has a width proportional to the rotational diffusion coefficient. In fact this result is model-independent. Only shape analysis of the far wings can discriminate between different models of molecular reorientation and explain the high-frequency pecularities of IR and FIR spectra (like Poley absorption). In the conclusion of Chapter 2 we attract the readers attention to the solution of the inverse problem which is the extraction of the angular momentum correlation function from optical spectra of liquids. 

Markovian theory of orientational relaxation implies that it is exponential from the very beginning but actually Eq. (2.26) holds for t zj only. If any non-Markovian equations, either (2.24) or (2.25), are used instead, then the exponential asymptotic behaviour is preceded by a short dynamic stage which accounts for the inertial effects (at t < zj) and collisions (at t < Tc). 

The first component in expression (2.53) corresponds to the long-time behaviour of K( t) described by Markovian perturbation theory, while the second term introduces a correction for times less than zj. Within this time interval (before the first collision occurs) the system should display the dynamic properties of free rotation ( inertial effects ). 

In Markovian approximation (zj =0) this quantity approaches the famous Debye plateau shown in Fig. 2.3 whereas non-Markovian absorption coefficient (2.56) tends to 0 when ft) — 0 as it is in reality. This is an advantage of the Rocard formula that eliminates the discrepancy between theory and experiment by taking into account inertial effects. As is seen from Eq. (2.56) and the Hubbard relation (2.28)... 

The central Lorentzian part of the IR spectrum (2.55) has the same shape as in the classical Debye theory and may be of various origins. The impact mechanism of reorientation can be confirmed judging by the shape of the wings only. The inertial effects show themselves in the asymptotic relation... 

Sack R. A. Relaxation process and inertial effects. 2. Free rotation in space. Proc. Phys. Soc. (London) B70, 414-26 (1957). 

Gross E. P. Inertial effects and dielectric relaxation, J. Chem. Phys. 23, 1415-23 (1955). 

BTU/hr. sq.ft. over a wide range of viscosities and rotational speeds. This is equivalent to the thermal resistance of a fluid film equal to about 1/2 the clearance between the helical agitator and the vessel wall. This represents Reynolds numbers in the range of 10 to 10. This is the region of creeping flow where, with no inertial effects, there is little displacement of the fluid adjacent to the wall. 

At Reynolds number above 10-20, a new flow regime is established. While still laminar, it is obviously unsymmetrical. The inertial effects, therefore, are important but do not dominate to the extent of making the flow turbulent. In this region, a stable trailing vortex is set up behind each blade. 

Figure 11. Flow patterns with an anchor agitator as in Figure 10 but at higher Reynolds numbers (above 10-20) where inertial effects become significant. Streamline schematic (12) shows stable trailing vortex.

This is most easily achieved by rotating the inner cylinder and keeping the outer fixed in the laboratory frame. Note, however, that this geometry leads to the formation of Taylor vortex motion if inertial effects become important (Reynolds number Re 1). Most rheo-NMR experiments are actually performed at low Re. In the cylindrical Couette, the natural coordinates are cylindrical polar (q, <(>, z) so the shear stress is denoted and is radially dependent as q 2. The strain rate across the gap is given by [2]... 

The forces that exist within a fluid at any point may arise from various sources. These include gravity, or the weight of the fluid, an external driving force such as a pump or compressor, and the internal resistance to relative motion between fluid elements or inertial effects resulting from variation in local velocity and the mass of the fluid (e.g., the transport or rate of change of momentum). 

Fig. 3. Thresholds of cavitation. Region A Bubble growth through rectified diffusion only. Region B Bubble growth through transient cavitation. RD, Threshold for rectified diffusion Rlt threshold for predomination of inertial effects RB, Blake threshold for transient cavitation. [After R. E. Apfel (S).]...

In comparison with the large amount of literature that is available on the deposition of particles from laminar fluid flows, literature on turbulent deposition is virtually non-existant [114]. It was mentioned that the trajectory and convective diffusion equations also apply when the fluid inertial effects are considered, including the case of turbulent flow conditions, provided one is able to express the fluid velocities explicitly as a function of position and time. 

With any viscometer the flow generated should ideally have only one non-zero velocity component, causing shearing in only one direction. The purpose of a viscometer is simultaneously to measure (or control) both the shear stress and the shear rate. Not only must the flow be laminar but viscous forces must be dominant, that is, inertial effects must be negligible. 

At higher frequencies, all of the ions formed in gas phase cannot arrive at the cathode within a half cycle because of the inertial effect of ions. The growth rate begins to decrease at the... 

In region III, the discharge is maintained only by ionization in the gas phase without electron injection from the cathode. Because of the inertial effect of ions and electrons, only small part of charged particles in the gas phase can arrive on the electrode. Therefore, polymerization may be induced principally by diffused free radicals and/or ion-electron pairs ... 

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