Effective inertia

The flow distribution in a manifold is highly dependent on the Reynolds number. Figure 14b shows the flow distribution curves for different Reynolds number cases in a manifold. When the Reynolds number is increased, the flow rates in the channels near the entrance, ie, channel no. 1—4, decrease. Those near the end of the dividing header, ie, channel no. 6—8, increase. This is because high inlet velocity tends to drive fluid toward the end of the dividing header, ie, inertia effect. 

Fig. 31. Bubble wall velocity vs time during cavitational collapse for different values of the parameter X defined as X ss 0.4 c iTl] p./fri/2 (Ph — Pv)i/2). X permits us to account for the viscous and inertia effects of the polymer solution (redrawn according to Ref. [122]) ...

The precision of the measured Nx values can be influenced by inertia. All Nr values of shear rates higher than 10 s 1 can be corrected for inertia effect using Eq. (43) ... 

In the later stages, bubble growth is controlled more and more by heat transfer to the bubble wall, although for a high-conductivity liquid such as sodium, inertia effects are dominant throughout most of the growth period. 

Role of Inertia Effects in the Sub-Barrier Transfer of Heavy Particles... 

The Hamiltonian in Eq. (104) may describe both the process of tunnel inversion or isomerization of a molecule and the inertia effects arising from the symmetric vibrations of the reaction complex AH- B in the cage of the solvent or solid matrix (Fig. 9). In the latter case, the coordinate and the frequency of the symmetric vibration correspond to R and w0. 

Here (x)t and (x)f denote the mean values of the relative coordinate x over the states of the proton in the first and second potential wells, respectively. Equation (107) shows that the inertia effects lead to a decrease of the activation factor in the transition probability due to an increase of the reorganization energy. The greater the mass, m of the tunneling particle and the frequency of the vibrations of the atom, w0, the greater is this effect. The above result corresponds to the conclusion drawn in Ref. 66. 

At 4kTh l > (fuo0)2, the first term in the exponent is greater than the absolute value of the second term and the inertia effect leads to an increase of the transition probability. 

If the motion of the center of mass is of quantum character (low temperatures), the inertia effect leads only to the renormalization of the resonance integral,... 

Weiss and Worsham 259 indicated that the most important factor governing mean droplet size in a spray is the relative velocity between air and liquid, and droplet size distribution depends on the range of excitable wavelengths on the surface of a liquid sheet. The shorter wavelength limit is due to viscous damping, whereas the longer wavelengths are limited by inertia effects. 

As noted in Chapters 2 and 3, deformation of fluid particles is due to inertia effects. For low Re and small deformations, Taylor and Acrivos (T3) used a matched asymptotic expansion to obtain, to terms of order We /Re,... 

For large bubbles where inertia effects are dominant, enclosed vertical tubes lead to bubble elongation and increased terminal velocities (G7). The bubble shape tends towards that of a prolate spheroid and the terminal velocity may be predicted using the Davies and Taylor assumptions discussed in Chapter 8, but with the shape at the nose ellipsoidal rather than spherical. The maximum increase in terminal velocity is about 16% for the case where 2 is small (G6) and 25% for a bubble confined between parallel plates (G6, G7) and occurs for the enclosed tube relatively close to the bubble axis. 

The results referred to in this section refer primarily to gaseous slugs and to large values of Eo or Eod where inertia effects tend to be dominant. Experimental results for liquid drops and for smaller bubbles and columns are lacking. 

The main prediction of this treatment is that the film thickness should increase gradually in the direction of flow due to the inertia effects. Substitution of values of the physical properties into these equations has shown that these effects are usually small for ordinary mobile liquids, such as water. 

Labuntsov (L2), 1957 Heat transfer to condensate films on vertical and horizontal surfaces. In laminar region, Nusselt equations are corrected for (a) inertia effects, (b) variation of physical properties with temperature, (c) effects of waves. In turbulent region various universal velocity profiles are used. Results compared with experimental data. 

Theoretical treatment of smooth laminar film flow on vertical surface, with and without gas flow, including inertia effects. Nusselt equations (N6, N7) are shown to be special cases of the present solutions. 

Fortunately, complications due to inertia effects do not affect these calculations at resonance. From S and S", the moduli (working in shear) G, G" and G can be deduced. Usually, a mass is added to the rubber test piece to reduce the resonant frequency to levels of practical interest and it is quite feasible to vary the mass at a constant frequency until the system is at resonance. 

Piezoelectric gages are very suitable for measuring rapid pressure changes because of the absence of inertia effect... 

The general theory of thermoelasticity is well documented in the took by Nowacki43 which also gives solutions for some physical problems. In particular those for the quasistatic case in which inertia effects can be neglected are derived from the work of Biot. However, there does not appear to be any experimental work on the relation of internal friction to the thermoelastic effect other than that on metals (Zener42, Nowick and Berry44 ). 

In the high crack velocity regime three different values of Kid can be assigned to one rate of crack propagation depending on the state of crack acceleration. This behaviour was ascribed to inertia effects associated with crack acceleration and deceleration. Such a hypothesis is corroborated by the computed K data (also shown in Fig. 9), which were obtained from a finite element model, taking into consideration the mentioned transient dynamic linear elastic effects [35]. 

Neglecting the inertia effects, the momentum equation becomes,... 

Derive an equation that will give the coating thickness in a blade coating operation schematically depicted in Fig. 6.74. Assume a Newtonian fluid and neglect inertia effects. 

O.A. Estrada, I.D. Lopez-Gomez, C. Roldan, M. del P. Noriega, W.F. Florez, and T.A. Osswald. Numerical simulation of non-isothermal flow of non-newtonian incompressible fluids, considering viscous dissipation and inertia effects, using radial basis function interpolation. Numerical Methods for Heat and Fluid Flow, 2005. 

It should be mentioned that for flows at high Reynolds numbers, inertia effects must be included in Eq. (8.53), hence, Eq. (8.56) should be modified accordingly. The interstitial velocities of solids and gas are related to the superficial velocities of solids and gas, respectively, by... 

Particles are ejected into the freeboard via two basic modes (1) ejection of particles from the bubble roof and (2) ejection of particles from the bubble wake, as illustrated in Fig. 9.19. The roof ejection occurs when the bubble approaches the surface of the bed, and a dome forms on the surface. As the bubble further approaches the bed surface, particles between the bubble roof and surface of the dome thin out [Peters et al., 1983]. At a certain dome thickness, eruption of bubbles with pressure higher than the surface pressure takes place, ejecting the particles present on top of the bubble roof to the freeboard. In wake ejection, as the bubble erupts on the surface, the inertia effect of the wake particles traveling at the same velocity as the bubble promptly ejects these particles to the freeboard. The gas leaving the bed surface then entrains these ejected particles to the freeboard. 

Without losing generality, in this section we only consider case (3), where the pipe bend is located in the vertical plane with a vertical gas-solid suspension flow at the inlet, as shown in Fig. 11.10. It is assumed that the carried mass and the Basset force are neglected. In addition, the particles slide along the outer surface of the bend by centrifugal force and by the inertia effect of particles. The rebounding effect due to particle collisions with the wall is neglected. 

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