Velocity distortion

Vfhere V Is the unit vector aimed along the sliding direction. The flux formula used here is re-trlcted to an isoviscous film. If temperature variation is to be considered, then factors to account for velocity distortion due to viscosity variation would have to be added (3). 

For defect sizing by TOED, use of L waves involves a penalty in resolution of almost a factor of two at a given frequency because of difference in velocity as compared to shear waves and use of SV waves runs into difficulties because of the mode conversion problems. Further, problems due to couplant thickness variations, surface roughness affects, beam skewing and distortion problems in anisotropic welds can also be expected. On the contrary, SH waves are not affected... 

Equation (B2.3.10) shows that the scattered intensity observed in the laboratory is distorted from that hr the CM coordinate system. Those products which have a larger laboratory velocity or a smaller CM velocity will be observed in the laboratory with a greater intensity. 

Figure 9.1 Distortion of flow streamlines around a spherical particle of radius R. The relative velocity in the plane containing the center of the sphere equals v, as r ...

Enough space must be available to properly service the flow meter and to install any straight lengths of upstream and downstream pipe recommended by the manufacturer for use with the meter. Close-coupled fittings such as elbows or reducers tend to distort the velocity profile and can cause errors in a manner similar to those introduced by laminar flow. The amount of straight pipe required depends on the flow meter type. For the typical case of an orifice plate, piping requirements are normally Hsted in terms of the P or orifice/pipe bore ratio as shown in Table 1 (1) (see Piping systems). 

The Coriolis veclor lies in the same plane as the velocity vector and is perpendicular to the rotation vector. If the rotation of the reference frame is anticlockwise, then the Coriolis acceleration is directed 90° clockwise from the velocity vector, and vice versa when the frame rotates clockwise. The Coriolis acceleration distorts the trajectory of the body as it moves rectilinearly in the rotating frame. 

Arbitrary-Lagrangian-Eulerian (ALE) codes dynamically position the mesh to optimize some feature of the solution. An ALE code has tremendous flexibility. It can treat part of the mesh in a Lagrangian fashion (mesh velocity equation to particle velocity), part of the mesh in an Eulerian fashion (mesh velocity equal to zero), and part in an intermediate fashion (arbitrary mesh velocity). All these techniques can be applied to different parts of the mesh at the same time as shown in Fig. 9.18. In particular, an element can be Lagrangian until the element distortion exceeds some criteria when the nodes are repositioned to minimize the distortion. 

Approaches used to model ozone formation include box, gradient transfer, and trajectoty methods. Another method, the particle-in-cell method, advects centers of mass (that have a specific mass assigned) with an effective velocity that includes both transport and dispersion over each time step. Chemistry is calculated using the total mass within each grid cell at the end of each time step. This method has the advantage of avoiding both the numerical diffusion of some gradient transfer methods and the distortion due to wind shear of some trajectory methods. 

The final term of Equation (6) corrects for the distortion of the ERS spectrum caused by velocity-dependent energy losses as the H ions pass through the stopper foil. 

It follows that as the peak velocity is inversely proportional to the distribution coefficient, then the higher concentrations in the peak will migrate faster than the lower concentrations. As a consequence, the peak is distorted with sharp front and a sloping back. This distortion is shown in Figure 9. 

The flow pattern of gas within the emulsion phase surrounding a bubble depends on whether the bubble velocity Ug is less than or greater than minimum fluidization velocity U . For Ubflow lines. For Ub> U , the much different case of Figure 4(B) results. Here a gas element which leaves the bubble eap rises much more slowly than the bubble, and as the bubble passes, it remms to the base of the bubble. Thus, a cloud of captive gas surrounds a bubble as it rises. The ratio of eloud diameter to bubble diameter may be written... 

This involves knowledge of chemistry, by the factors distinguishing the micro-kinetics of chemical reactions and macro-kinetics used to describe the physical transport phenomena. The complexity of the chemical system and insufficient knowledge of the details requires that reactions are lumped, and kinetics expressed with the aid of empirical rate constants. Physical effects in chemical reactors are difficult to eliminate from the chemical rate processes. Non-uniformities in the velocity, and temperature profiles, with interphase, intraparticle heat, and mass transfer tend to distort the kinetic data. These make the analyses and scale-up of a reactor more difficult. Reaction rate data obtained from laboratory studies without a proper account of the physical effects can produce erroneous rate expressions. Here, chemical reactor flow models using matliematical expressions show how physical... 

Flow distortion Nonuniform airstream velocity profile due to asymmetric... 

For intermediate drift rates (4 < BN < 8), when chain conformations are already distorted, deviates from linear behavior and goes through a maximum at some critical value Bf. of the field, confirming earlier findings by Pandey et al. [103,104]. This critical bias B at which the velocity starts to decrease depends rather weakly on the density Cobs, turns out to be reciprocal to chain length A, implying that only when the total force, /c = B,N 9, acting upon the whole driven molecule, exceeds a certain threshold, which does not depend on the size of the macromolecule, the chains start to get stuck in the medium. 

Figure 7-74. Approximate flame distortion due to lateral wind on jet velocity from flare stack. Reprinted by permission, American Petroleum Institute, API RP-521, Guide for Pressure Reiieving and Depressuring Systems, 3rd Ed., Nov. 1990 [33].

The major limitation of velocity transducers is their sensitivity to mechanical and thermal damage. Normal use can cause a loss of calibration and, therefore, a strict recalibration program is required to prevent data errors. At a minimum, velocity transducers should be re-calibrated every six months. Even with periodic re-calibration, however, velocity transducers are prone to provide distorted data due to loss of calibration. 

Experimental work with styrene in tubular reactors has been reported (39) where viscosities were relatively low due to conversions below 32%. However, Lynn ( ) has concluded that a laminar flow tubular reactor for styrene polymerization is probably technically infeasible due to the distortion in velocity... 

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