Velocity spatial

Note that the spatial velocity (u) is arbitrary and may be the material velocity (u). If the spatial velocity is the material velocity (u = v), then the region of space moves with the material and the Lagrangian forms of the equations are generated. If the spatial velocity is zero, then the region of space is fixed and the equations take the Eulerian form. 

Velocity-encoding 2D NMR imaging methods characterize general patterns of spatial velocity distributions and directly visualize different characteristics of flow behavior depending on the properties of the materials and operating param-... 

Fig. 5.3.5 Jo int spatial-velocity images of xenon undergoing Poiseuille flow in a pipe (id = 4 mm, DXe = 4.5 mm2 s-1, Vave =...

Fig. 5.3.6 j oint spatial-velocity images of xenon undergoing Poiseuille flow in a pipe (id = 4 mm, Vave = 27 mm s 1, D = 8 mm2 s 1) at 0.7 atm recorded with a protocol shown in Figure 5.3.4(A). Only particles at walls are selected by the edge enhancement filter . A modified imaging gradient time duration... 

Alignment between spin axis and spatial velocity for Crab and Vela pulsars (see for example Lai et al. 2001)... 

Initial spin period, magnetic field, spatial velocity, mass, radius etc. (plus possible correlations between them). 

The spatial velocity gradient a = grad va can be decomposed into symmetric and skew-symmetric parts as la = sym a + skw 1 = dQ + wQ., where da and wa are the deformation rate and the spin tensors, respectively. 

Figure 9.19 shows the ethylene molar yield (%) of the ethanol dehydration reaction versus the ethanol feed (mol) for a mixture of ethanol (70%) + H20 (30%), supplied with a spatial velocity of 5 h 1 to an isothermic fixed-bed flow reactor consisting of 20 cm3 of the bed filled with the H-CMT-C sample (0.2-0.6mm particle diameter) at 718 K [19,140],... 

The laboratory scale physical model of the catalytic sulfur dioxide oxidation is a 0.05 m-diameter reactor containing 3 mm-diameter pellets of catalyst over a height of 0.15 m. The bed is flushed through at 430 °C by a gas flow that contains 0.07 kmol S02/kmol total gas, 0.11 kmol 02/kmol total gas and 0.82 kmol N2/kmol total gas. The gas spatial velocity is 0.01 m/s. 

The quality of the product at the outlet of the first reactor at the start of the run at different temperatures was determined with the fresh demetallation catalyst and the spatial velocity of the first industrial reactor (IF). 

Intuitively, bubble coalescence is related to bubble collisions. The collisions are caused by the existence of spatial velocity difference among the particles themselves. However, not all collisions necessarily lead to coalescence. Thus modeling bubble coalescence on these scales means modeling of bubble collision and coalescence probability (efficiency) mechanisms. The pioneering work on coalescence of particles to form successively larger particles was carried out by Smoluchowski [109, 110]. 

Fig. 19. Si (left panel) and Mg (right panel) triplets (resonance, intercombination and forbidden lines) resolved by Chandra High Energy transmission Grating Spectroscopy. The data are shown by the solid black histogram and an arbitrarily scaled point-source version of the two-shock model (no spatial-velocity effects) is shown in red to suggest the relative similarity of the data and model G-ratios [(f+i) /r]. (Fig reproduced by permission of the AAS and courtesy of D. Dewey [140])...

FIGURE 8-l9b Joint spatial-velocity distribution images of water at 1970, 2090. 2310 and 3080 Reynolds numbers. The vertical axis is the position across the pipe and the horizontal axis represents the axial velocity (Li et al. 1994) (Reprinted by permission of Elsevier Science Ltd.)... 

A scheme of the estimation of the spatial velocity distribution from the measured tracer distribution is given and the several concepts are presented for the utilization of these dates for the modelling of hydrodynamic flow processes in soil columns ... 

Positron Emisssion Tomography 3-8 mm low tracer concentration, which not influences the geochemical regime measurement of spatial velocity by steady state flow possible flow detection also in single small pores (0 < 0.5 mm) special radioactive tracer necessary, commercial PET-cameras only for medical applications available... 

With narrow band LQ -radiation it was possible to measure the spatial velocity distribution of atomic hydrogen generated by the photodissociation of HI . Other applications of radiation included the... 

Again, as a start, we consider only a wave of constant form and constant speed v = dp/dT. This constant spatial velocity may also be expressed in terms of the appropriate partial derivatives as ... 

Step 1. A recursion from the base to the tip is required to calculate the positions, spatial velocities, Coriolis and gyroscopic terms for each of the rigid bodies. To proceed, the 6x6 spatial transformation matrix, between rigid bodies k and fc 1 must first be defined ... 

Here h and O3 denote the 3 x 3-dimensional identity and zero matrices, while the / operator refers to the cross-product tensor associated with Fk — Fk I, where Fk is the position vector that defines the reference frame for rigid body k. The spatial velocity, V i, can be computed from the following relation ... 

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