Transportation velocity, estimation

By use of the intercept method of van der Weij (1932) the transport velocities in sunflower hypocotyl sections (Fig. 3.4), as estimated from the intersections with the time axis of the extrapolated linear regression lines, amount to 5.9 mm h" and 3.7 mm h at the higher and lower donor concentrations, respectively. Similar estimated relationships between donor concentration and transport velocity estimations have been found for basipetal lAA transport in Coleus stems (Naqvi 1963), Zea coleoptiles (Naqvi and Gordon 1964, Naqvi 1976), and Avena coleoptiles (Newman 1963, 1970) and may be deduced from the shape of the arrival curves derived mathematically by Newman (1974) from his experimental data. On the other hand, velocities estimated by the intercept method have been reported not to be significantly different at different auxin concentrations in the donor, though the calculated values tended to be higher at increased donor concentration (e.g., van der Weij 1932 in Avena coleoptiles ... 

Estimation of Transportation Velocity of Solid Particles in Pipe Flow at Various Inclination Angles 1335... 

It can be shown that for a reservoir in steady state. To is equal to t, i.e. the turnover time is equal to the average residence time spent in the reservoir by individual particles (Eriksson, 1971 Bolin and Rodhe, 1973). This may seem to be a trivial result but it is actually of great significance. For example, if tq can be estimated from budget considerations by comparing fluxes and burdens in Equation (1) and if the average transport velocity (V) within the reservoir is known, the average distance (L = Vxr) over which the transport takes place in the reservoir can be estimated. 

For example, for the iron oxide dust considered in the previous case study, Table 2 suggested Vfmm = 18 to 20 m s1 (i.e., assuming an average industrial dust ) On analysis of the sample, it was found dp50 80 pm, which appeared to support this classification. However, upon further examination of the actual distribution of size, a significant proportion of the material was found > 1000 pm (e.g., large flakes). A minimum conveying velocity of at least Vjmm 25 m s 1 was estimated for this dust. This explains why the iron oxide material built up and eventually blocked branch II-IV, which was sized/balanced mainly for air distribution purposes and produced transport velocities < Vfi r... 

There has been no definitive theory proposed to predict the transport velocity. A simple empirical equation proposed by Bi and Fan (1992), given next, can be used for estimation of the transport velocity ... 

Example 11.3 Consider a gas-solid horizontal pipe flow. The pipe diameter is 50 mm. The particle used is 50 pm glass bead with the density of 2,500 kg/m3. The average particle volume fraction is 0.1 percent. The gas density and kinematic viscosity are 1.2 kg/m3 and 1.5 x 10-5m2/s, respectively. Estimate the minimum transport velocity and power consumption per unit length. 

Table 4.3 CNV97100 transport parameter estimated in whole small intestine, duodenum and ileum. Fits were performed simultaneously using Eqs. (26)-(29). No inhibitor was present. S.E. - standard error, CV % - coefficient of variation. Vmjotai maximal velocity in whole small intestine, VmQ maximal velocity in duodenum, Vmj maximal velocity in jejunum, Vmj maximal velocity in ileum. Vmo, Vmj, and Vmjotaj are secondary parameters computed from (CV % is the same).

The melt velocity estimated from transport models is a bit slower but still comparable to estimates from the dynamic melting models. For example, if we assume that Ra-excesses are produced at the bottom of a column 90 km deep and need to move to the surface in —3 half-lives, then wq —20myr. It should be stressed that this is a constraint on the average melt velocity across the entire melting column rather than a constraint on the maximum velocity near the surface. Moreover, the constraint from Equation (9) assumes that there is only a single porosity near the surface. Two-porosity models (next section) relax this constraint somewhat. 

Using equation [7] and x = 5-6 years, the frequency distribution of an instantaneous plutonium contamination for different boxes and different times was computed. When i is used a a variable, t as a fixed parameter, the penetration of 50% of transported contamination can be estimated after summing up the distribution frequencies. From this and from the corresponding times, the transportation velocity of PuOo is obtained very easily (Table I). 

This transportation velocity applies to a loamy soil and weather conditions involving about 1000 mm annual precipitation. Under conditions like this a percolation velocity of infiltrated precipitation vw = 100 cm/a was estimated by tracer experiments in the vicinity of Heidelberg (2). 

DEWEY 1957, 1964), with radioactive lAA and to follow its behavior in the plant, left as intact as possible. The natural auxin source was replaced by a lanolin paste containing lAA (in this case, " C-IAA). The new auxin source sustained natural elongation and growth movements of the stalk (Kaldewey 1957, 1962, 1965b). Seven hours later, the axis of the plant was cut several centimeters below the apex and supplied at the cut end of its base with agar receivers, twice each for 15-min periods. Then, a 5-mm section was excised and stood on fresh agar receivers to allow all the mobile auxin to move out, and the new basal cut surface of the remaining axis was successively supplied with another pair of receivers for 15-min periods. The radioactivity collected in the 15-min receivers and the section receivers, respectively, allowed an estimation of the transport intensity and transport density. It was possible, therefore, to calculate the transport velocity from these quantities [see Eq. (2)]. Further, auxin immobilized within the 5-mm sections could be determined by extraction (see Fig. 3.6). 

Short-term application of auxin to the apical cut surface of coleoptile sections, combined with an estimation of auxin accumulation with time in basal receivers which were replaced at brief intervals, was demonstrated by van der Weij (1932, p442ff) to be a means of calculating transport velocity. He observed that the auxin export rate (i.e., the transport intensity) increased initially to a maximum and then decreased. He assumed that the arrival time of the peak of transport intensity was the period of time needed by the auxin stream to traverse the segment. The velocity thus estimated (8mmh" ) was similar to the values of about 10mmh obtained with the intercept method. When labeled hormones became available, such pulse experiments were refined and modified. The duration of the pulse application could be reduced to 60 s (Shen-Miller 1973 a, b) and the receivers could be changed with great frequency to improve the estimation of the peak. 

Newman (1965, 1970) modified the penetration method by determining the profiles of mobile within decapitated, auxin depleted Avena coleoptiles supplied with agar donors containing " C-IAA. He plotted the amounts of radiocarbon collected in basal receivers of 1-mm sections against distance from the top. At the lowest concentration of auxin applied (0.3 pM), there was a linear decrease in the profile, while at higher donor concentrations the profiles were exponential. By determining the intersections of the profile plots with the distance axis, a transport velocity of about 10 mm h was calculated. This agrees closely with estimations from other methods. 

Sheldrake (1973 a) demonstrated by separation of the stem tissues of Nico-tiana internodes that the great majority of the strongly basipetal auxin transport took place in cells of the internal phloem and in cells close to the cambium. Very small amounts were transported in bark and pith preparations and none in xylem tissues. Using the intercept method of van der Weij (1932), he estimated velocities of about 5 mm h for the transport of l- C-IAA in complete stem sections, in inner tissue segments containing the internal phloem, and in xylem + cambium + bark section. The transport densities were similar to each other in the two latter preparations. Lower transport densities were found in the bark and in exclusively pith sections having transport velocities of 3.8 and 3.1 mm h S respectively. In all cases, however, a small amount of radioactivity was found in basal receivers considerably in advance of the time intercepts calculated from the linear parts of the auxin arrival curves (Fig. 3.3). Thus, even in homogenous tissues, auxin molecules appear to move at different velocities. 

The mass flow rate or throughput of the bulk material can be estimated if the net transport velocity, trough and material geometry and bulk density are known. Assuming the displacement equation (6.12) holds, then the horizontal velocity can be written as ... 

The average transport velocity of the bulk solid can then be estimated by a general expression ... 

The dependence of the kinetic sorption parameters on the concentration of the adsorbent in the suspension of the batch-experiment is not negligible. Neglecting this concentration dependence for reversible sorption leads to wrong estimations of the transport velocity of the pollutant in sediment or soil. Therefore, environmentally relevant batch-experiments have to be made at adsorbent concentrations true to nature. If this is not possible, corrective calculations under the model conditions described could be performed as an approximation. 

TRANSPORT PARAMETERS AND CORRELATIONS 11.4.1 Darcian Velocity Estimation... 

Namikas, S.L., Bauer, B.O., and Sherman, D.J. 2003. Influence of averaging interval on shear velocity estimates for aeolian transport modelling. Geomorphology 53(3-4) 235-245. 

A mass transfer coefficient can be defined as the vertical dispersion coefficient (cm /s or m /h) divided by the mean path length (cm or m) between the water compartments, yielding a transport velocity (cm/s or m/h). This in turn can be multiplied by the area of transfer (cm or m ) to give a hypothetical volumetric exchange flow rate (cm /s or m /h). In the absence of data for a specific system, an initial estimate of 0.02 cm /s or 0.0072 m /h can be assumed and the sensitivity of the model results to this parameter evaluated. If the value proves to be critical, measurements of temperature profiles may be desirable as a basis for estimating the mass transfer rate. 

Phonon transport is the main conduction mechanism below 300°C. Compositional effects are significant because the mean free phonon path is limited by the random glass stmcture. Estimates of the mean free phonon path in vitreous siUca, made using elastic wave velocity, heat capacity, and thermal conductivity data, generate a value of 520 pm, which is on the order of the dimensions of the SiO tetrahedron (151). Radiative conduction mechanisms can be significant at higher temperatures. 

Early models used a value for that remained constant throughout the day. However, measurements show that the deposition velocity increases during the day as surface heating increases atmospheric turbulence and hence diffusion, and plant stomatal activity increases (50—52). More recent models take this variation of into account. In one approach, the first step is to estimate the upper limit for in terms of the transport processes alone. This value is then modified to account for surface interaction, because the earth s surface is not a perfect sink for all pollutants. This method has led to what is referred to as the resistance model (52,53) that represents as the analogue of an electrical conductance... 

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