Flux averages

The enormous volume of the oceans results in an average turnover time of more than 2600 years, compared to less than 10 days for atmospheric water. Although the reservoir is much smaller than the oceans, the cryosphere has the longest turnover time due to the small input flux. Average turnover times for all seven reservoirs, calculated from the data in Fig. 6-3, are shown in Table 6-3. 

Fig. 10.4 Measured breakthrough curve of bromide with CTRW and advection-dispersion equation (ADE) fits. Here, the quantity j represents the normafized, flux-averaged concentration (top) Complete breakthrough curve, (bottom) Region identified by the bold-framed rectangle in the top plot. Note the difference in scale units between the plots. Pressure head h=-10cm water velocity v=2.82 cm/h. The dashed tine is the best advection-dispersion equation solution fit. The soUd line is the best CTRW fit. (Cortis and Berkowitz 2004)...

Parker, J. C., and van Genuchten, M. Th. (1984). Flux-averaged and volume-averaged concentrations in continuum approaches to solute transport, Water Resources Research, 20(7), 866-872. 

The observation that the rate constant may be expressed in terms of an auto-time-correlation function of the flux, averaged over an equilibrium ensemble, has a parallel in statistical mechanics. There it is shown, within the frame of linear response theory, that any transport coefficients, like diffusion constants, viscosities, conductivities, etc., may also be expressed in terms of auto-time-correlation functions of proper chosen quantities, averaged over an equilibrium ensemble. 

In Table IV, we see that established techniques for velocity measurement allow us to determine the average momentum flux, average velocity, turbulent intensities, and shear stress. Next on the list, to complete the flow field description, is the fluctuation mass flux, and first on the combustion field list is the temperature and major species densities of the flame gases. 

Fig. 23 The monomer conversion in particles with different initial droplet sizes at various average free radical fluxes (average of ten runs, in s ). Filled squares 0.02 filled triangles 0.05 filled circles 0.1 (from [107])...

Estimation of long-term dissolution rate constants (Kl t) from 2-6 week surface flux averages and "apparent" mineral solubilities. 

Table 1 - Solar energy flux averaged over the Earth during T-Tauri phase (Values in parentheses correspond to today).

Figure 44 Tentative model of global ocean carbonate cycle. Fluxes are in units of lO molCyr as (Ca,Mg)C03 and represent estimates of fluxes averaged over the most recent glacial-interglacial transition (after Mackenzie and Morse, 1992).

Burial Rate of Mn. Analysis of sediment cores provided a closer look at the dynamics of Mn within the sediments. Figure 5 combines results from three sediment cores taken at the deepest site of Lake Sempach. Two cores were taken in January 1991 and one in May 1988. The arrows indicate the flux-averaged Mn concentrations of settling material at depths of 20 and 81 m, respectively. The time scale in Figure 5 was calculated with 137Cs dating (41) by using Ps = 1.84 g/m2 per day as the sediment accumulation rate. 

A large CCRO effect was observed in the 3N8 membranes the permeate fluxes increased by an average of about five-fold with recirculation. The increase in flux corresponded to a decrease in effective osmotic pressure difference from about 340 psi to about 6 psi. When recirculation was stopped, the permeate fluxes decreased immediately, indicating that the CCRO effect was reversible and that the flux increases were not due to membrane damage. The test was repeated with new membrane samples at 800 psi. Under RO conditions the permeate flux averaged 3.8 gfd under CCRO conditions the average flux increased by about six-fold to 23 gfd. This flux increase was comparable to those observed in the 400 psi experiments. 

A relation is needed between these measurable quantities and R, the intrinsic rejection coefficient defined by Equation 4. First, is defined as the local axial solute flux averaged over the fiber cross-section with axial diffusion negligible. 

This is a reasonable assumption for the cross flow system in which the length of the initial region may be small in comparison to the total conduit length. The reason is that, ulike the batch cell system where average flux is 2 orders of magnitude less than pure solvent flux, average flux in cross flow systems is only 10 times less than pure solvent flux. 

The neutron flux is the product of the neutron density and the neutron speed. Assuming that all the neutrons are travelling at the same speed, equal to the average speed, c , the reactor flux averaged over the complete core, Xavf> neutrons/mVs will be the product ... 

It is shown in Glasstone and Sesonske (1981) that in the steady state, the flux averaged over the core radius at height z, x(z)< will ol>cy the relationship. 

Xave reactor flux averaged over the complete core... 

For mobile solutes, flux averaged concentrations are defined as the ratio of solute flux to soil liquid flux through a given area, i.e. 

For some systems, heat input to different regions of the surface is adjusted to obtain a specific boundary condition—often to approximate an isothermal wall. This is most easily done with a number of small heating elements that can be individually adjusted to maintain a constant wall temperature. The local heat flux, or at least the heat flux averaged over the size of each individual heater, can be determined from the power input to the heaters. These heaters can be placed quite close to the surface. 

For an average blackbody temperature of the Earth-atmosphere system Te defined on the basis of (4.4), the longwave emitted flux averaged over the globe is... 

For regcle experiments, the above procedure was repeated three times. The permeate was collected, sampled and filtered another two times without redispersion of the cake. Samples were taken during each recycle step and the total feed volume was about 1.5 L. Membrane flux averaged over an interval of filtration was calculated as... 

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