Net expansion factor

For flow of compressible fluids use the net expansion factor Y (see later discussion) [3] ... 

For the discharge of compressible fluids from the end of a short aiping length into a larger cross section, such as a larger pipe, vessel, or atmosphere, the flow is considered adiabatic. Corrections are applied to the Darcy equation to compensate for fluid property changes due to the expansion of the fluid, and these are known as Y net expansion factors [3]. The corrected Darcy equation is ... 

Figure 2-38A. Net expansion factor, Y, for compressible flow through pipe to a larger flow area. By permission, Crane Co., Technical Paper U410, Engineering Div., 1957. Also see 1976 edition.

Y = net expansion factor from Figures 2-38A or 2-38B AP = differential pressure (equal to inlet gauge pressure when discharging to atmosphere)... 

These calculations show that the volume dependency of a gas-phase reaction is a function not only of the stoichiometry, but also of the inerts content of the reacting mixture. The sensitivity of volume to conversion is lowered as the inerts increase. The expansion factor, eA, is positive for reactions producing a net increase in moles, negative for a decrease in moles, and eA= 0 for reactions producing no net changes and at constant volume. 

We note that A q depends on the current rate, rn, of desorption, which we do not know, plus various known system constants. Since the other terms in equation 5.68 are known, one can in principle measure the net rate of desorption r using the I/O expansion factor alone, no analysis of the output stream is required and one is not troubled by the mixing going on in the void volume. When we include the expansion factor for ka, the temperature ratio for km cancels out that for fo leaving the very simple expression ... 

The I/O expansion factor will not be much different from the molar expansion fee-tor but it may be measurable. If so, it may provide a simple way of measuring net desorption rates. The kind of device that would make this technique viable is a differential flow rate or differential flow velocity meter. Since temperature does not enter into equation 5.69, this device would compare the flow rates of the inlet and a cooled outlet stream at a convenient common temperature, say the temperature at which inlet flow is metered. 

Recall that the reabsorption of Na+ ions is accompanied by reabsorption of Cl- ions, which diffuse down their electrical gradient, and by reabsorption of water, which diffuses down its osmotic gradient. The net result is an expansion of plasma volume and consequently an increase in blood pressure. Therefore, the regulation of sodium reabsorption is important in the long-term regulation of blood pressure. As such, aldosterone and ANP, as well as the factors involved in their release, are discussed further in subsequent sections. 

Net Forces on a Differential Control Volume Based on a differential control volume (i.e vanishingly small dimensions in each of three spatial coordinates), we write the forces on each of the six faces of the control volume. The forces are presumed to be smooth, continuous, differentiable, functions of the spatial coordinates. Therefore the spatial variations across the control volume in each coordinate direction may be represented as a first-order Taylor-series expansion. When the net force is determined on the differential control volume, each term will be the product a factor that is a function of the velocity field and a factor that is the volume of the differential control volume 8 V. 

The net effect of these factors is that all producers and users are under increasing pressure to develop and implement environmentally sensitive fertilizer production and use, technologies, and more efficient pollution abatement processes and installations. As retrofitting and expansions of existing fadlities and new developments are contemplated, there will be significant scope for improving the contribution of the fertilizer industry to sustainable development. 

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