Mass flux calculating

In principle, the sizing of membranes consists of determining the cross-sectional area needed to achieve specifications with respect to recovery and selectivity of components. The mass flux calculation of a component Nj follows the expression ... 

One final comment about these mass flux calculations is necessary. Deposition of effluent particles on the sea bottom is by no means permanent. Several processes acting alone or in concert may result in the removal of the effluent particle from its original site of deposition. These processes include (1) physical removal resulting from bottom-current or storm-surge resuspension and (2) chemical removal resulting from ingestion or disturbance (bioturbation). The simultaneous effect of several of these processes has been considered by Hendricks (4). 

Interfacial Contact Area and Approach to Equilibrium. Experimental extraction cells such as the original Lewis stirred cell (52) are often operated with a flat Hquid—Hquid interface the area of which can easily be measured. In the single-drop apparatus, a regular sequence of drops of known diameter is released through the continuous phase (42). These units are useful for the direct calculation of the mass flux N and hence the mass-transfer coefficient for a given system. 

Once the mass flux G has been determined. Fig. 6-21r or Q>-2 h can be used to determine the pressure at any point along the pipe, simply by reducing 4fL/D and computing p From the Figures, given G, instead of the reverse. Charts for calculation between two points in a pipe with known flow and known pressure at either upstream or downstream locations have been presented by Loeb (Chem. Eng., 76[5], 179-184 [1969]) and for known downstream conditions By Powley (Can. J. Chem. Eng., 36, 241-245 [1958]). 

Equation (6-128) does not require fric tionless (isentropic) flow. The sonic mass flux through the throat is given by Eq. (6-122). With A set equal to the nozzle exit area, the exit Mach number, pressure, and temperature may be calculated. Only if the exit pressure equals the ambient discharge pressure is the ultimate expansion velocity reached in the nozzle. Expansion will be incomplete if the exit pressure exceeds the ambient discharge pressure shocks will occur outside the nozzle. If the calculated exit pressure is less than the ambient discharge pressure, the nozzle is overexpanded and compression shocks within the expanding portion will result. 

Range of concentration within the settling zone, Y = 3.0 (slurry) —5.67 (feed). First, calculate the variation of mass flux through the unit between inlet and outlet... 

Two-phase flow pattern maps, observed by Revellin et al. (2006), are presented in Fig. 2.31 in mass flux versus vapor quality, and superficial liquid velocity versus superficial vapor velocity formats calculated from the test results as follows ... 

Available data sets for flow boiling critical heat flux (CHF) of water in small-diameter tubes are shown in Table 6.9. There are 13 collected data sets in all. Only taking data for tube diameters less than 6.22 mm, and then eliminating duplicate data and those not meeting the heat balance calculation, the collected database included a total of 3,837 data points (2,539 points for saturated CHF, and 1,298 points for subcooled CHF), covering a wide range of parameters, such as outlet pressures from 0.101 to 19.0 MPa, mass fluxes from 5.33 to 1.34 x lO kg/m s, critical heat fluxes from 0.094 to 276 MW/m, hydraulic diameters of channels from 0.330 to 6.22 mm, length-to-diameter ratios from 1.00 to 975, inlet qualities from —2.35 to 0, and outlet thermal equilibrium qualities from -1.75 to 1.00. 

Figure 5. An example of the use of concentrations to assess changes in sediment mass accumulation taken from McManus et al. (1998). The upper panel shows the measured °Thxs, calculated from measured °Th concentrations by correction for detrital °Th, and for the effects of age using 5 0 stratigraphy (see Appendix). Because the supply of °Th to the sediment is a constant, low °Th represent times of rapid sediment mass accumulation. The calculated mass flux is shown in the lower panel. Dramatic increases in mass flux are observed during all but one of the Heinrich events, shown by the gray bands.

In inverted annular flow dryout, liquid mass flux is low enough and wall heat fluxes are high enough to cause vapor to be generated rapidly near the wall, forming a vapor annulus surrounding a liquid core (Fig. 4.176). The vapor generation near the wall occurs so quickly that the velocities of the two phases are about equal, or S = 1, so the expression for the void fraction at dryout, ado, can be calculated from the known dryout quality, Ydo ... 

Quandt (1962) measured the values of (CfICm - 1) at various axial positions of an air-water mixture flow in a 0.25-in. X 3-in. channel and converted the raw data to the exchange mass flux, pLV(, as shown in Figure 5-23. He also measured the film velocity Vf by injecting a pulse of dye into the liquid film and recording its transport time between two photocells. Such measured data are shown in Figure 5.24. By using the measured values for Vf, the liquid film thickness t may be calculated as... 

The science of chemical kinetics is concerned primarily with chemical changes and the energy and mass fluxes associated therewith. Thermodynamics, on the other hand, is concerned with equilibrium systems. .. systems that are undergoing no net change with time. This chapter will remind the student of the key thermodynamic principles with which he should be familiar. Emphasis is placed on calculations of equilibrium extents of reaction and enthalpy changes accompanying chemical reactions. 

By solving Eqs. (4) and (7) simultaneously, the mass flux can be calculated provided the wall shear stress is known as a function of particle superficial volume flow rate. Botterill and Bessant (1973) have proposed several relationships for shear stress, however, these are not general. LaNauze (1976) also proposed a method to measure this shear stress experimentally. 

Calculate the mass flux (kg/m2 s) for the following tank leaks given that the storage pressure is equal to the vapor pressure at 25°C ... 

The first step in the relief sizing calculation for two-phase vents is to determine the mass flux through the relief. This is computed using Equation 4-104, representing choked two-phase flow through a hole ... 

Find the density p from an equation of state at Pi,TSi for the phase densities pc and pL, and the reciprocal of the homogeneous specific volume vH. Calculate the mass flux from... 

Due to the change in the average velocity w, it is more convenient in calculations for compressible flow in pipes of constant cross-sectional area to work in terms of the mass flux G. This is the mass flow rate per unit flow area and is sometimes called the mass velocity. If the mass flow rate is constant, as will usually be the case, then G is constant when the area is constant. The relationship between G and u is given by... 

An ideal gas in which the pressure P is related to the volume V by the equation PV = 75 m2/s2 flows in steady isothermal flow along a horizontal pipe of inside diameter d, = 0.02 m. The pressure drops from 20000 Pa to 10000 Pa in a 5 m length. Calculate the mass flux assuming that the Fanning function factor/= 9.0 x 10 3... 

Mass fluxes of alkali elements transported across the solid-solution interfaces were calculated from measured decreases in solution and from known surface areas and mineral-to-solution weight-to-volume ratios. Relative rates of Cs uptake by feldspar and obsidian in the batch experiments are illustrated in Figure 1. After initial uptake due to surface sorption, little additional Cs is removed from solution in contact with the feldspars. In contrast, parabolic uptake of Cs by obsidian continues throughout the reaction period indicating a lack of sorption equilibrium and the possibility of Cs penetration into the glass surface. 

Stationary, traveling wave solutions are expected to exist in a reference frame attached to the combustion front. In such a frame, the time derivatives in the set of equations disappear. Instead, convective terms appear for transport of the solid fuel, containing the unknown front velocity, us. The solutions of the transformed set of equations exist as spatial profiles for the temperature, porosity and mass fraction of oxygen for a given gas velocity. In addition, the front velocity (which can be regarded as an eigenvalue of the set of equations) is a result from the calculation. The front velocity and the gas velocity can be used to calculate the solid mass flux and gas mass flux into the reaction zone, i.e., msu = ps(l — e)us and... 

Equations (25) and (30) have also been tested under more severe conditions. The numerical data used in the simulations are shown in Table 3. Figure 5(a) shows the results obtained from eq. (25) vs the results obtained from the exact analytical solution [eq. (26)]. Figure 5(b) shows the results obtained from eq. (30) vs the results obtained from the exact analytical solution [eq. (26)]. From Fig. 5(a) it can be seen that the mass fluxes cannot be predicted on the basis of Pick s law. It turned out that eq. (30) could predict the mass flux in 75% of the situations resulting in an error typically less than 5%. By examining other situations and making additional calculations it turned out that errors exceeding 5% occurred in the following cases ... 

A closer examination of the results obtained for run 12 from Table 2 (K g = 2 x 10 m/s) revealed that an increasing reaction rate constant produced a decreasing dimensionless mass flux n. This surprising effect has been studied in more detail by calculating as a function of the reaction rate constant where K tg has been taken equal to lx 10" m/s in order to enlarge the computed effects. The results of the calculations are shown in Fig. 8. In this figure three lines are shown which correspond to the following reaction kinetics ... 

From the information about the mass flux of the conversion gas it is possible to calculate the latent heat flux of combustion contained in the conversion gases from the relationship... 

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