Acceleration mass average

The term [Apfjf is the mass-average acceleration of the fluid seen by the particles due in part to momentum transfer between phases, and Af f is due to forces in the fluid phase. The term Gf]f can be evaluated using Eq. (4.80) ... 

Thermodynamic activity information is required in the dilute solution regime where Henry s law is applicable. For an ideal mixture, activities are synonymous with mole fractions, and the slope of ua vs. xa is unity at infinite dilution. Hence, the thermodynamic derivative in the denominator of equation (25-91) is approximated by unity. Since fluid B is quiescent, the mass-average velocity of the mixture is essentially zero. The consequences of this condition are that v 0 and the pressure gradient balances the gravitational force on fluid B, as expected for a hydrostatic situation. Since there is no acceleration or forced diffusion for the continuum of fluid B, it is reasonable to set gs 0. Under these conditions, equation (25-91) yields ... 

It should be noted that the acceleration component is dominant in the last part of the pipe, where, because of the rapid pressure drop and the low absolute pressure, the specific volume of the gas increases sharply. This effect is more pronounced at high mass flow rates with large values of mass flow ratio, 3 (= mjm,). As shown in Figures 3.44a and 3.446, the average friction coefficient is affected by the mixture mass flow rate m, the mass flow ratio 3, and the diameter of the pipe D. The Re is defined as... 

An averaged value of cos 4> is dependent on the detection geometry) was used in evaluating AE1. A detailed analysis performed by Mills (1981) allowed for the fact that the Ps underwent acceleration for a significant proportion of its lifetime. From this he was able to deduce that the shifted annihilation line arose from a system with a mass-to-charge... 

It is clear from Fig. 4.5 that the data for ,c>p are considerably concentrated over 85% of the values are in the range 4.3 to 6.2, and the average value is 5.34. This fact indicates that ,c>p can be considered to remain essentially constant and that, consequentially, Eq. (4.11) describes well the pressure drop behavior due to the acceleration and collisions of the particles. Therefore the combined consideration of the two kinds of collisions, i.e., the collisions of particles on the wall and between particles, is reasonable and feasible. It should be noted that, as described by Eqs. (4.5) and (4.6), for a given impinging velocity u0, the velocity of particles at the outlet of the accelerating tube depends on the length of the tube Lac, the particles to gas mass flow rate ratio and the mean diameter of particles dv. Therefore Eq. (4.11) actually... 

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