Weight fraction, defined

Figure 11.3 shows the entrainment flux measured at the outlet of the unit and the fines weight fraction (defined as particle sizes smaller than 44 microns) for the bed and entrained material as a function of time. As the fines concentration began to decrease in the bed, the entrainment rate increased rapidly to a peak approximately 10 times the initial rate. Further depletion of fines from the bed resulted in a subsequent drop in the entraimnent rate. For the commercial unit, the highly variable entrainment rates appeared to be due to the extreme sensitivity to the fines concentration. The dipleg was not designed to handle the presumed tenfold increase in the entrainment rate and often flooded as a result. 

Throughout this discussion we have used the numerical fraction of molecules in a class as the weighting factor for that portion of the population. This restriction is not necessary some other weighting factor could be used equally well. As a matter of fact, one important type of average encountered in polymer chemistry is the case where the mass fraction of the ith component is used as the weighting factor. Defining the mass of material in the ith class as mj, we write... 

The second term in brackets in equation 36 is the separative work produced per unit time, called the separative capacity of the cascade. It is a function only of the rates and concentrations of the separation task being performed, and its value can be calculated quite easily from a value balance about the cascade. The separative capacity, sometimes called the separative power, is a defined mathematical quantity. Its usefulness arises from the fact that it is directly proportional to the total flow in the cascade and, therefore, directly proportional to the amount of equipment required for the cascade, the power requirement of the cascade, and the cost of the cascade. The separative capacity can be calculated using either molar flows and mol fractions or mass flows and weight fractions. The common unit for measuring separative work is the separative work unit (SWU) which is obtained when the flows are measured in kilograms of uranium and the concentrations in weight fractions. 

Let us define an average density at inlet using weight fractions. 

It is obvious, but worth emphasising, that the sum of the individual component flows in any stream cannot exceed the total stream flow. Also, that the sum of the individual molar or weight fractions must equal 1. Hence, the composition of a stream is completely defined if all but one of the component concentrations are given. 

In these experiments, the lack of a well-defined supernatant region leads to an uncertainty in the weight-fraction values for each solution, with the error being less in the steeper parts of the curves. The plateau region... 

Calculation of Processing Capacities. The processing capacity of a membrane (V,/Sf) is defined as the volume of charge (feed solutions) that 1 m2 of film surface can handle per day in a batch concentration process to increase the solute weight fraction from z, to Zf at a given operating pressure. The following relationship has been derived by Sourirajan and Kimura (12) ... 

The content of volatiles is often used as a measure of the degree of oxidation of carbon blacks. This is defined as the weight loss on heating at 950 °C (DIN 53552). Typical values for the weight fraction of volatiles are 1-3% for furnace blacks, 4-8% for gas blacks, and up to 25% for oxidized gas blacks. 

Let wx be a probability distribution (e.g. the weight fraction of a polymer) of finding an event (the degree of polymerization), where x is an integer. Then the corresponding generating function W (s) is defined as the sum over all the events wx multiplied by a variable s raised to the x-th power... 

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