Alternate Representation and Calculation

This is a quadratic equation that may be solved for y, whereby y, may be obtained in terms of x-. The representation is not yet complete, however, for there coexists the material balance 

An algebraic solution requires that the material balance be substituted into the quadratic form, which yields a new quadratic form, which in turn must be solved for a value of, say, y. or x, depending on which variable is eliminated. The result in principle is identical to that of the previous sections and depends on the value specified for, say, V/F. 

Note that the previously derived expression in the form 

This expression may be solved for y vs. x, for parameters of (P/Pj) and (Py/Pi). It is an approach advocated in a communication from Uzi Mann of the Department of Chemical Engineering at Texas Tech University. The explicit solution for y turns out to be a quadratic equation, and graphical 

For the record, performing the multiplication and collecting terms, the preceding equation converts to 

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