Equation 11.84 represents any operating line relating the composition of the vapour yn rising from a plate to the composition of the liquid reflux entering the plate, or alternatively it represents the relation between the composition of the vapour and liquid streams between any two plates. From equation 11.83, it may be seen that all such operating lines pass through a common pole N of coordinates xd and Hd.

Alternatively, noting that the right-hand side of equations 11.77, 11.78 and 11.79 are independent of conditions below the feed plate, a stream N may be defined with mass equal to the difference between the vapour and liquid streams between two plates, of composition xd and of enthalpy Hd. The three quantities Vn, Ln+1, and N are then on a straight line passing through N, as shown in Figure 11.27.

Below the feed plate a similar series of equations for material and heat balances may be written as:

Putting: then:


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