Modeling a Desalinator

It is useful to define some variables to represent quantities such as the flow rate of salt in stream 1. First, we assign letters for the principal components. Let water = W, salt = 5, and total = T. It is prudent to choose obvious and mnemonic letters, such as W for water, so that when you see W in an equation you can immediately translate to water. Labeling water as some obtuse Greek character such as will complicate your analysis unnecessarily. Finally, we will use the nomenclature that F represents the flow rate of component i in stream n. Thus, the flow rate of salt in stream 1 translates to Fs,.  

We now translate the design into mathematics using the conservation of mass given in Eq. (3.9). We start with The total flow rate of stream 1 entering equals the total flow rate of stream 2 exiting plus the total flow rate of stream 3 exiting. With our nomenclature, this translates to 

Similarly we can write mass balances on water and salt water  

Equations (3.10), (3.11), and (3.12) are related because the sum of the individual components equals the total. The total flow rate of a stream is the sum of the component flow rates. For each stream we can write 

In other words, mass is an extensive property. This is not true for the total temperature, an intensive property Tj Ts + Tw- 

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