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7.3.1 Is the ``common'' model valid?

Is the mass balance really satisfied in the ``common'' model? Lets examine this point. Equation ([*]) states that the mass (volume, under constant density) balance is exist.
    (7.9)

So, what is the condition on to satisfy this condition? Can be a constant as stated in assumption 1? To study this point let derive an expression for . Utilizing equation ([*]) yields
    (7.10)

From the machine characteristic, equation ([*]), it can be shown that
    (7.11)



Substituting equation ([*]) into equation ([*]) yield,
    (7.12)

It can be shown that equation ([*]) can be transformed into
    (7.13)



According to the ``common'' model , and are independent of the gate area, . The term is not a constant and is a function of (possibility other parameters).



To maintain the mass balance must be a function at least of the gate area, . Since the ``common'' diagram assumes that is a constant it diametrically opposite the mass conservation principle. Moreover, in the ``common'' model, a major assumption is that the value of depends on the metal, therefore, the mass balance is probably never achieved in many cases. This violation demonstrates, once for all, that the ``common'' diagram is erroneous.



Figure: as to be relocated
Figure: as A3 to be relocated

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