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