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## 9.2.2 Miller's model

Miller and his student, in the early 90's, constucted a model to account for the frinction in the venting system. They based their model on the following assumptions:

1. No heat transfer
2. Isothermal flow (constant temperature) in the entrance to vent (according to the authors in the presentation)
3. Fanno flow in the rest vent
4. Air/gas obeys the ideal gas model

Miller and his student described the calculation procedures for the two case as choked and unchoked conditions. The calculations for the choked case are standard and can be found in any book about Fanno flow but with an interesting twist. The conditions in the mold and the sleeve are calculated according the ambient condition (see the smart quote of this Chapter)2. The calculations about unchoked case are very interesting and will be discussed here in a little more details. The calculations procedure for the unchoked as the following:

• Assume number (entrance Mach number to the vent) lower than for choked condition
• Calculate the corresponding star (choked conditions) , the pressure ratio, and the temperature ratio for the assume number
• Calculate the difference between the calculated and the actual .
• Use the difference to calculate the double stars (theoretical exit) conditions based on the ambient conditions.
• Calculated the conditions in the die based on the double star conditions.
Now the mass flow out is determined by mass conservation.

Of course, these calculations are erroneous. In choked flow, the conditions are determined only and only by up-steam and never by the down steam3. The calculations for unchoked flow are mathematical wrong. The assumption made in the first step never was checked. And mathematically speaking, it is equivalent to just guessing solution. These errors are only fraction of the other other in that model which include among other the following: one) assumption of constant temperature in the die is wrong, two) poor assumption of the isothermal flow, three) poor measurements etc. On top of that was is the criterion for required vent area.

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