The first model dealing with the extraction of air from the cavity was done by Sachs. In this model, Sachs poro:sachs developed a model for the gas flow from a die cavity based on the following assumptions: 1) the gas undergoes an isentropic process in the die cavity, 2) a quasi steady state exists, 3) the only resistance to the gas flow is at the entrance of the vent, 4) a ``maximum mass flow rate is present'', and 5) the liquid metal has no surface tension, thus the metal pressure is equal to the gas pressure. Sachs also differentiated between two cases: choked flow and un-choked flow (but this differentiation did not come into play in his model). Assumption 3 requires that for choked flow the pressure ratio be about two between the cavity and vent exit.
Almost the same model was repeat by several researchers1. All these models, with the exception of Veinik poro:veinik2, neglect the friction in the venting system. The vent design in a commercial system includes at least an exit, several ducts, and several abrupt expansions/contractions in which the resistance coefficient ( see [#!poro:shapiro!#, page 163]) can be evaluated to be larger than 3 and a typical value of is about 7 or more. In this case, the pressure ratio for the choking condition is at least 3 and the pressure ratio reaches this value only after about 2/3 of the piston stroke is elapsed. It can be shown that when the flow is choked the pressure in the cavity does not remain constant as assumed in the models but increases exponentially.