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## 7.4.1 The reform model

Equation () can be transformed into dimensionless from as
 (7.15)

Where:

reduced pressure,

reduced flow rate,


Eckert poro:ecksimilarity also demonstrated that the gravity effects are negligible12. Assuming steady state13 and utilizing Bernoulli's equation between point (1) on plunger tip and point (3) at the gate area (see Figure ) yields

 (7.16)

where:

velocity of the liquid metal

the liquid metal density

energy loss between plunger tip and gate exit

subscript

1 		 plunger tip

2 		  entrance to runner system

3 		 gate


It has been shown that the pressure in the cavity can be assumed to be about atmospheric (for air venting or vacuum venting) providing vents are properly designed Bar-Meir at el poro:genickvac,poro:genickair14. This assumption is not valid when the vents are poorly designed. When they are poorly designed, the ratio of the vent area to critical vent area determines the build up pressure, , which can be calculated as it is done in Bar-Meir et al poro:genickair. However, this is not a desirable situation since a considerable gas/air porosity is created and should be avoided. It also has been shown that the chemical reactions do not play a significant role during the filling of the cavity and can be neglected [#!poro:genickreac!#].

The resistance in the mold to liquid metal flow depends on the geometry of the part to be produced. If this resistance is significant, it has to be taken into account calculating the total resistance in the runner. In many geometries, the liquid metal path in the mold is short, then the resistance is insignificant compared to the resistance in the runner and can be ignored. Hence, the pressure at the gate, , can be neglected. Thus, equation () is reduced to

 (7.17)

The energy loss, , can be expressed in terms of the gate velocity as

 (7.18)

where is the resistance coefficient, representing a specific runner design and specific gate area.

Combining equations (), () and () and rearranging yields

 (7.19)

where
 (7.20)

Converting equation () into a dimensionless form yields
 (7.21)

When the Ozer Number is defined as
 (7.22)

The significance of the Oz number is that this is the ratio of the effective'' maximum energy of the hydrostatic pressure to the maximum kinetic energy. Note that the Ozer number is not a parameter that can be calculated a priori since the is varying with the operation point.

15For practical reasons the gate area, cannot be extremely large. On the other hand, the gate area can be relatively small in this case Ozer number where is a number larger then 2 ().

Solving equations () with () for , and taking only the possible physical solution, yields

 (7.23)

which is the dimensionless form of equation ().

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