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4.5.1 Series Connection

The flow rate in different locations is a function of the temperature. Eckert poro:ecksimilarity demonstrated that the heat transfer is insignificant in the duration of the filling of the cavity, and therefore the temperature of the liquid metal can be assumed almost constant during the filling period (which in most cases is much less 100 milliseconds). As such, the solidification is insignificant (the liquid metal density changes less than 0.1% in the runner); therefore, the volumetric flow rate can be assumed constant:
    (4.8)

Clearly, the pressure in the points is different and

    (4.9)

However the total pressure loss is composed of from all the small pressure loss
    (4.10)

Every single pressure loss can be written as
    (4.11)

There is also resistance due to parallel connection i.e. y connections, y splits and manifolds etc. First, lets look at the series connection (see Figure [*]).
Figure: A connection in series
where:

 the resistance in the bend 

length of the duct (vent),
friction factor, and


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