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6.1.2 Connecting runner seqments

Design of connected runner secments have insure that the flow rate at each secment has to be designed one. In Figure [*]a branches i and j are connected to branch at point K. The pressure drop (difference) on branches i and j has to be the same since the pressure in the mold cavity is the same for both secments. The sum of the flow rates for both branch has to be equal to flow rate in branch
    (6.3)

The flow rate in every branch is related to the pressure difference by
    (6.4)

Where the subscrit i in this case also means any branch e.g. i, j and so on. For example, one can write for branch j
    (6.5)

Utilizing the mass conservation for point K in which and the fact that the pressure difference, , is the same thus we can write
    (6.6)

where we can define equalent resistance by
    (6.7)

Lets further manipolte the equations to get some more important relationships. Using equation ([*]) and equation ([*])
    (6.8)

The flow rate in a branch j can be related to flow rate in branch i and corresponding resistances
    (6.9)

Using equation ([*]) and equation ([*]) one can obtain
    (6.10)

Solving for the resistance ratio since the flow rate is known
    (6.11)


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