Newtonian Isothermal Screw and Die Characteristic Curves

When extruding a Newtonian fluid through a die, the throughput is directly proportional to the pressure build-up in the extruder and inversely proportional to the viscosity as stated in 

Substituting eqn. (6.18) into eqn. (6.16), we arrive at the volumetric throughput for a single screw pump with a particular die, described by 

In order to maximize the throughput for a particular screw-die combination we set the variation of eqn. (6.19) with respect to channel depth, h, to zero as 

It is interesting to point out that for a die with a pressure flow through a slit, or sets of slits, the optimum channel depth is directly proportional to the die gap. Decreasing the die gap by a certain percentage will result in an optimum channel depth that is reduced by the same percentage. To determine the optimum helix angle we can re-write eqn. (6.23) for this specific application, 

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