The analysis of a problem through dimensional analysis, if it is possible, will inevitably lead to a solution of the scale-up problem. Dimensional analysis can almost invariably be applied to aspects of the scale-up problem. A dimensional analysis will immediately indicate whether or not the forces or stresses of interest are likely to increase on scale-up. This warns of a likely scale-up problem. The analysis of flow problems follows the same procedure as that used for heat transfer. Again the key idea is that most of the conclusions obtained from conventional, difficult analyses can be obtained quickly and easily through dimensional analysis. The result of dimensional analysis is unchanged, but the dimensionless term containing screw length becomes the dependent variable, describing filled length, and the dimensionless term containing screw output becomes an independent variable. In general, for each additional parameter needed to describe the non-Newtonian behavior of material, new characteristic dimensionless group will appear in the analysis.