Based on the energy balance of the melt zone for the heating capacity results

$$\Pi_6 = \frac{\dot{q} L_{sz} \left(1 - \frac{\beta}{\pi}\right)}{h v \rho c_v \Delta T_{sz}} \tag{1}$$

The expression in brackets in Equation 6 can be considered as an approximately constant value [3]. Are, furthermore, constant material values assumed and is the velocity replaced, the ratio of heat flow densities of the model design and the main design derive:

$$\frac{\dot{q}}{\dot{q}_0} = \frac{L_{sz,0} h D N}{L_{sz} h_0 D_0 N_0} = \frac{\Delta T_{sz}}{\Delta T_{sz,0}} = \left(\frac{D}{D_0}\right)^{1-\psi-\chi} \frac{\Delta T_{sz}}{\Delta T_{sz,0}} \tag{2}$$

By assuming a constant melt temperature at the screw tip for both the model design and the main design, it consequently has to apply

$$\chi = \psi - \omega \tag{3}$$

to obtain identical heat flow densities. The melt flow, which is to be metered, derives as before by inserting the exponent into the throughput equation $\frac{\dot{m}}{\dot{m}_0} = \frac{\dot{V}}{\dot{V}_0} = \left(\frac{D}{D_0}\right)^{2+\psi-\chi}$.