The starting point for this approach is the characteristic value Π5. of the melt conveying zone (see table). By assuming a constant melt temperature at the screw tip and in conjunction with the requirements specified beforehand (see table), the viscosity ratio of model design and main design results:

$$\frac{\eta}{\eta_0} = \left(\frac{D}{D_0}\right)^{2\psi+\chi-2-\omega} \tag{1}$$

Furthermore, the shear rate can be described by the following relation:

$$\frac{\dot{\gamma}}{\dot{\gamma}_0} = \left(\frac{D}{D_0}\right)^{1-\psi-\chi} \tag{2}$$

If both terms are logarithmized and the diameter ratio is eliminated, one receives:

$$\lg\frac{\eta}{\eta_0} = \frac{2\psi + \chi - 2 - \omega}{1 - \psi - \chi} \lg\frac{\dot{\gamma}}{\dot{\gamma}_0} \tag{3}$$

According to Equation 1, at a constant temperature for the viscosity function it also applies:

$$\lg\frac{\eta}{\eta_0} = (n - 1) \lg\frac{\dot{\gamma}}{\dot{\gamma}_0} \tag{4}$$

By that method the screw speed exponent for a constant specific energy input derives:

$$\chi = \frac{n - n\psi + 1 + \omega - \psi}{n} \tag{5}$$

By inserting the screw speed exponent into Eq. $\frac{\dot{m}}{\dot{m}_0} = \frac{\dot{V}}{\dot{V}_0} = \left(\frac{D}{D_0}\right)^{2+\psi-\chi}$ the respective throughput for this operating point results.