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Beide Seiten der vorigen RevisionVorhergehende Überarbeitung
Nächste Überarbeitung		Vorhergehende Überarbeitung
en:grundlagenhandbuch:scale-up [2026/09/04 11:02] – [Model Theory] paalen:grundlagenhandbuch:scale-up [2026/09/04 11:04] (aktuell) – [Model Theory] paal
Zeile 12: Zeile 12:
 $$P + \dot{Q} = \dot{m} c_v \Delta T + p \dot{V} \tag{1}$$ $$P + \dot{Q} = \dot{m} c_v \Delta T + p \dot{V} \tag{1}$$
  
-By transformation the theorem derives in a dimensionless form:+By rearranging the equation, the following dimensionless form is obtained:
  
 $$\frac{P}{\dot{m} c_v \Delta T} + \frac{\dot{Q}}{\dot{m} c_v \Delta T} = 1 + \frac{p \dot{V}}{\dot{m} c_v \Delta T} \tag{2}$$ $$\frac{P}{\dot{m} c_v \Delta T} + \frac{\dot{Q}}{\dot{m} c_v \Delta T} = 1 + \frac{p \dot{V}}{\dot{m} c_v \Delta T} \tag{2}$$
Zeile 89: Zeile 89:
 $$\frac{T}{T_0} = \left(\frac{\dot{\gamma}}{\dot{\gamma}_0}\right)^{-\xi} \tag{14}$$ $$\frac{T}{T_0} = \left(\frac{\dot{\gamma}}{\dot{\gamma}_0}\right)^{-\xi} \tag{14}$$
  
-In reference to the melt conveying zone, with the prerequisites specified in the table the underlying principles for the screw speed exponent and for the flight depth exponent thus derive as described in the table. In doing so, the material values ρ, λ and $c_v$ were assumed invariant.+With regard to the melt conveying zone, with the prerequisites specified in the table the underlying principles for the screw speed exponent and for the flight depth exponent thus derive as described in the table. In doing so, the material values ρ, λ and $c_v$ were assumed invariant.
  
 **Table:** Screw speed and channel depth exponents **Table:** Screw speed and channel depth exponents