Unterschiede

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--- en:berechnungen:schergeschwindigkeit [2025/07/03 13:34] – cschall
+++ en:berechnungen:schergeschwindigkeit [2025/09/03 11:48] (aktuell) – [Shear rate] neelest
@@ Zeile 1: / Zeile 1: @@
 ====== Shear rate und shear deformation ======
+-> [[..:grafische_darstellung_der_ergebnisse:scherdeformationsgradient_und_schergeschwindigkeit|For the graphical representation of shear rate and shear deformation]]
 ===== Shear rate=====
+The shear rate can, as a first approximation, be described by:
+$$\dot \gamma = \frac{v_0}{h}$$
+$$\text{with}$$
+$$v_0 = \pi \cdot n \cdot D$$
+and the channel height $h$.
+This equation is applied for shear and mixing sections. However, it only describes a simple drag flow of Newtonian fluids. For shear-thinning (pseudoplastic) fluids, the average shear rate is somewhat higher (also due to the superposition with pressure flow). As an approximation for conventional screw channels, the following relation applies:
+$$\dot \gamma = \frac{exp(0,055 \cdot \pi_\dot m)}{cos(\varphi)} \cdot \frac{v_0}{h}$$
+where $\pi_\dot m$ is the [[schlepp-druckstroemung|dimensionless throughput]] and $\varphi$ is the [[..:eingabe_der_schneckendaten:schneckenzonen|helix (flight) angle]].
 ===== Shear deformation=====
+The shear deformation $\overline{\gamma}$ describes the deformation of a volume element that is sheared due to a shear rate. Thus, shear deformation is the product of shear rate and residence time.
+$$\overline{\gamma}= \dot \gamma \cdot \ t$$
+This is integrated along the screw length. The cumulative shear deformation gradient is a measure of the laminar mixing effect.
 ===Further topics===