======Drag pressure flow ======

-> [[..:grafische_darstellung_der_ergebnisse:schlepp-druckstroemung|Graphical representation of the drag pressure flow]]

The dimensionless flow rate $π_{\dot m}$ describes the actual mass flow in relation to the mass flow caused by the drag flow. In the one-dimensional case, neglecting all boundary influences, a $π_{\dot m} = 1$ therefore means that there is a pure drag flow.

The dimensionless flow rate is defined as follows:

$$π_{\dot m} = \frac{2 \cdot \dot m}{ρ \cdot i \cdot h \cdot b \cdot v_{0z}}$$
$$\text{with}$$
$$v_{0z}=v_0 \cdot cos(\varphi)=\pi \cdot N \cdot D \cdot cos(\varphi)$$
$$\text{and}$$
$$tan(\varphi)=\frac{t}{\pi D}$$

with the mass flow rate $\dot m$, the density $\rho$, the number of turns $i$, the channel height $h$, the channel width $b$, the cylinder speed in the channel direction $v_{0z}$, the rotational speed $N$, the nominal diameter $D$, the pitch angle $\varphi$ and the pitch $t$.

The dimensionless pressure gradient $\pi_p$ describes the influence of the pressure gradients on the overall flow. This value therefore describes the mass flow of a pressurised flow. A value of 0 therefore means that there is no pressurised flow and thus a pure drag flow. A value of 1, on the other hand, means that the pressure gradient results in a pressurised flow that is identical in size to the drag flow. In this case, the resulting mass flow rate is 0. The dimensionless pressure gradient is defined as follows

$$\pi_p = \frac{h^{1+n}}{6 \cdot K \cdot v_{0z}^n} \frac{\Delta p}{Z}$$

with the channel depth $h$, the [[en:materialdaten:rheologische_materialdaten|flow_law_exponent]] $n$, the [[en:materialdaten:rheologische_materialdaten|consistency_factor]] $K$, the cylinder velocity in the channel direction $v_{0z}$ and the pressure difference $\Delta p$ on the channel length $Z$.

The following applies to the one-dimensional case described so far:

$$\pi_\dot m = 1 - \pi_p$$

The two dimensionless key figures mentioned above can be used to deduce the flow
field in the screw. $π_{\dot m} = 1$ describes a flow that consists purely of a drag flow. There is
no pressure gradient here which opposes this flow. $π_{\dot m} = 0$ on the other hand means
that no material is conveyed. Here, the effective pressure is so high that the drag flow
cannot move against it. If $π_{\dot m} > 1$, the pressure flow supports the drag flow. This is
the case with negative pressure gradients, as is often the case in grooved barrel extruders, for example. $π_{\dot m}$ usually moves between 0 and 1. The closer $π_{\dot m}$ is to 0,
the better the mixing effect due to the pressure profile overlapping each other, but t
worse the conveying effect.

The following graph shows various characteristic flow profiles for different drag and
pressure flows for the Newtonian case.

{{ :berechnungen:schlepp_druckstroemung:abb_schlepp_druckstroemung_de_en.svg?nolink&600 |}}

With structurally viscous materials, the curve deviates further and further with decreasing power law coefficients (see following diagram); this is taken into account in the calculation. The figure only shows the one-dimensional case. Taking into account the influence of the web, the cross-flow and the channel curvature, a $\pi_\dot m < 1$ also results for a pure drag flow ($\pi_p = 0$).

{{ :berechnungen:schlepp_druckstroemung:abb_pi_p_pi_v_de_en.svg?nolink&600 |}}

===Further topics===
  * [[en:berechnungen:einfache_berechnung|]]
  * [[en:berechnungen:prozess_iterieren]]
  * [[en:berechnungen:durchsatz|]]
  * [[en:berechnungen:druckverlauf|]]
  * [[en:berechnungen:aufschmelzverlauf|]]
  * [[en:berechnungen:temperaturverlauf|]]
  * [[en:berechnungen:leistung_und_schubspannungen|]]
  * [[en:berechnungen:schergeschwindigkeit]]
  * [[en:berechnungen:verweilzeit|]]
  * [[en:berechnungen:verweilzeitverteilung|]]
  * [[en:berechnungen:materialabbau|]]
  * [[en:berechnungen:faserlaengenabbau|]]
  * [[en:berechnungen:entgasungskennzahlen|]]
  * [[en:berechnungen:festigkeitsberechnung|]]
  * [[en:berechnungen:schlepp-druckstroemung|]]
  * [[en:berechnungen:feststofffoerderung|]]
  * [[en:berechnungen:verarbeitung_von_mischungen|]]
  * [[en:berechnungen:wandgleitende_materialien|]]
  * [[en:berechnungen:nutbuchsenberechnung|]]
  * [[en:berechnungen:kompressionsverhaeltnisse|]]