Reference ID: MET-099B | Process Engineering Reference Sheets Calculation Guide
Introduction & Context
The drag flow component represents the theoretical maximum volumetric throughput of a single‑screw extruder operating under zero back‑pressure conditions, and a detailed single‑screw extruder throughput calculation provides the methodology for quantifying this value. In process engineering, this calculation is fundamental for sizing extrusion equipment, such as pasta presses, where the screw geometry and rotational speed dictate the primary transport mechanism of the material. By isolating the drag flow, engineers can establish a baseline performance metric before accounting for pressure‑driven backflow (leakage) or rheological resistance. This calculation is typically employed during the initial design phase to ensure the screw configuration meets the required production capacity while maintaining laminar flow regimes.
Methodology & Formulas
The drag flow is derived from the linear velocity profile of the material within the screw channel. Assuming a no-slip condition at the barrel wall and the screw root, the flow rate is calculated as the product of the channel cross-sectional area and the average velocity of the material relative to the barrel. The following variables are utilized:
\(D\): Screw diameter (m)
\(H\): Channel depth (m)
\(W\): Channel width (m, measured perpendicular to the flight)
\(\theta\): Helix angle (degrees). If using computational software, convert to radians: \(\theta_{\text{rad}} = \theta_{\text{deg}} \cdot \pi / 180\).
\(N\): Rotational speed (\(\text{s}^{-1}\))
First, the rotational speed in revolutions per minute is converted to revolutions per second:
\[ N = \frac{N_{\text{RPM}}}{60} \]
The drag flow component represents the theoretical maximum volumetric throughput of a single‑screw extruder operating under zero back‑pressure conditions, and it is a key input for the feed section capacity calculation used to size extrusion equipment such as pasta presses, where the screw geometry and rotational speed dictate the primary transport mechanism of the material.
\[ Q_{\text{drag}} = \frac{\pi \cdot D \cdot N \cdot W \cdot H \cdot \cos(\theta)}{2} \]
To convert the resulting volumetric flow rate from cubic meters per second to practical industrial units, the following conversions are applied:
The accuracy of this model relies on specific geometric and operational constraints. The following table outlines the thresholds required to maintain the validity of the drag flow estimation:
The drag flow component is determined by the geometry of the screw channel and the rotational speed of the screw. For process engineers, the calculation typically involves:
Defining the channel depth (\(H\)) and width (\(W\)) based on the screw flight profile.
Applying the drag flow equation \(Q_{\text{drag}} = \frac{1}{2} \pi D N W H \cos\theta\), which assumes a Newtonian fluid behavior and a linear velocity profile.
Accounting for the helix angle (\(\theta\)) of the screw flight to resolve the velocity vector.
Multiplying the channel cross-sectional area (\(W \cdot H\)) by half the down-channel velocity of the barrel surface relative to the screw (\(\frac{1}{2} \pi D N \cos\theta\)).
While the drag flow model provides a baseline, real-world process conditions often introduce discrepancies. Key factors include:
Non-Newtonian fluid behavior, specifically shear-thinning effects that alter the velocity profile and make the average velocity deviate from the simple \(V/2\) assumption.
Pressure flow components (\(Q_p\)) that act in opposition to the drag flow, reducing net throughput.
Leakage flow over the screw flights due to clearance gaps between the flight and barrel wall.
Thermal expansion of the screw and barrel, which can change the effective channel depth and clearance.
In ideal drag flow, viscosity is not a direct variable in the volumetric flow rate equation (\(Q_{\text{drag}}\)). However, for process engineers, it remains critical because:
High viscosity increases the pressure gradient required to push material through downstream tooling, which indirectly reduces the net flow rate by increasing the pressure-driven backflow component.
Viscous dissipation generates heat, which changes the local temperature and subsequently the fluid rheology, potentially invalidating the isothermal and Newtonian assumptions.
The assumption of a linear velocity profile across the channel depth is only valid if the viscosity remains constant. Shear-thinning fluids exhibit a more plug-like profile, altering the drag flow contribution.
Worked Example: Drag Flow Component for a Single-Screw Pasta Extruder
In a pasta production line, a single-screw extruder conveys dough through a die. When the die is open (no back pressure), the maximum theoretical flow rate is the drag flow component. This example calculates the drag flow for a given screw geometry and rotation speed.
Convert rotational speed to revolutions per second.
\[
N_{\text{s}} = \frac{N_{\text{RPM}}}{60} = \frac{100.0}{60} = 1.667~\text{s}^{-1}
\]
Compute the cosine of the helix angle.
\[
\cos\theta = \cos(18.0^\circ) = 0.9511
\]
Check \(H/D\) ratio for validity.
\[
\frac{H}{D} = \frac{0.01}{0.1} = 0.1
\]
This lies within the empirical range of \(0.05\)–\(0.2\), so the calculation is valid.
Check helix angle for validity.
The angle \( \theta = 18.0^\circ \) lies within \(10^\circ\)–\(30^\circ\), confirming applicability.
Check rotational speed for shear heating concerns.
\(N_{\text{s}} = 1.667~\text{s}^{-1}\) is less than \(10~\text{s}^{-1}\), so the risk of excessive shear heating is low.
Compute the numerator quantity.
\[
\text{Numerator} = \pi \cdot D \cdot N_{\text{s}} \cdot W \cdot H \cdot \cos\theta
\]
Substituting the known values:
\[
\text{Numerator} = 3.1416 \cdot 0.1 \cdot 1.667 \cdot 0.095 \cdot 0.01 \cdot 0.9511 = 4.7307 \times 10^{-4}
\]
