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Single-Screw Extruder Drag Flow Rate (Throughput Capacity)

Calculates theoretical open-discharge volumetric drag flow rate Qd generated by the rotating screw in the metering zone of a single-screw plastics extruder.

Mathematical Canonical Relation

Q_d = \frac{1}{2} \pi^2 D^2 H N \sin\theta \cos\theta

Plain Formula: Qd = 0.5 * pi^2 * D^2 * H * N * sin(theta) * cos(theta)

Live Engineering Parameter Solver

Input your production or test values below for instant, verified output.

Verified Engine

Screw Diameter D (mm) (mm)

D_mm

Range: 25 – 150 mm

Channel Depth H (mm) (mm)

H_mm

Range: 1 – 10 mm

Screw Speed (RPM) (RPM)

N_rpm

Range: 10 – 200 RPM

Melt Density (g/cm³) (g/cm³)

melt_rho

Range: 0.6 – 1.4 g/cm³

Calculated Engineering Result:

76.9 kg/h (28.1 cm³/s)

Engineering Verification:Theoretical maximum drag flow at zero head pressure.

When & Where to Apply

Use when sizing single-screw extruders or estimating maximum theoretical melt throughput before subtracting pressure flow backflow.

Common Engineering Pitfalls

Forgetting that actual output Q is lower than Qd due to head pressure backflow Qp and leakage Ql
Using screw speed in RPM instead of rev/second when computing in SI units

Physical Assumptions & Validity Limits

Isothermal Newtonian melt behavior in metering channel
Flat plate channel unwrapping approximation (H << D)
No wall slip at barrel or screw surfaces

Variable Symbols, SI Units & Dimensional Specifications

Symbol	Variable Meaning	SI Unit	Typical Industrial Range
Q_d	Volumetric drag flow rate	cm³/s (or kg/h)	—
D	Screw outside diameter	mm	65
H	Metering channel depth	mm	3.5
N	Screw rotational speed	RPM	80
\theta	Screw flight helix angle (standard square pitch is 17.65°)	degrees	17.65

Worked Industrial Numerical Example: 65 mm HDPE Pipe Extruder Metering Drag Output

Problem Statement:

A 65 mm single-screw extruder operates at 80 RPM with metering channel depth H = 3.5 mm and standard square pitch helix angle theta = 17.65°. Melt density is 0.76 g/cm³. Calculate volumetric drag output and mass throughput in kg/h.

Step-by-Step Numerical Solution:

Convert units: D = 6.5 cm, H = 0.35 cm, N = 80/60 = 1.333 rev/s
Calculate angle term: sin(17.65°) * cos(17.65°) = 0.3032 * 0.9529 = 0.2889
Compute Qd = 0.5 * pi^2 * (6.5)^2 * 0.35 * 1.333 * 0.2889 = 28.18 cm³/s
Calculate mass throughput: 28.18 cm³/s * 0.76 g/cm³ * 3600 / 1000 = 77.1 kg/h

Final Answer: Qd = 28.2 cm³/s (77.1 kg/h)

💡 Engineering Interpretation: At zero head pressure, maximum theoretical throughput is 77.1 kg/h. In actual pipe extrusion against 200 bar die pressure, net output will be approx 70–80% of Qd (55–62 kg/h).

Authoritative Technical Reference & Source Provenance

Principles of Polymer Processing by Zeev Tadmor & Costas Gogos (Wiley-Interscience, 2006), 2nd Edition, Page 360-375.

Connected Curriculum Lesson

Single Screw Extrusion Drag Flow, Pressure Flow & Die Characteristic

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