Polymer Processing, Plastics Extrusion & Rheology Engineering
Single-Screw Extruder Drag Flow & Die Operating Point Formula
Calculate Open-Discharge Drag Flow Q_d (L/hr), Coupled Screw-Die Operating Throughput Q_op (L/hr), Back-Pressure Throttle Loss (%), and Die Head Melt Pressure Delta_P (MPa).
Intersecting screw and die lines cancels Newtonian viscosity mu out of Q_op—yet head pressure scales directly with mu!
In a polymer single-screw extruder metering channel pumping molten polyethylene, polypropylene, or PET through a forming die, forward Couette Drag Flow Q_drag = alpha * N is opposed by reverse Poiseuille Back-Pressure Flow Q_press = (beta / mu) * Delta_P, while the extrusion die obeys Q_die = (K_die / mu) * Delta_P (with geometric drag constant alpha in cm³/rev, screw pressure constant beta in cm^4, die conductance K_die in cm^4, screw speed N in RPM, and melt viscosity mu in Pa·s)! Setting Q_screw = Q_die solves the exact Operating Point: Actual Volumetric Throughput is Q_op = Q_drag * (K_die / (beta + K_die))—independent of Newtonian melt viscosity mu!—whereas Operating Die Head Pressure Delta_P_MPa = (alpha * (N / 60) * mu) / (10,000 * (beta + K_die)) rises proportionally with mu!
Verify on a 60 mm Polyolefin Metering Screw—Drag_Constant alpha = 25.0 cm³/rev (B2), Screw_Pressure_Constant beta = 0.08 cm^4 (B3), Die_Conductance K_die = 0.12 cm^4 (B4), Screw_Speed N = 80.0 RPM (B5), and Melt_Viscosity mu = 400.0 Pa·s (B6): Open-Discharge Drag Flow Q_d hits (25 * 80 * 60) / 1,000 = 120.00 L/hr (E2), Operating Extrudate Flow Q_op equals 120 * (0.12 / 0.20) = 72.00 L/hr (E3), Back-Pressure Flow Reduction equals 40.00% (E4), and Die Head Melt Pressure hits 6.67 MPa (66.7 bar, E5)!
| Extruder-Die Operating KPI (alpha=25, beta=0.08, Kdie=0.12, 80 RPM, 400 Pa·s) | Formula | Verified Output |
|---|---|---|
| Open-End Drag Flow Qd (L/hr) | (alpha_cm3_rev * RPM * 60) / 1000 | 120.00 L/hr |
| Operating Throughput Qop (L/hr) | Qd_L_hr * (K_die / (beta + K_die)) | 72.00 L/hr (40.00 @ Kdie = 0.04) |
| Back-Pressure Loss Ratio (%) | (beta / (beta + K_die)) * 100 | 40.00% (66.67% @ Kdie = 0.04) |
| Die Head Pressure dP (MPa) | (alpha*(RPM/60)*mu) / (10000*(beta+Kdie)) | 6.67 MPa (11.11 MPa @ Kdie = 0.04) |
Coupled Screw-Die Extrusion Operating Throughput & Head Pressure Formula
Validate alpha > 0, beta > 0, K_die > 0, Screw_RPM > 0, and Melt_Viscosity mu > 0!
=LET(al_d, B2, bt_s, B3, kd_c, B4, rp_m, B5, mu_p, B6, IF(OR(al_d <= 0, bt_s <= 0, kd_c <= 0, rp_m <= 0, mu_p <= 0), "Invalid Extruder Input", LET(qd_l, (al_d * rp_m * 60) / 1000, ROUND(qd_l * (kd_c / (bt_s + kd_c)), 2))))Restricted Thin-Slit Sheet Die Back-Pressure Surge Check (Set Die Conductance K_die = 0.04 cm^4)
Swap to a tighter thin-gauge sheet die (K_die B4 drops from 0.12 to 0.04 cm^4): Operating Throughput E3 drops to 40.00 L/hr (66.67% back-pressure throttling in E4) while Die Head Pressure E5 surges from 6.67 MPa up to 11.11 MPa!
=IF(ISTEXT(E3), E3, ROUND((B2 * (B5 / 60) * B6) / (10000 * (B3 + B4)), 2))Try the example
Use the original values or change them to test your understanding.