T5 · Processing / MachineMould & Die DesignGATE 2027 Syllabus (XE5)Shop-Floor Standard

Hagen-Poiseuille Circular Runner Pressure Drop

Calculates the viscous hydraulic pressure drop (DeltaP in bar) across a round injection mold runner channel of diameter d and length L.

Mathematical Canonical Relation

\Delta P_{runner} = \frac{128 \cdot \mu \cdot Q \cdot L}{\pi \cdot d^4}

Plain Formula: DeltaP = (128 * mu * Q * L) / (pi * d^4)

Live Engineering Parameter Solver

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

Verified Engine

Runner Diameter (mm) (mm)

d_mm

Range: 2.5 – 12 mm

Runner Length (mm) (mm)

L_mm

Range: 10 – 400 mm

Flow Rate (cm³/s) (cm³/s)

Q_cm3s

Range: 5 – 150 cm³/s

Viscosity (Pa·s) (Pa·s)

mu_Pas

Range: 50 – 1000 Pa·s

Calculated Engineering Result:

0 bar (0 MPa)

Engineering Verification:Acceptable pressure drop.

When & Where to Apply

Use when sizing cold runners or balancing multi-cavity feed layouts to avoid excessive pressure drop.

Common Engineering Pitfalls

Pressure drop scales inversely with diameter to 4th power (1/d^4) — small size reductions drastically increase pressure drop!

Physical Assumptions & Validity Limits

Laminar viscous flow through circular pipe
Incompressible melt flow
Apparent viscosity mu evaluated at runner shear rate

Variable Symbols, SI Units & Dimensional Specifications

Symbol	Variable Meaning	SI Unit	Typical Industrial Range
\Delta P	Pressure drop loss	bar (MPa)	—
\mu	Melt dynamic viscosity	Pa·s	250
Q	Volumetric flow rate	cm³/s	35
L	Runner length	mm	120
d	Runner diameter	mm	6.0

Worked Industrial Numerical Example: 8-Cavity Mold Cold Runner Pressure Drop

Problem Statement:

Calculate the pressure drop across a 6.0 mm round runner of length 120 mm carrying polypropylene melt (viscosity mu = 250 Pa·s) at flow rate Q = 35 cm³/s (35,000 mm³/s).

Step-by-Step Numerical Solution:

Compute d^4: 6.0^4 = 1,296 mm^4
Substitute into Hagen-Poiseuille: DeltaP = (128 * 0.000250 MPa·s * 35000 mm³/s * 120 mm) / (3.14159 * 1296 mm^4)
Numerator = 134,400
Denominator = 4,071.5
Calculate DeltaP: 33.01 MPa = 330.1 bar

Final Answer: DeltaP = 330 bar (33 MPa)

💡 Engineering Interpretation: Runner pressure loss is 330 bar. Increasing runner diameter to 7.0 mm drops pressure loss to 178 bar, saving 152 bar machine injection pressure.

Authoritative Technical Reference & Source Provenance

Injection Mold Design Handbook by Viktor Lowen (Hanser, 2013), 1st Edition, Page 102-108.

Connected Curriculum Lesson

Runner System Balancing & Pressure Drop Analysis

Study Full Lesson