Question

A polymer melt being extruded through a spinneret hole of circular cross-section exhibits a die-swell ratio of 2.2. The extrusion velocity and volumetric flow rate during this extrusion process are 20 m/min and \(2.6 \times 10^{-8}\) m\(^3\)/s, respectively. The maximum diameter (mm) of the extruded melt after exit from the spinneret hole (rounded off to 2 decimal places) is:

Hint:

Die-swell is the expansion of the polymer melt diameter due to the elasticity of the material. It is often used to calculate the extrudate size after it leaves the die.

Answer 1

Correct Answer: 0.64

1. Calculate spinneret hole diameter ($D_0$): \begin{align} Q &= A_0 \times v
A_0 &= \frac{Q}{v} = \frac{\SI{2.6e-8}{\meter^3/\second}}{\SI{0.333}{\meter/\second}}
&= \SI{7.81e-8}{\meter^2}
D_0 &= \sqrt{\frac{4A_0}{\pi}} = \sqrt{\frac{4 \times \SI{7.81e-8}{\meter^2}}{\pi}}
&= \SI{3.15e-4}{\meter} = \SI{0.315}{\milli\meter} \end{align} 2. Calculate extruded diameter ($D$): \begin{align} D &= B \times D_0
&= 2.2 \times \SI{0.315}{\milli\meter}
&= \SI{0.693}{\milli\meter} \end{align} Final Answer: The maximum diameter of the extruded melt is \boxed{0.69\,\si{\milli\meter}}.