Question

The diameter of an extruder barrel = 85 mm and its length = 2.00 m. The screw rotates at 55 rev/min, its channel depth = 8.0 mm, and its flight angle = 18°. Head pressure at the die end of the barrel = 10.0(10^6) Pa. Viscosity of the polymer melt = 100 Pa- s

(a) Find the volume flow rate of plastic at the die end of the barrel.
________ x 10^-6 m^3/s

Answer 1

Qx = 9.10
`9.10^5 * 10^(-6)` m³/s

Step-by-step explanation:

given data

diameter = 85 mm

length = 2 m

depth = 9mm

N = 60 rev/min

pressure p = 11 ×
`10^6` Pa

viscosity n = 100 Pas

angle = 18°

so Qd will be

Qd = 0.5 × π² ×D²×dc × sinA × cosA ..............1

put here value and we get

Qd = 0.5 × π² × ( 85
`* 10^(-3)` )²× 9
`* 10^(-3)` × sin18 × cos18

Qd = 94.305 ×
`10^(-6)` m³/s

and

Qb = p × π × D × dc³ × sin²A ÷ 12 × n × L ............2

Qb = 11 ×
`10^(6)` × π × 85
`* 10^(-3)` × ( 9
`* 10^(-3)` )³ × sin²18 ÷ 12 × 100 × 2

Qb = 85.2 ×
`10^(-6)` m³/s

so here

volume flow rate Qx = Qd - Qb ..............3

Qx = 94.305 ×
`10^(-6)` - 85.2 ×
`10^(-6)`

Qx = 9.10
`9.10^5 * 10^(-6)` m³/s