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

Answer:

Qx = 9.10$9.10^5 \times 10^{-6}$ m³/s  

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 $\times 10^{-3}$ )²× 9  $\times 10^{-3}$  × 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 $\times 10^{-3}$  × ( 9  $\times 10^{-3}$ )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$9.10^5 \times 10^{-6}$ m³/s