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HW-10-01-08s-Ch13

# HW-10-01-08s-Ch13 - IE 215 Solutions for Problems due Oct 1...

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IE 215 Solutions for Problems due Oct 1, 2008 (Ch 13) 13.1 The diameter of an extruder barrel is 65 mm and its length = 1.75 m. The screw rotates at 55 rev/min. The screw channel depth = 5.0 mm, and the flight angle = 18 ° . The head pressure at the die end of the barrel is 5.0 x 10 6 Pa. The viscosity of the polymer melt is given as 100 Pas. Find the volume flow rate of the plastic in the barrel. Solution : Q d = 0.5 π 2 (65x10 -3 ) 2 (55/60)(5x10 -3 )sin 18 cos 18 = 95,560x10 -9 (0.3090)(0.9510) = 28.081 x 10 -6 m 3 /s p = 5 MPa = 5x10 6 n/m 2 Q b = π (5x10 6 )(65x10 -3 )(5x10 -3 ) 3 (sin 18) 2 /12(100)(1.75) = 5.804(10 -6 ) m 3 /s Q x = 28.081 - 5.804 = 22.277 x 10 -6 m 3 /s. 13.7 An extruder barrel has a diameter of 2.5 in. The screw rotates at 60 rev/min; its channel depth = 0.20 in, and its flight angle = 17.5 ° . The head pressure at the die end of the barrel is 800 lb/in 2 and the length of the barrel is 50 in. The viscosity of the polymer melt is 122 x 10 -4 lb-sec/in 2 . Determine the volume flow rate of the plastic in the barrel. Solution : Q d = 0.5 π 2 (2.5) 2 (1)(.2)sin 17.5 cos 17.5 = 0.5(12.337)(0.3007)(0.9537) = 1.769 in 3 /sec Q b = π (800)(2.5)(.2) 3 (sin 17.5) 2 /12(122x10 -4 )(50) = 0.621 in 3 /sec Q x = 1.769 - 0.621 = 1.148 in 3 /sec.

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