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# chapter7hmwk - EMA4666C 7.1 DATA DR:= 20 CHAPTER 7 PROBLEM...

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EMA4666C CHAPTER 7 PROBLEM SOLUTIONS 7.1 DATA: D R 20 := D 300 := µ m m dot 0.10 := kg/hr per fiber n 0.5 := m 2000 := Pa-s n G 3000 := Pa ρ 960 := kg/m 3 DETERMINE : Range of allowable distances between spinneret and the take-up wheel, L SOLUTION : Stability Analysis of Fiber Spinning (Fisher and Denn) presented on page 142 of the text is used to solve this problem. Approximated from Figure 7.2 (page 142), the stable regime of De 1/n for a draw ration of 20 and n=0.5 lies between 0.0275 and 0.055. These values correspond to values for De ranging from 0.167 to 0.235. De low 0.167 := De high 0.235 := To solve this problem, the speed of the polyethylene as it emerges from the spinneret, v 0 , must be computed. Recall: Q=(m dot / ρ )=v 0 A where Q is the volumetric flowrate and A is the area of flow A π D10 6 2 2 := m 2 v 0 m dot ρ A 1 3600 := v 0 0.409 = m/s The allowable range for L can be computed using equation 7.2 (page 142) L high m3 n1 () 2 v 0 GDe low := L low 2

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chapter7hmwk - EMA4666C 7.1 DATA DR:= 20 CHAPTER 7 PROBLEM...

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