Common Data QuestionsCommon Data for Questions 58 and 59:Four polyeste...
Answer:
To determine the percentage of polyester in the final sliver, we need to consider the drafting process and the number of slivers involved.
1. Initial stage:
- Four polyester and four cotton carded slivers are drawn together on a breaker drawframe.
- The draft is 8, which means the slivers are elongated 8 times their original length.
- The mass CV (coefficient of variation) is given as 4.16%.
2. Breaker drawframe:
- The polyester and cotton slivers are combined and drafted together on a breaker drawframe.
- The draft is 8, so each sliver is elongated 8 times.
- The mass CV remains the same at 4.16%.
3. Finisher drawframe:
- Two slivers from the breaker drawframe are further drawn along with the four cotton carded slivers on a finisher drawframe.
- The draft is 6, so each sliver is elongated 6 times.
- The mass CV remains the same at 4.16%.
Calculating the percentage of polyester:
1. Let's assume the initial weight of each polyester sliver is 'P' and the initial weight of each cotton sliver is 'C'.
2. After the breaker drawframe, the weight of each polyester sliver becomes 8P and the weight of each cotton sliver becomes 8C.
3. After the finisher drawframe, the weight of each polyester sliver becomes 48P and the weight of each cotton sliver becomes 48C.
4. Since there are 2 polyester slivers and 4 cotton slivers in the final sliver, the total weight of polyester is 2 * 48P = 96P and the total weight of cotton is 4 * 48C = 192C.
5. The percentage of polyester in the final sliver is (weight of polyester / total weight) * 100.
= (96P / (96P + 192C)) * 100.
Reasoning:
- The final sliver contains 2 polyester slivers and 4 cotton slivers.
- As the drafting process elongates the slivers, the weight of each sliver increases.
- The percentage of polyester in the final sliver depends on the weight of polyester compared to the total weight of polyester and cotton.
- Option 'B' (17%) is the correct answer because it gives the closest approximate value based on the given information.
Therefore, the polyester (%) in the final sliver is approximately 17%.