Question

A 50 tex yarn with mass CV of 12.5 % is produced from staple polyester fibres each of 4.5 denier fineness. The index of irregularity of the yarn, (rounded off to two decimal places), is\(\underline{\hspace{2cm}}\).

Answer 1

Correct Answer: 1.25

To determine the index of irregularity of the yarn, we need to follow these steps:

1. First, understand the given parameters: The yarn has a linear density of 50 tex, a mass coefficient of variation (CV) of 12.5%, and is made from fibres with a fineness of 4.5 denier.
2. The index of irregularity (I_I) is calculated using the formula: II = (CV / CVIdeal), where CVIdeal = (1/√N) and N is the number of fibres in the yarn’s cross-section.
3. To find N, use the formula: N = (Yarn Tex / Fibre Denier) × 9, where 1 denier = 9 tex.
4. Calculate N using the given values: N = (50 / 4.5) × 9 ≈ 100.
5. Calculate CVIdeal: CVIdeal = (1/√100) = 0.1 or 10%.
6. Compute the index of irregularity: II = (12.5 / 10) = 1.25

Therefore, the index of irregularity of the yarn is 1.25.