GATE (TF) Textile 2009 Question Paper Solution | GATE/2009/TF/33

Question 33 (Textile Engineering & Fibre Science)

The packing coefficient of a yarn with 100 fibres is increased by 10%, the percentage change in yarn diameter will be approximately

(A)	– 16.9
(B)	– 10.9
(C)	– 4.9
(D)	4.9

[Show Answer]

Option C is correct

Given in the question-

Let the initial packing coefficient=k1

Then,final packing coefficient(k2)=k1+k1 x 10%

k2=1.1 k1

By formula-

$Diameter of the yarn(d)=4.44 \times 10^-3 \times \sqrt \frac{tex}{k \times \rho}$

Hence,

Diameter is inversaly proportional to the square root of the packing coefficient(k)

$\frac{d_1}{d_2}=\frac{\sqrt k_2}{\sqrt k_1}$

$\frac{d_1}{d_2}=\frac{\sqrt (1.1 \times k_1)}{\sqrt k_1}$

$\frac{d_1}{d_2}=\sqrt 1.1$

$\frac{d_1}{d_2}=1.05$

$\frac{d_2}{d_1}=\frac{1}{1.05}$

Both side minus by 1-

$(\frac{d_2}{d_1})-1=(\frac{1}{1.05})-1$

$(\frac{d_2}{d_1})-1=-0.047$

$(\frac{d_2}{d_1}-1) \times 100=-0.047 \times 100$

$(\frac{d_2}{d_1}-1) \times 100=-4.7$

i.e. ,the percentage change in yarn diameter will be approximately=-4.9 (Ans)

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Frequently Asked Questions | FAQs

What is packing in yarn?

In the context of yarn production, packing refers to the arrangement of fibers within a yarn and the amount of space they occupy. It relates to the compactness and density of the fibers within the yarn structure. The packing coefficient, also known as the packing factor or packing density, is a quantitative measure of this arrangement and is used to describe the degree of fiber packing within a yarn.
The packing coefficient is calculated as the ratio of the actual mass of fibers in a unit length of yarn to the theoretical mass of fibers that could occupy the same length if they were perfectly packed without any gaps or spaces. It is typically expressed as a decimal or a percentage.
A higher packing coefficient indicates a denser arrangement of fibers within the yarn, meaning that there are fewer gaps or spaces between the fibers. A lower packing coefficient suggests a looser arrangement with more open spaces.
The packing coefficient is influenced by various factors, including the fiber properties (such as fineness, length, and crimp), the spinning process parameters (such as twist level and drafting), and the yarn structure (such as the number of plies or the presence of blending fibers).
Achieving an optimal packing coefficient is important for yarn quality and performance. A higher packing coefficient can result in improved yarn strength, evenness, and dimensional stability. It can also contribute to better dye penetration and color uniformity. However, excessively high packing coefficients may lead to reduced yarn flexibility and increased processing difficulties.
Conversely, a lower packing coefficient may result in yarns with lower strength, increased hairiness, and reduced resistance to abrasion or pilling. It may also affect the appearance and handle of the fabric produced from such yarns.
Optimizing the packing coefficient requires balancing various factors, including the desired yarn properties, the fiber characteristics, and the specific spinning process conditions. Adjustments in drafting, twist level, and fiber selection can influence the packing coefficient and allow for the production of yarns with the desired characteristics.

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