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## Relation between Yarn Dia and Yarn Count

Relation between Yarn Dia and Yarn Count
B.Sc. in Textile Engineer
Noakhali Textile Engineering College
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Yarn Count:
Yarn count which expresses the coarseness or fineness of yarn used in textile. According to Textile Institute, ‘Count is a number indicating the mass per unit length or the length per unit mass of yarn.’’

Relation between Yarn Dia and Yarn Count:
Pierce approached the problem from a consideration of the apparent specific volume of a yarn. By experiment an apparent specific volume of 1.1 for cotton yarns was obtained.

So, specific volume of yarn = 1.1 cm3/gm

i.e., The weight of 1.1 cm3 yarn = 1 gm

Let, yarn count = N tex

Weight of 1000 m yarn is N gm

Length of N gm yarn is 1000 m

1000 m       1000 X 100
Length of 1.0 gm yarn is ………. Or …………… cm
N                   N

So, length of 1.1 cm3 (volume) yarn is 105/N cm

Since, the volume = Cross section X Length

=> 1.1 cm3 = π X (d/2)2 X (105/N) cm          [Where, d = dia of yarn in cm]

d2       105
=> 1.1 cm3 = π X X ………… cm
4         N

1.1 X 4 X N
=> d2 = ……………………
π X 105

=> d = √[(1.1 X 4 X N)/ π X 105] cm

0.375
=>d = ………√N cm
100

=> d ∞√N              [For direct system]

Converting cm to inches and Tex to cotton count;

0.375           √590.5        1
d (inches) = ………….. X ……… X ……….          [Tex X Ne = 590.5]
100             √ Ne       2.54

3.6
=> d = ……………
100√Ne

1
=>d = …………
28√Ne

1
=>d ∞  ……                                              [For indirect system]
√N

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