Relation between Yarn Dia and Yarn Count

Yarn Count:
Yarn count 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.’’ The relation between yarn dia and yarn count will be discussed below.

Yarn Dia and Yarn Count Relation

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, the 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, the 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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