**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 cm^{3} (volume) yarn is 105/N cm

Since, the volume = Cross-section X Length

=> 1.1 cm^{3} = π X (d/2)2 X (105/N) cm [Where, d = dia of yarn in cm]

…………………………d^{2}……..105

=> 1.1 cm^{3} = π X …… X ………… cm

………………………….4……….N

…………….1.1 X 4 X N

=> d^{2} = ……………………

………………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