**Relation between Yarn Dia and Yarn Count**

**Rakib Hawlader**

B.Sc. in Textile Engineer

Noakhali Textile Engineering College

Cell: +8801812478393

**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 cm

^{3}/gm
i.e., The weight of 1.1 cm

^{3}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 cm

^{3}(volume) yarn is 10^{5}/N cm
Since, the volume = Cross section X Length

=> 1.1 cm

^{3}= π X (d/2)^{2}X (10^{5}/N) cm [Where, d = dia of yarn in cm]
d

^{2}10^{5}
=> 1.1 cm

^{3}= π X**…**X**…………**cm
4 N

1.1 X 4 X N

=> d

^{2}=**……………………**
π X 10

^{5}
=> d = √[(1.1 X 4 X N)/ π X 10

^{5}] 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**