# Calculation of Package Density in Yarn Dyeing

Package Density in Yarn Dyeing:
Package density has an important effect on yarn dyeing. When packages is too soft then liquor flowing through it will find the course of least resistance and cause channeling, which leaves some parts of the package relatively undyed or lighter. If the packages are wound too hard, a point can be reached where the flow of liquor is impeded to such an extent that poor dying or none may occur. In this article, we will discuss yarn package density in yarn dyeing.

The ratio of mass and volume is called density.

Density = ρ
Mass = m
Volume = v

Here,

m = (Bobbin weight with yarn – Bobbin weight without yarn) gm.
v = π (R12 – R22) × h

R1 = Outer radius of the bobbin (with yarn).
R2 = Inner radius of the bobbin..

Say, for example,

Outer Radius, R1=16.3/2 = 8.15 cm.
Inner Radius, R2 = 6.96/2 =3.48 cm.
Height = 16 cm..

We know = πr2h.

So, total volume, V1 = π R12h
=3.1416 X (8.15) 2 X 16
=3339 cm3

Steel bobbin, V2= π R22h
= 3.1416 X (3.48)2 X16.
= 609 cm3

Original volume = (3339-609) = 2730 cm3

Package Density, ρ = m/v
= (1395-235)/2730
= 0.42 gm/cm3.

Package density in soft winding for cotton must be 0.36 to 0.40 gm/ cm3 and for polyester or CVC, it would be higher than 0.40 gm/cm3.

### Calculation of Package Density in Yarn Dyeing

We measure the package density of different bobbins in this section which are:

 Count (Ne) Package density (gm/cm3) 20s 0. 387 24s 0. 375 26s 0. 382 28s 0. 35 30s 0. 345 34s 0. 37 40s 0. 378

For filament (Polyester):

 Count (denier) Package density (gm/cm3) 30 0. 44 75 0. 376 100 0. 46

For spun yarn:

 Count (denier) Package density (gm/cm3) 40/2 0. 39 50/2 0. 4197

For CVC yarn:

 Count (Ne) Package density (gm/cm3) 30s 0. 40 26s 0. 39

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```Author of this Article:
Rana Sohel
Executive Engineer
Sunman Textile Mills Ltd. Chittagong
Cell: +8801912-420118
Email: [email protected]```

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