# Textile Calculation

## Calculation of Package Density in Yarn Dyeing

Calculation of Package Density in Yarn Dyeing
Rana Sohel
Executive Engineer
Sunman Textile Mills Ltd. Chittagong
Cell: +8801912-420118
Email: rsohel07tex@gmail.com

Package Density in Yarn Dyeing:
Package density has important effect on yarn dyeing. When package are 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 dyeing or none may occur. In this article we will discuss on yarn package density before dyeing.
 Maintaining 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,

R1=16.3/2 = 8.15 cm.
R2 = 6.96/2 =3.48 cm.
Height = 16 cm..

We know = πr
2h.

So, total volume,
V1 = π R12h
=3.1416 X (8.15)
2 X 16
=3339 cm
3

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.

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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