**Calculation of Yarn Package Density**

**Package weight and density:**

The package weight and density are two important parameters which are to be standardized for uniform and trouble free dyeing.The packages may be soft or hard these should conform to the standards, when too soft 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. The package weight and dimensions depends upon the type of the machine, its flow rate, automation, type and construction of the yarn to be dyed, dye class to be used and type of package holder to be used. The typical density norms for

**different types of yarns**is between 350-450 gm/ltr.

Yarn package |

**Package Density calculation:**

**We know,**

M – m

**Package Density**=

**………………………**gm/cm3 ;

2π (2R2 – r2)h

**Where,**

M= Total package wt

m = Bobbin wt; r =Bobbin dia

R= Total package dia ;

R= Total package dia ;

h= Bobbin length or height.

If Package wt 1150 gm, bobbin wt 140gm, package dia 174mm, bobbin dia 65mm, height 149mm,then

1150-140

2 X 3.1416 X {(8.7)2 – (6.5)2 X 14.9

= 0.33 gm/cm3

510 X 1000 X 60 X 8 X 3 X 1.0936 X 0.85

=

840 X 30 X 2.2046

= 12287.95 kg/day

= 12 tons

If Package wt 1150 gm, bobbin wt 140gm, package dia 174mm, bobbin dia 65mm, height 149mm,then

1150-140

**Package Density**=**……………………………………………….**gm/cm32 X 3.1416 X {(8.7)2 – (6.5)2 X 14.9

= 0.33 gm/cm3

**Production calculation:**
No. of spindle X M/C speed (m/min) X 60 X 8 X 3 X 1.0939 X efficiency

840 X

**Production per day**=**…………………………………………………...........………………………**840 X

**Count**X 2.2046510 X 1000 X 60 X 8 X 3 X 1.0936 X 0.85

=

**…………………………………………………………………**840 X 30 X 2.2046

= 12287.95 kg/day

= 12 tons

mistake in the formula. 2 wouldn't be multiplied with R square.

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