**Mathematical Problems of Sizing in Weaving**

**What is Sizing?**

Sizing is the process of applying protective adhesive coating on the yarn surface. This is the most important segment of weaving preparatory process. Better the quality of sizing higher the weaving efficiency & vice versa. It helps to increase the tensile or breaking strength for cellulose yarn. Due to sizing of yarn, increases the elasticity of yarn, weight of yarn, frictional resistance etc.

**Formulas of Sizing in Weaving:****A. Total length of yarn sized**= Total length of warp X No of ends

**B. Total wt of size on warp**= Wt of sized warp – Wt of unsized warp

Length of warp in yds

**C. Count of sized yarn**=

**…………………………………**X No of ends

840 X Wt of sized warp in lbs

Wt of size

**D. % of size on warp**=

**……………………**X 100%

Wt of unsized warp

**Mathematical Problems of Sizing in Weaving**

**A. The calculated production of a high speed slasher is 100 yds per min. If the efficiency of the machines is 75%. Calculate the following.**

- The actual production per day of 8 hrs
- The total length of yarn if the total ends is 3250
- The total wt of sized warp if it is sized to 10% and the
**count**of unsized are 40’s

**1. Calculated production per day of 8 hrs**= 100 X 60 X 8 yds

= 48000 yds

75

**The actual production per day of 8 hrs**= 48000 X

**……**yds

100

= 36000 yds

**(ANS)**

**2. The total length of yarn sized**= Total length of warp X No of ends

= 36000 X 3250 yds

= 117000000 yds

**(ANS)**

Total length of warp in yds

**3. The total wt of sized warp in lbs**=

**……………………………**+ 10%

840 X Count

117000000

=

**……………..**+ 10%

840 X 40

= 3482 + 10%

= 3830 lbs

**(ANS)**

B. The actual production of high speed slasher sizing machine is 32,400 yds per day of 8 hrs. If Calculated speed is 90 yds per min, find out the efficiency.

B. The actual production of high speed slasher sizing machine is 32,400 yds per day of 8 hrs. If Calculated speed is 90 yds per min, find out the efficiency.

**Solution:**

We know,

32400

**Actual production in yds per hour**=

**………**yds

8

= 4050 yds

**Calculated production in yds per hr**= 90 X 60 yds

= 5400 yds

Actual production

**Efficiency**=

**………………………**X 100%

Calculated production

4050

=

**………**X 100%

5400

= 75%

**(ANS)**

**C. A Beam of 250 kg contains sized yarn of 15% take up if the sized count 40.87 ‘s. Calculate unsized count.**

**Solution:**

We know,

100

**Count of sized yarn**= Count of unsized yarn X

**…………………**

100 + % of size

100

**Or,**40.87 = Count of unsized yarn X

**…………**

100 + 15

**Or,**Count of unsized yarn = 47 ‘s

**(ANS)**