Question

A chute feed system feeds a fibre batt of linear density 300 g/m to a card. The waste extracted by the card is 5% and the total mechanical draft is 100. The linear density (ktex) of card sliver (correct up to 2 decimal places) is:

Hint:

In fibre processing, mechanical draft refers to the ratio of the final length to the original length of the fibre. The linear density of the sliver can be calculated by considering the amount of fibre processed and the draft factor.

Answer 1

Step 1: Understanding the problem. The linear density of the fibre batt is given as 300 g/m. The waste extracted by the card is 5%, which means 95% of the batt is converted into sliver. The total mechanical draft is 100, which means the length of the fibre is increased by a factor of 100. 
Step 2: Calculate the mass of fibre after carding. The total mass of the fibre batt is reduced by 5% due to waste. Therefore, the mass of the fibre that is actually processed is:

Mass after carding = 300 g/m × 0.95 = 285 g/m

Step 3: Apply the mechanical draft. The mechanical draft is 100, meaning the length of the fibre is increased by a factor of 100. Therefore, the linear density of the card sliver is:

Linear density of card sliver = 285 / 100 = 2.85 g/m

Step 4: Convert to ktex. The unit ktex is defined as grams per 1000 meters. To convert the linear density of the sliver into ktex:

Linear density in ktex = 2.85 / 1000 = 2.80 ktex