Question

A woven fabric has weft yarn of 24 tex and pick density of 25 per cm. It is desired to replace only the weft with a 6 tex yarn of the same packing density. The pick density per cm required to keep the fabric cover the same (answer in integer) is _________.

Hint:

To maintain the same fabric cover, ensure that the product of the new yarn tex and pick density equals the initial fabric cover.

Answer 1

Given: Original weft yarn: 24 tex, pick density = 25/cm New weft yarn: 6 tex (same packing density) 
Key Concepts: Yarn diameter ($d$) $\propto \sqrt{{tex}}$ To maintain fabric cover: $\frac{d}{{spacing}}$ must stay constant Spacing ($s$) = $\frac{1}{{pick density}}$ 
Step 1: Find Yarn Diameter Ratio \[ \frac{d_2}{d_1} = \sqrt{\frac{6}{24}} = \sqrt{\frac{1}{4}} = \frac{1}{2} \] New yarn is half the diameter of original.
Step 2: Maintain Fabric Cover \[ \frac{d_1}{s_1} = \frac{d_2}{s_2} \implies d_1 P_1 = d_2 P_2 \] \[ P_2 = P_1 \times \frac{d_1}{d_2} = 25 \times 2 = 50 \] Final Answer: \[ \boxed{50} \]