Question

A yarn is unravelled from a woven fabric specimen of 1 m $\times$ 1 m size. If the length of the straightened yarn is 1.1 m, then the crimp percentage (in integer) is ________________.

Hint:

Crimp percentage measures the amount of curl or distortion of the yarn in comparison to its straightened length. It is a crucial property for evaluating the quality and uniformity of yarn in fabric production.

Answer 1

Correct Answer: 10

The crimp percentage (\(C\)) is a measure of the extension of the yarn compared to its original length when the yarn is straightened. It gives an indication of the amount of curl or wave the yarn has when it is taken from the fabric. The formula for calculating the crimp percentage is: \[ C = \frac{L_0 - L_f}{L_0} \times 100 \] Where:
- \(L_0\) is the original length of the fabric specimen before the yarn is straightened (1 m in this case).
- \(L_f\) is the final length of the straightened yarn (1.1 m).
The formula calculates the difference between the original length of the fabric and the length of the straightened yarn, which represents the crimp. Dividing this difference by the original length gives the relative amount of crimp as a fraction, and multiplying by 100 converts it into a percentage. Now, substituting the given values:
- \(L_0 = 1\) meter (the length of the fabric specimen),
- \(L_f = 1.1\) meters (the length of the straightened yarn).
We can now compute the crimp percentage: \[ C = \frac{1.1 - 1}{1} \times 100 = \frac{0.1}{1} \times 100 = 10% \] Thus, the crimp percentage of the yarn is \( \boxed{10} % \).