Question

For an ideal blend mixing of fibres, $\pi$ value should be equal to

• A. 0
• B. 1
• C. 2
• D. 1.2

Hint:

• Brennan's Index of Blend Irregularity ($\pi$) is a measure of blend uniformity.
• $\pi = 1$ represents a perfectly random (ideal) distribution of fibers in the blend.
• Values of $\pi>1$ indicate poorer blending (more irregularity).
• The goal in textile blending is to achieve a $\pi$ value as close to 1 as possible.

Answer 1

The Correct Option is B

The "$\pi$ value" in the context of fiber blend mixing often refers to an Index of Blend Irregularity, such as Brennan's Index. This index compares the observed variance of the blend proportion in small samples of the blend (e.g., cross-sections of a sliver or yarn) to the theoretical variance that would be expected if the fibers were distributed completely at random. Brennan's Index $\pi = \frac{\text{Observed Variance}}{\text{Random Variance}} = \frac{\sigma^2_{obs}}{\sigma^2_{random}}$.

• If $\pi = 1$, the blend is as uniform as a perfectly random mixture. This is considered an ideal random blend.
• If $\pi>1$, the blend is more irregular (less uniform) than a random mixture.
• If $\pi<1$, the blend is more uniform than random (which is rare and might imply segregation or patterning rather than true homogeneity).

Therefore, for an ideal (perfectly random) blend mixing of fibers, the $\pi$ value should be equal to 1. \[ \boxed{1} \]