Yarn Manufacturing

Step 1: Understanding willowing.
Willowing is an opening and cleaning process used to loosen fibre tufts and remove loose impurities such as dust, leaf particles, and trash.
Step 2: Role in fibre processing.
In cotton processing, willowing is one of the earliest operations in the blow room line. It prepares cotton fibres for further cleaning and opening.
Step 3: Analysis of other fibres.
Wool uses scouring and carding, sisal uses decortication, and coir uses retting and defibering, not willowing.
Step 4: Conclusion.
Therefore, willowing machines are used in cotton processing.

Step 1: Understanding viscose spinning requirements.
Viscose solution must have sufficient viscosity to form a continuous filament during extrusion through the spinneret without breaking.
Step 2: Importance of higher viscosity.
Low-viscosity solutions lead to filament breakage, while excessively high viscosity causes processing difficulties. An optimum range is required.
Step 3: Standard industrial practice.
In viscose rayon manufacturing, the viscose dope viscosity is typically maintained between 150 and 200 poise for stable spinning.
Step 4: Conclusion.
Therefore, the correct viscosity range is 150--200 poise.

Step 1: Understanding hollow fibre production.
Hollow fibres require a continuous void at the centre of the fibre along its length. This is achieved by controlled polymer flow during extrusion.
Step 2: Role of spinneret geometry.
An annular concentric spinneret consists of two concentric openings—an outer ring for polymer flow and an inner core for creating the hollow region.
Step 3: Analysis of options.
C-shaped, rectangular, and triangular spinnerets produce special solid cross-sections but do not generate a central hollow channel.
Step 4: Conclusion.
Therefore, an annular concentric spinneret is used to produce hollow fibres.

Step 1: Understanding packing density and porosity.
Packing density represents the fraction of space occupied by fibres in a yarn, whereas porosity represents the fraction of void space present in the yarn structure. Both are complementary structural parameters.
Step 2: Establishing the relationship.
As packing density increases, the void space within the yarn decreases proportionally. Hence, porosity decreases whenever packing density increases, and vice versa.
Step 3: Correlation interpretation.
Since one parameter increases exactly when the other decreases in a linear manner, the relationship is perfectly inverse.
Step 4: Conclusion.
Therefore, the correlation coefficient between packing density and porosity is .

Step 1: Understanding the concept.
In a ring frame, the linear speed of the traveller is equal to the peripheral speed of the ring. The traveller speed depends on the ring diameter and the spindle speed. The relationship between traveller speed, ring diameter, and spindle speed is given by:
where:
= linear speed of traveller (m/s)
= ring diameter (m)
= spindle speed (rpm)
Step 2: Substituting the given values.
Given:
Rearranging the formula to find ring diameter:
Step 3: Calculation.
Step 4: Converting into millimetres.
This value is closest to 37.7 mm among the given options.
Step 5: Conclusion.
Hence, the appropriate ring diameter for the given operating conditions is approximately 37.7 mm.

Step 1: Understanding pilling resistance.
Pilling resistance refers to the ability of a yarn or fabric to resist the formation of pills on the surface due to abrasion during use. Yarns with better fibre binding and fewer protruding fibres show higher pilling resistance.
Step 2: Characteristics of different yarns.
Air vortex yarn: Fibres are tightly wrapped around a straight core, resulting in minimal hairiness and excellent fibre binding. This provides the highest resistance to pilling.
Open end yarn: Has wrapper fibres and moderate hairiness, offering better pilling resistance than ring yarn but lower than air vortex yarn.
Ring yarn: Has higher fibre hairiness due to twisting, which increases the tendency of fibres to protrude and form pills.
Step 3: Comparing pilling resistance.
Based on fibre structure and hairiness:
Step 4: Conclusion.
Thus, the correct order of pilling resistance is Air vortex yarn > Open end yarn > Ring yarn.