Question

100 kg oven dry warp yarns were sized to the add-on of 8% and dried to overall moisture content of 10%. The final mass of the sized yarn will be

• A. 125 kg
• B. 120 kg
• C. 130 kg
• D. 135 kg

Hint:

When overall moisture content is given, remember that dry mass equals (100% − moisture %) of the total mass. Always divide the dry mass by the dry fraction to get the final mass.

Answer 1

The Correct Option is B

Step 1: Understanding the given data.
The oven dry mass of warp yarn is given as 100 kg. Since the yarn is oven dry, it contains no moisture initially. The yarn is sized with an add-on of 8%, which means additional solid material is added based on the original dry weight of the yarn.
Step 2: Calculating the mass after sizing (dry basis).
Add-on of 8% means:
\[ \text{Size added} = 8% \text{ of } 100 = 8 \text{ kg} \] Therefore, the total dry mass of the sized yarn becomes:
\[ 100 + 8 = 108 \text{ kg} \] Step 3: Interpreting overall moisture content.
The overall moisture content of 10% means that moisture constitutes 10% of the final mass, and the dry material constitutes 90% of the final mass.
Step 4: Calculating the final mass of the sized yarn.
Since 108 kg represents 90% of the final mass:
\[ \text{Final mass} = \frac{108}{0.90} = 120 \text{ kg} \] Step 5: Conclusion.
Hence, the final mass of the sized yarn after adding size and accounting for moisture content is 120 kg.

Answer 2

Instead of dividing by 0.90 directly, this can be solved by thinking in terms of the ratio between dry material and moisture in the final sized yarn.

The starting oven-dry warp yarn is 100 kg. With an 8% add-on of size (calculated on the dry weight), the size added is
\( 8\% \times 100 = 8 \text{ kg} \), so the total dry (sized) mass, before any moisture is picked up, is
\[ 100 + 8 = 108 \text{ kg} \]

Now, the finished sized yarn has an overall moisture content of 10%, meaning that for every 100 kg of finished yarn, 10 kg is moisture and 90 kg is dry material. So the ratio of moisture to dry material in the final yarn is
\[ \frac{\text{moisture}}{\text{dry}} = \frac{10}{90} = \frac{1}{9} \]

Since the dry portion of the finished yarn is the 108 kg already calculated, the moisture picked up is
\[ \text{moisture} = \frac{108}{9} = 12 \text{ kg} \]

Adding this moisture to the dry sized mass gives the final mass of the sized yarn:
\[ 108 + 12 = 120 \text{ kg} \]

Therefore, the correct answer is 120 kg.