Knitted Fabric Loop Density Calculation

This solution determines the loop density per square centimeter for a knitted fabric using the provided loop length, wale constant, and course constant.

Loop Density Formula

Loop density ($D$) is the number of loops per unit area. For this calculation, using the given constants, the relevant formula is:

$ D = \frac{K_w \times K_c}{L^2} $

Where:

• $D$ = Loop density (loops/cm$^2$)
• $K_w$ = Wale constant
• $K_c$ = Course constant
• $L$ = Loop length (cm)

Step-by-Step Calculation

1. Identify Given Values:

   • Wale constant ($K_w$): $4.2$
   • Course constant ($K_c$): $5.5$
   • Loop length ($L$): $0.5$ cm

2. Calculate Loop Length Squared:

   $ L^2 = (0.5 \text{ cm})^2 = 0.25 \text{ cm}^2 $

3. Apply the Formula:

   Substitute the known values into the formula:

   $ D = \frac{4.2 \times 5.5}{0.25 \text{ cm}^2} $

4. Calculate the Numerator:

   $ D = \frac{23.1}{0.25 \text{ cm}^2} $

5. Compute the Density:

   $ D = 92.4 \text{ loops/cm}^2 $

6. Round to Nearest Integer:

   Rounding $92.4$ to the nearest integer gives $92$.

The calculated loop density is 92 loops/cm$^2$.