The formula to calculate the Circle Packing Density (D) is:
\[ D = \frac{N \times A_c}{A_t} \]
Where:
Circle packing density refers to the proportion of a given area that is occupied by circles when they are packed together as closely as possible. This concept is often used in various fields such as material science, logistics, and mathematics to optimize space and resource utilization. The density is a measure of how efficiently the circles fill the container area, and it is expressed as a ratio or percentage. Higher density values indicate more efficient packing, while lower values suggest that there is more unused space within the container.
Let's say the number of circles (N) is 10, the area of one circle (A_c) is 3 square units, and the area of the container (A_t) is 50 square units. Using the formula:
\[ D = \frac{10 \times 3}{50} = 0.6 \]
So, the circle packing density (D) is 0.6 or 60%.
Formula: \( \eta = \frac{V_{packed}}{V_{total}} \)
Example: \( \eta = \frac{500}{1000} \)
Formula: \( \eta = \frac{L_{packed}}{L_{total}} \)
Example: \( \eta = \frac{30}{50} \)
Formula: \( \rho = \frac{m}{A} \)
Example: \( \rho = \frac{10}{3.14} \)
Formula: \( \eta = \frac{\pi}{3\sqrt{2}} \)
Example: \( \eta = \frac{3.14}{3\sqrt{2}} \)
Formula: \( \eta = \frac{\rho_{packed}}{\rho_{bulk}} \)
Example: \( \eta = \frac{2.5}{1.2} \)
Formula: \( \eta = \frac{n \cdot A_{circle}}{A_{rectangle}} \)
Example: \( \eta = \frac{5 \cdot 3.14}{20} \)
Formula: \( \eta = \frac{A_{packed}}{A_{total}} \)
Example: \( \eta = \frac{15}{25} \)
