How is the efficiency of a filter calculated?

The efficiency of a filter is calculated using the formula (Beta - 1) / Beta, where Beta (β) represents the ratio of the number of particles upstream of the filter to the number of particles downstream of it. This formula effectively quantifies how well the filter is performing in removing particles from the fluid passing through it.

To understand this further, consider that a high Beta value indicates a significant reduction in the number of particles, hence a higher efficiency. By subtracting one from Beta, we account for the total particles being filtered out relative to the total particles initially present. Dividing by Beta then provides a percentage that indicates the fraction of particles removed by the filter.

This mathematical relationship makes it clear why this specific formula is used: it directly relates the filtering capacity to the incoming and outgoing particle concentrations, giving a clear measure of performance. In practical applications, this allows engineers to compare different filters and determine their effectiveness based on the operational needs of a system.