Atkinson's formula for mine ventilation is a practical relationship that links the pressure drop in a mine airway to the airflow and the resistance of that airway. In its commonly used form, the formula is written as:
Δp = R × Q²
where Δp is the pressure drop along the airway, Q is the airflow (quantity) passing through it, and R is the Atkinson resistance of the airway. This quadratic relationship reflects the fact that frictional losses in turbulent airflow are approximately proportional to the square of the velocity, and hence to the square of the airflow for a given cross-sectional area.
The Atkinson formulation is convenient for mine ventilation because it simplifies complex fluid dynamics into a single resistance term R that can be estimated or measured for each airway. R depends on factors such as airway length, cross-sectional area, perimeter, roughness of the walls, and any obstructions like supports, equipment or bends. Once R is known, engineers can calculate pressure drops for different airflows and determine the fan pressure needed to overcome the total resistance of the network.
In practice, Atkinson's formula is used extensively in mine ventilation network calculations. Each airway in the network is represented as a branch with a specific resistance R, and the pressure drop in that branch is written as Δp = RQ². The sum of pressure drops around each loop and the continuity of flow at each junction are then used (often with the Hardy Cross or similar methods) to balance the network and find a consistent set of flows and pressures that satisfy the entire system.
Atkinson's formula is conceptually similar to the Darcy–Weisbach equation used in general fluid mechanics. However, instead of explicitly using friction factors, hydraulic diameters and fluid properties for each calculation, mine ventilation practice embeds these effects into the Atkinson resistance R, which is easier to use for repetitive design and simulation work.
Understanding and applying Atkinson's formula allows ventilation engineers to estimate how changes in airway size, lining, roughness or equipment placement will affect pressure losses and fan duties. It is also essential when evaluating the impact of closing or opening certain routes, adding booster fans or reconfiguring the ventilation system during the life of a mine.
In summary, Atkinson's formula for mine ventilation expresses the pressure drop in an airway as the product of a resistance coefficient and the square of the airflow (Δp = R × Q²). It is a cornerstone of practical mine ventilation design and network analysis.
