Bepaling van Pi-termen

To determine Pi terms using the Buckingham Pi theorem, consider the example of analyzing lift force on an airplane wing.

Relevant variables here include the lift force generated by the wing, air density, wing area, velocity of the aircraft, and air viscosity.

Each variable is expressed in fundamental dimensions, such as mass, length, and time, to provide a consistent basis for constructing dimensionless terms.

The number of Pi terms is determined by subtracting the fundamental dimensions from the total variables.

In this case, five variables and three dimensions yield two Pi terms. Three variables, air density, velocity, and wing area, are then chosen as repeating variables to cover all dimensions, ensuring they are independent.

The remaining variables—lift force and viscosity—are combined with the repeating variables to form dimensionless Pi terms.

Each Pi term is verified to ensure it is dimensionless by confirming that all units cancel out. The final Pi terms simplify the original variables into expressions that capture the essential characteristics of the lift system.