We develop a mathematical model of the lung that can estimate independently the air flows and pressures in the upper bronchi. It accounts for the lung multi-scale properties and for the air-tissue interactions. The model equations are solved using the Discrete Fourier Transform, which allows quasi instantaneous solving, in the limit of the model hypotheses. With this model, we explore how the air flow--volume curves are affected by airways obstruction or by change in lung compliance. Our work suggests that a fine analysis of the flow-volume curves might bring information about the inner phenomena occurring in the lung.