The time-varying flow is studied experimentally in an anatomically accurate model of the human airways from the mouth through several generations of bronchial branching. The airway geometry is obtained from the CT scan of a healthy adult male of normal height and build. The three-component, three-dimensional mean velocity field is obtained throughout the entire model using phase-locked Magnetic Resonance Velocimetry. A pulsatile pump drives a sinusoidal waveform (inhalation and exhalation) with frequency and stroke-length such that the mean trachea Reynolds number at peak inspiration is Re = 4200 and the Womersley number is α = 1. Integral parameters are defined to quantify the degree of velocity profile nonuniformity (related to axial dispersion) and secondary flow strength (lateral dispersion), with implications drawn for the transport of particles. It is found that both parameters can vary non-trivially across successive bronchial generations, different bronchial paths, and during inhalation as compared to exhalation. They are particularly sensitive to local geometric features found in realistic anatomies, such as generation length and branching angle, and can be influenced by the moderate oscillation frequency of the bulk flow.