In analogy with the classical concept of mass-flux-based streamlines, we define angular momentum transport (AMT) lines as an aerodynamic functional diagnostic tool. The AMT lines are the ones whose tangents are given by the average angular momentum flux. The mathematical and physical properties of these AMT lines are exploited to study the generation, removal, and transport of angular momentum in turbomachinery components. We illustrate the concept by visualizing AMT lines in two relatively simple flows, namely, vaneless incompressible diffuser and von Karman flow (a model of centrifugal compressors). Next, we apply the proposed diagnostic tool to flow in a return channel. A return channel is a part of a multistage centrifugal compressor stage. Its principal function is to remove angular momentum. In this work, we apply the diagnostic tool of AMT lines to a Reynolds-averaged Navier Stokes (RANS) simulation and a wall-modeled large eddy simulation (LES) of flow in the return channel. We show that AMT lines give us insights into the AMT process that are otherwise not available with conventional visualization tools.