This presentation features experimental footage of nonlinear dispersive hydrodynamics in the viscous fluid conduit system, where lighter, lower viscosity interior fluid is injected into the bottom of a column of highly viscous exterior fluid. Buoyancy causes the invasive fluid to rise, and steady injection leads to the formation of a fluid-filled pipe. Careful control of the injection rate allows for the dilation of the pipe and the generation of localized, solitary traveling waves or solitons and dispersive shock waves at the two-fluid interface. Dispersive shock waves are the conservative analog of more familiar viscous shock waves. The key mathematical and physical features that govern these structures, nonlinearity and dispersion, are applicable to superfluids, nonlinear diffraction patterns in optics, quantum matter waves in Bose-Einstein condensates, tsunamis in shallow water, and many more. The controlled laboratory setting explored here enables the creation and study of previously inaccessible, highly coherent phenomena such as the interactions of solitons and dispersive shock waves. In addition, these features can be modeled and predicted mathematically, revealing their universality in all media that exhibit dispersive hydrodynamics.