This books studies an important class of fluid dynamics known as displacement flows. These frequently occur in chemical and food processing, in waxy crude oil pipeline restart flows, and in the transport of mined slurries and pulp. The defining characteristic is the displacement of a fluid by a second fluid having a greater density. We integrate experimental, analytical and computational methods to study displacement flows in slightly inclined pipes and channels. This was primarily motivated by the flows that occur during oil and gas well construction, particularly primary cementing: a process by which cement is pumped into a well to seal it by displacing the drilling mud. During this process, fluid mixing or bypassing results in cement contamination, which compromises the seal. This has very serious environmental and safety consequences if fluids leak. For example, in April 2010, the Macondo well explosion took the lives of 11 workers, and released approximately 5 million barrels of oil into the Gulf of Mexico; the immediate cause was failure of the primary cementing operation. We study and analyse the fluid dynamics behind the primary cementing operation.