Expressing the net effect of shear (Fluid Dynamics with Olivier Cleynen)

How to deal with all the dimensions of shear as it applies to a fluid particle in fluid dynamics? Let's sort things out step by step. Part of a series of theory and solved problem videos from https://fluidmech.ninja/ The slides in this video, with links to sources, are at https://fluidmech.ninja/slides/5v1.pdf