The amoroso-robinson relation is a fancy term that explains how the thickness of a fluid changes as it moves in a pipe. Imagine if you were pouring syrup into a straw, the syrup gets thicker as it gets closer to the bottom because it has less space to move around. This is a bit like how the thickness of a fluid changes when it moves through a pipe.
So, the relation tells us that the thickness of the fluid in a pipe depends on how fast it's moving, how big the pipe is, and some special stuff about the fluid itself (like how sticky or runny it is). Scientists use this relation to figure out how to design pipes so that they don't get clogged up or break. It's pretty cool!