viscosity

Viscosity is a fluid's internal friction, its resistance to flowing. It is what makes honey ooze slowly while water splashes freely, why cold syrup pours more stubbornly than warm, and why stirring thick paint is hard work. It answers the everyday question: why do some fluids flow easily and others reluctantly?

Precisely, viscosity measures how strongly the layers within a fluid resist sliding past one another. When you drag one layer of fluid across another, it takes a shearing force to keep it moving, and viscosity is the constant linking that force to the rate of shearing. For a simple (Newtonian) fluid, the shear stress equals the viscosity times the velocity gradient: tau = mu × (dv/dy), where mu (the Greek letter mu) is the viscosity, and dv/dy is how fast the flow speed changes from one layer to the next. Its SI unit is the pascal-second (Pa s). A high viscosity, like honey's, means the layers grip each other strongly; a low viscosity, like water's or air's, means they slip easily.

Viscosity is why real pipes lose pressure along their length, why lubricating oil protects an engine, and why a spoon slows down when you pull it through treacle. One honest note: viscosity is exactly the property an ideal fluid ignores, which is why ideal-fluid results like Bernoulli's must be applied with care to real, sticky fluids. Viscosity also changes with temperature, dropping for liquids as they warm (warm honey flows faster) but rising slightly for gases.