A topic in the Open Knowledge Graph — a free, open map of 15,290 topics and the order to learn them in.
A Newtonian fluid obeys Newton's law of viscosity: shear stress τ = μ(du/dy), where μ is the dynamic viscosity and du/dy is the velocity gradient (shear rate). The no-slip condition requires that fluid in contact with a solid boundary moves at the boundary's velocity. Non-Newtonian fluids (shear-thinning, shear-thickening, Bingham plastics) have viscosity that depends on shear rate, making them fundamentally different from Newtonian ones like water and air.
Derive Couette flow (flow between parallel plates with one moving) from Newton's viscosity law to see how a linear velocity profile emerges. Compare viscosities of different fluids in tables and connect units (Pa·s = kg/(m·s)) to physical meaning.
You already know from fluid properties and continuum mechanics that a fluid deforms continuously under shear stress — unlike a solid, which deforms to a fixed amount and stops. But what determines the rate of deformation? Viscosity is the answer: it quantifies how much resistance a fluid offers to being sheared. The physical picture is one of fluid layers sliding past one another. Faster layers drag slower layers forward through molecular momentum exchange; slower layers drag faster layers backward. This internal friction, averaged over enormous numbers of molecular collisions, is what Newton's law of viscosity captures in a single equation.
Newton's law of viscosity states τ = μ(du/dy): the shear stress τ (force per unit area) between adjacent fluid layers equals the dynamic viscosity μ times the velocity gradient du/dy. A Newtonian fluid is defined precisely by this linear relationship — doubling the shear rate du/dy doubles the shear stress τ. Water and air are Newtonian across virtually all engineering conditions. The viscosity μ has units of Pa·s and depends strongly on temperature: water's viscosity drops by a factor of three between 20°C and 70°C (molecular mobility increases with thermal energy), while air's viscosity increases modestly with temperature (more frequent molecular collisions transfer more momentum). Kinematic viscosity ν = μ/ρ combines viscosity and density into a single parameter that governs how momentum diffuses through a fluid; it appears naturally in the Reynolds number Re = VL/ν.
The no-slip condition — that fluid immediately at a solid boundary moves at exactly the boundary's velocity — follows from molecular physics: fluid molecules collide with the wall, exchange momentum, and match its velocity. This is not an assumption imposed for convenience; it is an empirical observation holding for virtually all engineering flows. Its consequence is immediately practical: even a flow with high free-stream velocity has zero velocity at every solid wall, creating a velocity gradient du/dy and therefore a shear stress τ at every surface. Without the no-slip condition, viscosity would be irrelevant at walls — the entire study of boundary layers, pipe friction, and drag depends on it.
Non-Newtonian fluids break the linear τ–(du/dy) relationship in characteristic ways. Shear-thinning fluids (blood, ketchup, many polymer solutions) have viscosity that decreases with shear rate — they flow more easily when stirred faster, which is why ketchup suddenly pours after vigorous shaking. Shear-thickening fluids (dense cornstarch suspensions) stiffen under rapid deformation — the basis of "oobleck" that behaves as a solid under impact. Bingham plastics (toothpaste, mayonnaise) act as solids below a yield stress and flow only above it. Recognizing whether a fluid is Newtonian or not matters enormously in design: pipe and pump sizing formulas derived from Newton's viscosity law will give wrong answers for non-Newtonian fluids, sometimes catastrophically so in polymer processing, food engineering, and biological flow applications.