Viscosity Demystified: Newtonian Fluids, Boundary Layers, and Temperature Effects

Overview

Viscosity is the internal friction that resists fluid flow. This video builds intuition from everyday liquids like water, oil, honey, and pitch, then connects what we feel at a wall to the mathematics that governs flow. The no-slip condition at a boundary creates a velocity gradient that drives viscous forces, shaping how fluids move in pipes and around surfaces. The talk introduces the linear relationship between shear stress and velocity gradient, encapsulated by Newton's law of viscosity for Newtonian fluids.

Along the way, it distinguishes dynamic viscosity from kinematic viscosity, relates strain rate to deformation, and previews how temperature and pressure influence viscosity across liquids and gases. The session closes with non-Newtonian fluids and practical engineering implications.

Introduction to Fluid Viscosity

Viscosity is a fundamental property that quantifies a fluid’s internal friction and its ability to resist shear. The video begins with familiar liquids, explaining that layers moving at different speeds generate shear stress between them. The wall in contact with the fluid imparts a large shear stress, producing the no-slip condition where fluid velocity at the boundary is zero. This boundary behavior, together with the velocity profile across the fluid, highlights how viscosity damps or smooths out velocity differences in moving layers.

Newtonian Fluids and Newton's Law of Viscosity

For many liquids, shear stress is proportional to the velocity gradient DU/DY. The proportionality constant μ is the dynamic viscosity. Fluids that obey this linear relationship are Newtonian, and μ characterizes how easily the fluid flows under applied shear. The slope of the velocity profile near the wall is large where shear stresses are large, and small in the far field where layers move nearly in lockstep, illustrating how viscosity links microscopic interactions to macroscopic motion.

From Stress to Strain Rate

The analysis connects shear stress to the rate at which strain is applied rather than to the total strain itself, drawing a parallel to Hooke’s law for solids but with a key difference: fluids deform continuously under sustained shear. Newton’s law for viscosity can be rearranged to emphasize the rate of strain, clarifying why fluids resist motion more or less depending on μ and the velocity gradient.

Units and Distinctions: Dynamic vs Kinematic Viscosity

Dimensional analysis shows dynamic viscosity μ in pascal seconds (Pa s) and kinematic viscosity ν = μ/ρ in square meters per second. The centipoise (cP) and the poise are traditional units for dynamic viscosity, with water at room temperature about 1 cP. The talk also introduces the practical magnitudes of common fluids: engine oil around 500 cP, honey about 10 000 cP, and even extreme cases like pitch, which drops very slowly in the pitch drop experiment, demonstrating how viscosity can span many orders of magnitude.

Temperature, Pressure, and Their Effects

Viscosity changes with temperature and pressure. In liquids, viscosity decreases with increasing temperature as molecules more readily overcome cohesive forces. In gases, viscosity increases with temperature because increased molecular motion enhances intermolecular collisions. These trends are captured by empirical correlations such as Andrade’s equation for liquids and Sutherland’s equation for gases, with constants determined experimentally. Pressure has a smaller effect and is often neglected in basic analyses.

Flow Near Boundaries and the Inviscid Limit

Viscosity influences the boundary layer and the pressure drop along pipes. In high Reynolds number flows, engineers sometimes approximate the flow as inviscid away from boundaries, using Euler or Bernoulli equations for simpler analysis. The video discusses when this inviscid assumption is valid and when viscous terms cannot be neglected, emphasizing why real engineering problems remain fundamentally viscous near surfaces.

Non-Newtonian Fluids and Real-World Examples

Not all fluids obey Newton’s law; some exhibit nonlinear shear-stress versus strain-rate relationships. Shear-thinning fluids, such as paint, become less viscous as the rate of shear increases, aiding application, while shear-thickening fluids stiffen under high shear. These behaviors require more complex constitutive models beyond Newton's law to predict flow accurately.

Key Takeaways for Engineering and Science

Viscosity is central to Reynolds number calculations, flow stability, and laminar versus turbulent transitions. It governs the energy losses and pressure drops in pipes, lubrication in machinery, and the behavior of a wide range of liquids and gases. By linking microscopic molecular interactions to macroscopic flow properties, viscosity provides a unifying lens for understanding fluid dynamics across disciplines.