Viscosity
Viscosity is a measure of a fluid's resistance to deformation or flow under an applied shear stress, arising from internal friction between adjacent fluid layers moving at different velocities. Dynamic (absolute) viscosity quantifies the shear stress needed to produce a unit velocity gradient, while kinematic viscosity is the ratio of dynamic viscosity to fluid density. Viscosity governs flow behaviour in lubrication, blood circulation, polymer processing, and aerodynamics.
Key Formula
τ = μ × (du/dy)
LaTeX: \tau = \mu \frac{du}{dy}
| Symbol | Meaning | Unit |
|---|---|---|
| τ | Shear stress | Pa |
| μ | Dynamic viscosity | Pa·s (or N·s/m²) |
| du/dy | Velocity gradient perpendicular to flow direction | s⁻¹ |
Worked Example
Problem
A fluid occupies the 2 mm gap between two parallel plates of area 0.5 m². The top plate moves at 0.4 m/s relative to the stationary bottom plate. The dynamic viscosity of the fluid is 0.03 Pa·s. Calculate the shear force required.
Solution
Step 1 — Velocity gradient: du/dy = 0.4 / 0.002 = 200 s⁻¹. Step 2 — Shear stress: τ = μ × (du/dy) = 0.03 × 200 = 6 Pa. Step 3 — Shear force: F = τ × A = 6 × 0.5 = 3 N.
Answer
F = 3 N
Dynamic Viscosity of Common Fluids at 20 °C
| Fluid | Dynamic Viscosity (Pa·s) | Kinematic Viscosity (m²/s) | Flow Character |
|---|---|---|---|
| Air | 1.81 × 10⁻⁵ | 1.51 × 10⁻⁵ | Very low resistance |
| Water | 1.00 × 10⁻³ | 1.00 × 10⁻⁶ | Low viscosity |
| Blood (whole) | 3.0 × 10⁻³ | ~3 × 10⁻⁶ | Moderate, non-Newtonian |
| Motor oil (SAE 30) | ~0.1 | ~1.1 × 10⁻⁴ | High viscosity |
| Honey | ~2–10 | ~2–10 × 10⁻³ | Very high viscosity |
| Glycerol | 1.41 | 1.12 × 10⁻³ | High viscosity |
Interactive Tools
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Related Terms
Laminar Flow
Laminar flow is a smooth, orderly regime of fluid motion in which fluid particles travel in parallel layers (laminae) without lateral mixing or cross-current fluctuations. It occurs at low Reynolds numbers (typically Re < 2300 in pipes) where viscous forces dominate over inertial forces, producing a parabolic velocity profile in pipe flow. Laminar flow is essential in microfluidics, blood flow in capillaries, lubrication engineering, and precision chemical dosing.
Reynolds Number
The Reynolds number (Re) is a dimensionless quantity that predicts the flow regime of a fluid by comparing inertial forces to viscous forces within the flow. A low Reynolds number indicates that viscous forces dominate, resulting in smooth laminar flow, while a high value signals that inertial forces dominate, leading to turbulent flow. It is indispensable in scaling model experiments to full-size systems, designing pipelines, and predicting aerodynamic behaviour around aircraft and vehicles.
Drag Force
Drag force is the resistive force exerted by a fluid on a body moving through it, acting opposite to the direction of relative motion and composed of pressure drag (form drag) and skin-friction drag. For objects moving at moderate to high speeds, drag is proportional to the square of velocity, the fluid density, the frontal area, and a dimensionless drag coefficient that depends on shape and flow regime. Understanding and minimising drag is critical in vehicle and aircraft design, sports engineering, and offshore structure analysis.
From Latin "viscosus" (sticky), itself from "viscum" (mistletoe or birdlime — a sticky substance made from mistletoe berries). The term entered scientific use in the 17th century; Newton's law of viscosity was formulated in his "Principia" (1687).