Viscosity

Viscosity measures a fluid’s resistance to flow. High viscosity means thick and slow (honey, molasses); low viscosity means thin and runny (water, alcohol). The everyday word “thick” conflates several properties; viscosity isolates the resistance-to-shear specifically. Two paint cans with identical density and pigment can have radically different viscosities depending on the binder system.

Units

• Pascal-second (Pa·s) — the SI unit. Water at 20°C is 0.001 Pa·s.
• Poise (P) or centipoise (cP) — cgs unit. 1 cP = 1 mPa·s. Water at 20°C is 1 cP, which makes it the natural reference value. Industrial viscosity is almost always quoted in cP.
• Saybolt Universal Seconds (SUS) — empirical industry unit, common in oil and lubricant specs. A drainage time, not a fundamental property; conversion to cP is approximate and depends on density.

Reference viscosities (cP, at 20°C unless noted)

• Air: 0.018
• Water: 1.0 (by convention)
• Milk: 3
• Olive oil: 84
• Motor oil (10W-30, cold): 100-200
• Maple syrup: 200
• Glycerine: 1,400
• Honey: 10,000
• Ketchup: 50,000-100,000 (shear-thinning — viscosity drops when shaken)
• Molasses: 100,000
• Peanut butter: ~250,000
• Pitch: 230 billion (famously dripping in the Pitch Drop Experiment, started 1927; only ~9 drops have fallen)

Temperature dependence

Viscosity drops sharply with temperature for liquids — honey straight from the fridge is unworkably thick; warmed honey pours like syrup. This is why engine oil has “multi-grade” ratings (5W-30, 10W-40, etc.): the W (winter) number refers to cold-temperature viscosity, the second number to hot-temperature. A 5W-30 stays pourable at cold start (low cold-W rating = lower cold viscosity) and maintains protective film thickness at operating temperature (30 = appropriate hot viscosity).

Gas viscosity, counter-intuitively, rises with temperature — opposite to liquids. The mechanism is different: in a liquid, viscosity comes from intermolecular forces that weaken when molecules move faster; in a gas, viscosity comes from momentum transfer between layers, which increases with molecular speed.

Newtonian vs non-Newtonian fluids

Most simple liquids (water, oil, honey) are Newtonian: viscosity is constant regardless of how fast you stir. Many real-world fluids aren’t. Ketchup is shear-thinning: viscosity drops under shear (which is why shaking the bottle helps). Cornstarch slurry (“oobleck”) is shear-thickening: punch it and it acts solid, sit on it and you sink. Blood, paint, magma, and most industrial slurries are non-Newtonian to some degree.

Worked example

Compute the pressure drop across a 10-metre length of horizontal pipe carrying a viscous fluid. Use the Hagen-Poiseuille equation for laminar flow: ΔP = (8 · μ · L · Q) / (π · r⁴), where μ is dynamic viscosity, L = pipe length, Q = volumetric flow rate, r = pipe radius. For water (μ = 0.001 Pa·s), 1 cm radius, 10 m length, flowing at 1 L/min (1.67×10⁻⁵ m³/s): ΔP = (8 × 0.001 × 10 × 1.67e−5) / (π × (0.01)⁴) ≈ 42.5 Pa — negligible. Switch to motor oil at 0.2 Pa·s (200× more viscous) at the same flow and the pressure drop becomes 8,500 Pa, requiring a pump that water didn’t. Switch to honey at 10 Pa·s and you need 425 kPa (4.2 bar) — at which point you redesign the system around a wider pipe, because the fourth-power dependence on radius means doubling r drops ΔP by 16×.

When and why it matters

Viscosity drives equipment sizing in chemical processing, fuel-injector calibration in engines, oil-grade selection in cold climates (a 5W-30 stays pourable at −30°C; a 20W-50 turns to molasses and shears the oil pump on startup), printability of inks and 3D-printer filaments, paintability of coatings (too low = drips, too high = brush marks), and even the “mouthfeel” engineering of beverages (the difference between full-fat and skim milk on the tongue is largely viscosity, not flavour). Medical: blood viscosity is monitored in haematology because high-viscosity blood (polycythaemia, hyperviscosity syndromes) raises stroke risk via reduced microcirculation. Reference: ISO 3104 — Petroleum products: Determination of kinematic viscosity.