Page contents
What are dynamic viscosity and kinematic viscosity?
Dynamic viscosity μ measures the resistance of a fluid to shear: it is the ratio between the friction stress between two layers of fluid and their velocity gradient. Its SI unit is the pascal-second (Pa·s); the millipascal-second, equal to the centipoise (1 mPa·s = 1 cP), is also used. Kinematic viscosity ν is the dynamic viscosity divided by the density, ν = μ / ρ, in m²/s or in centistokes (1 cSt = 1 mm²/s). Water at 20 °C has a dynamic viscosity of 1.0 mPa·s and a kinematic viscosity of 1.0 cSt; the viscosity of liquids decreases as temperature rises, that of gases increases.
Viscosity formulas and units
- τ: shear stress between two layers of fluid, in Pa
- μ (mu, sometimes η): dynamic viscosity, in Pa·s; dV/dy: velocity gradient perpendicular to the flow, in s⁻¹
- ν (nu): kinematic viscosity, in m²/s; ρ: density, in kg/m³
Conversions: 1 Pa·s = 1,000 mPa·s = 1,000 cP = 10 poise; 1 m²/s = 10⁶ cSt = 10⁴ stokes; 1 cSt = 1 mm²/s. Example: ISO VG 46 oil at 40 °C, ν = 46 cSt and ρ = 870 kg/m³, so μ = 46·10⁻⁶ × 870 = 0.040 Pa·s = 40 mPa·s.
Viscosity table of common liquids and gases
| Fluid | T (°C) | μ (mPa·s) | ρ (kg/m³) | ν (mm²/s = cSt) |
|---|---|---|---|---|
| Water | 20 | 1.00 | 998 | 1.00 |
| Water | 50 | 0.55 | 988 | 0.55 |
| Water | 80 | 0.36 | 972 | 0.37 |
| Sea water | 20 | 1.08 | 1,025 | 1.05 |
| Air (1 atm) | 20 | 0.018 | 1,20 | 15.1 |
| Air (1 atm) | 100 | 0.022 | 0,95 | 23.1 |
| ISO VG 46 hydraulic oil | 40 | 40 | 870 | 46 |
| Diesel fuel | 20 | 3.5 | 840 | 4.2 |
| Petrol | 20 | 0.6 | 740 | 0.8 |
| Ethanol | 20 | 1.2 | 789 | 1.5 |
| Glycerol | 20 | 1 410 | 1,260 | 1,120 |
| Mercury | 20 | 1.55 | 13,546 | 0.11 |
Detailed explanations and calculation in Mecaflux
Two layers of fluid which move close to each other generate a frictional force which is
proportional to :
- their surface,
- their relative velocity (one with respect to the other)
and inversely proportional to the distance which separates them.
(detail of the integrated viscosity converter mecaflux)
Dynamic viscosity:
the proportionality factor that binds the surface, the velocity and the distance to the frictional force, is the coefficient of dynamic viscosity n. the legal unit of dynamic viscosity is the pascal second (pas-s) or Poiseuille (PI). This ratio varies depending on the temperature and the fluid.
kinematic viscosity:
if we divide the coefficient of dynamic viscosity by the density of the fluid, we obtain a ratio used in some formulas this report is named kinematic viscosity and its unit is m² / s. Designated also Stokes (St) or centistokes (cSt).1m²/s=10 000St=1 000 000cSt
in the tab "Major head loss" (pipes friction pressure losses) , an editor of fluid viscosity, allows you to choose a fluid and temperature, this choice determines the dynamic viscosity.
The editor of fluids allows you to set / save viscosity for a gas or liquid of your choice depending on the temperature and record it in the database Viscosity of your software. A database viscosities of fluids, gases or liquids, is incorporated into mecaflux with about 85 liquids and 35 gas , whose dynamic viscosity is given as a function of temperature. By selecting the temperature of the fluid of your choice, you refresh the dynamic viscosity, kinematic viscosity, temperature and density of your fluid , when calculating major head loss or minor head losses.
The editor of fluid viscosity:
It is also possible to directly enter the dynamic viscosity that you want, when calculating major or minor head loss.
An interface named viscometer "home maid" allows you to evaluate the dynamic viscosity of a fluid with " basics utensils" (Menu Tools mecaflux) 
the unit and its viscosity tab converter to convert the kinematic viscosity and dynamic viscosity
Frequently asked questions
What is the difference between dynamic and kinematic viscosity?
Dynamic viscosity μ (Pa·s) characterises the internal friction of the fluid; kinematic viscosity ν (m²/s) is μ divided by the density ρ. The Reynolds number uses ν; head losses can be calculated with either, as long as ρ is known.
How do I convert centipoise to centistokes?
ν (cSt) = μ (cP) / relative density. For water, with a density of 1, 1 cP = 1 cSt. For an oil of density 0.87, 40 cP corresponds to 46 cSt. The converter on this page also handles SSU and Engler degrees.
How does viscosity change with temperature?
The viscosity of liquids falls sharply as temperature rises: water goes from 1.8 mPa·s at 0 °C to 0.28 mPa·s at 100 °C, and a hydraulic oil can be divided by ten between 20 and 80 °C. The viscosity of gases increases slightly with temperature.
How do I allow for the viscosity of my own fluid in head loss calculations?
The fluid editor of Mecaflux Standard gives the dynamic and kinematic viscosity of 120 liquids and gases at the temperature of your installation, and you can create your own fluid from its data sheet; the Reynolds number, the flow regime and the friction factor of each run then follow automatically. For an oil, a food fluid or a viscous chemical, Mecaflux carries out the study of your project with the right properties, or offers training on the software applied to your own installation.