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For kinematic viscosity, the SI unit is m^2/s. In engineering, the unit is usually Stoke or centiStoke, with 1 Stoke = 0.0001 m^2/s, and 1 centiStoke = 0.01 Stoke. For liquid, the dynamic viscosity is usually in the range of 0.001 to 1 Pascal-second, or 1 to 1000 centiPoise. The density is usually on the order of 1000 kg/m^3, i.e. that of water.
A centipoise is one hundredth of a poise, or one millipascal-second (mPa⋅s) in SI units (1 cP = 10 −3 Pa⋅s = 1 mPa⋅s). [4] The CGS symbol for the centipoise is cP. The abbreviations cps, cp, and cPs are sometimes seen. Liquid water has a viscosity of 0.00890 P at 25 °C at a pressure of 1 atmosphere (0.00890 P = 0.890 cP = 0.890 mPa⋅s).
For liquids, it corresponds to the informal concept of thickness; for example, syrup has a higher viscosity than water. [2] Viscosity is defined scientifically as a force multiplied by a time divided by an area. Thus its SI units are newton-seconds per square meter, or pascal-seconds. [1]
In practice the unit has never been widely accepted and most international standards bodies do not include the poiseuille in their list of units. The third edition of the IUPAC Green Book , for example, lists Pa⋅s ( pascal - second ) as the SI-unit for dynamic viscosity, and does not mention the poiseuille.
where (in SI units): is the frictional force – known as Stokes' drag – acting on the interface between the fluid and the particle (newtons, kg m s −2); μ (some authors use the symbol η) is the dynamic viscosity (Pascal-seconds, kg m −1 s −1); R is the radius of the spherical object (meters);
1 reyn = 1 lb f s in −2. It follows that the relation between the reyn and the poise is approximately 1 reyn = 6.89476 × 10 4 P. In SI units, viscosity is expressed in newton-seconds per square meter, or equivalently in pascal-seconds. The conversion factor between the two is approximately 1 reyn = 6890 Pa s.
μ is the dynamic viscosity of the fluid (Pa·s = N·s/m 2 = kg/(m·s)); Q is the volumetric flow rate, used here to measure flow instead of mean velocity according to Q = π / 4 D c 2 <v> (m 3 /s). Note that this laminar form of Darcy–Weisbach is equivalent to the Hagen–Poiseuille equation, which is analytically derived from the ...
A is the pipe's cross-sectional area (A = πD 2 / 4 ) (m 2), u is the mean velocity of the fluid (m/s), μ (mu) is the dynamic viscosity of the fluid (Pa·s = N·s/m 2 = kg/(m·s)), ν (nu) is the kinematic viscosity (ν = μ / ρ ) (m 2 /s), ρ (rho) is the density of the fluid (kg/m 3), W is the mass flowrate of the fluid (kg/s).