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The Reynolds number Re is taken to be Re = V D / ν, where V is the mean velocity of fluid flow, D is the pipe diameter, and where ν is the kinematic viscosity μ / ρ, with μ the fluid's Dynamic viscosity, and ρ the fluid's density. The pipe's relative roughness ε / D, where ε is the pipe's effective roughness height and D the pipe ...
The SI unit of kinematic viscosity is square meter per second (m 2 /s), whereas the CGS unit for kinematic viscosity is the stokes (St, or cm 2 ·s −1 = 0.0001 m 2 ·s −1), named after Sir George Gabriel Stokes. [29] In U.S. usage, stoke is sometimes used as the singular form.
The acceleration of gravity g and the kinematic viscosity of the fluid ν are known, as are the diameter of the pipe D and its roughness height ε. If as well the head loss per unit length S is a known quantity, then the friction factor f D can be calculated directly from the chosen fitting function.
μ is the dynamic viscosity of the fluid (Pa·s or N·s/m 2 or kg/(m·s)) ν is the kinematic viscosity of the fluid (m 2 /s). The Brezina equation. The Reynolds number can be defined for several different situations where a fluid is in relative motion to a surface.
The roughness of the pipe surface influences neither the fluid flow nor the friction loss. In turbulent flow , losses are proportional to the square of the fluid velocity , V 2 ; here, a layer of chaotic eddies and vortices near the pipe surface, called the viscous sub-layer, forms the transition to the bulk flow.
Consequently, if a liquid has dynamic viscosity of n centiPoise, and its density is not too different from that of water, then its kinematic viscosity is around n centiStokes. For gas, the dynamic viscosity is usually in the range of 10 to 20 microPascal-seconds, or 0.01 to 0.02 centiPoise. The density is usually on the order of 0.5 to 5 kg/m^3.
Dimensionless numbers (or characteristic numbers) have an important role in analyzing the behavior of fluids and their flow as well as in other transport phenomena. [1] They include the Reynolds and the Mach numbers, which describe as ratios the relative magnitude of fluid and physical system characteristics, such as density, viscosity, speed of sound, and flow speed.
is the wall coordinate: the distance y to the wall, made dimensionless with the friction velocity u τ and kinematic viscosity ν, + is the dimensionless velocity: the velocity u parallel to the wall as a function of y (distance from the wall), divided by the friction velocity u τ, is the wall shear stress,