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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 ...
which depends only on equilibrium state variables like temperature and density (equation of state). In general, the trace of the stress tensor is the sum of thermodynamic pressure contribution and another contribution which is proportional to the divergence of the velocity field. This coefficient of proportionality is called volume viscosity.
The Reynolds and Womersley Numbers are also used to calculate the thicknesses of the boundary layers that can form from the fluid flow’s viscous effects. The Reynolds number is used to calculate the convective inertial boundary layer thickness that can form, and the Womersley number is used to calculate the transient inertial boundary thickness that can form.
In this view, the data at different roughness ratio ε / D fall together when plotted against R ∗, demonstrating scaling in the variable R ∗. The following features are present: When ε = 0, then R ∗ is identically zero: flow is always in the smooth pipe regime. The data for these points lie to the left extreme of the abscissa and ...
The SI unit of dynamic viscosity is the newton-second per square meter (N·s/m 2), also frequently expressed in the equivalent forms pascal-second (Pa·s), kilogram per meter per second (kg·m −1 ·s −1) and poiseuille (Pl). The CGS unit is the poise (P, or g·cm −1 ·s −1 = 0.1 Pa·s), [28] named after Jean Léonard Marie Poiseuille.
Drag coefficients in fluids with Reynolds number approximately 10 4 [1] [2] Shapes are depicted with the same projected frontal area. In fluid dynamics, the drag coefficient (commonly denoted as: , or ) is a dimensionless quantity that is used to quantify the drag or resistance of an object in a fluid environment, such as air or water.
In this section our central macroscopic variables and parameters and their units are temperature [K], pressure [bar], molar mass [g/mol], low density (low pressure or dilute) gas viscosity [μP]. It is, however, common in the industry to use another unit for liquid and high density gas viscosity η {\displaystyle \eta } [cP].
Dynamic modulus (sometimes complex modulus [1]) is the ratio of stress to strain under vibratory conditions (calculated from data obtained from either free or forced vibration tests, in shear, compression, or elongation).