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Fluid dynamicists define the chord Reynolds number R = Vc/ν, where V is the flight speed, c is the chord length, and ν is the kinematic viscosity of the fluid in which the airfoil operates, which is 1.460 × 10 −5 m 2 /s for the atmosphere at sea level. [19]
The following formula describes the viscous stress tensor for the special case of Stokes flow. It is needed in the calculation of the force acting on the particle. In Cartesian coordinates the vector-gradient is identical to the Jacobian matrix. The matrix I represents the identity-matrix.
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.
A key tool used to determine the stability of a flow is the Reynolds number (Re), first put forward by George Gabriel Stokes at the start of the 1850s. Associated with Osborne Reynolds who further developed the idea in the early 1880s, this dimensionless number gives the ratio of inertial terms and viscous terms. [4]
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.
μ = Dynamic viscosity (SI units: N s/m 2) ʋ = Kinematic viscosity (SI units: m 2 /s) There are few ways to maintain kinematic similarity. To keep the Reynolds number the same, the scaled-up model can use a different fluid with different viscosity or density. We can also change the velocity of the fluid to maintain the same dynamic ...
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.
A particle with a low Stokes number follows fluid streamlines (perfect advection), while a particle with a large Stokes number is dominated by its inertia and continues along its initial trajectory. In the case of Stokes flow , which is when the particle (or droplet) Reynolds number is less than about one, the particle drag coefficient is ...