What length do you use for Reynolds number?

What length do you use for Reynolds number?

Reynolds number is a dimensionless number linking viscosity, density, and a reference length. The reference length can be : The inside diameter of the duct (for flows in pipes) For the study of the geometric body drag, unshaped, this reference length is the width of the frontal area (perpendicular to flow)

What is a Stokes particle?

Stokes’ law describes the settling of spheres in a Newtonian fluid. A spherical particle placed in a Newtonian fluid will sink if the buoyant force does not match or exceed the gravitational force on the sphere. The net downward force on a sphere is the difference between the settling force and the buoyant force.

How is Reynolds number calculated?

Reynolds number (Rn) is defined as Rn=(ρVL)/μ=(VL)/ν, where V is the fluid velocity relative to the body and L is a typical length.

What is Reynolds number for laminar flow?

Internal Flow

Flow type	Reynolds Number Range
Laminar regime	up to Re=2300
Transition regime	2300
Turbulent regime	Re>4000

What is characteristic length formula?

In computational mechanics, a characteristic length is defined to force localization of a stress softening constitutive equation. The length is associated with an integration point. For 2D analysis, it is calculated by taking the square root of the area.

How do you find the characteristic length in Reynolds number?

How to determine the characteristic length in reynolds number calculations in general? I understand that the reynolds number is given by the expression Re=ρvLμ, where ρ is the density, v is the fluid velocity and μ is the dynamic viscosity. For any given fluid dynamics problem, ρ, v, and μ are trivially given.

What are the four conditions of Stokes law?

Conditions under which Stoke’s law is valid are: The fluid through which the body moves must have infinite extension. The body is perfectly rigid and smooth. There is no slip between the body and the fluid. The motion of the body does not give rise to turbulent motion.

What is the units of viscosity?

Dynamic viscosity: The SI physical unit of dynamic viscosity (μ) is the Pascal-second (Pa s), which is identical to 1 kg m−1 s−1. The physical unit for dynamic viscosity in the centimeter gram second system of units (cgs) is the poise (P), named after Jean Poiseuille.

What is characteristic length of cylinder?

If your object is a cylinder in vertical orientation, the convective length scale is the height H of the cylinder. If your object is a cylinder placed horizontally the characteristic length is determined by the diameter D of the cylinder.

What is the definition of the Stokes number?

The Stokes number Stk, named after George Gabriel Stokes (1819-1903), is a dimensionless number corresponding to the behavior of particles suspended in a fluid flow. The Stokes number is defined as the ratio of the characteristic time of a particle to a characteristic time of the flow or of an obstacle: Stk = t0 ⋅ u0 I0

What is the characteristic time of Stokes flow?

In the case of Stokes flow, which is when the particle (or droplet) Reynolds number is less than unity, the particle drag coefficient is inversely proportional to the Reynolds number itself. In that case, the characteristic time of the particle can be written as where is the particle density,…

What are the Stokes numbers for large particles?

For the case of particles with a diameter size of 70 μm (large particles) with gas flows of Reynolds numbers of 15,000 and 64,000, the Stokes numbers evaluated for these particles are much greater than unity.

What is the correction factor for Stokes number?

The correction factor f = 1 + 0.15 Re p 0.687 is a function of the particle’s Reynolds number Re p, which is defined as D p | u − v | / v with the particle diameter Dp. The Stokes number is the ratio of the particle’s momentum response time to the flow-field time scale: