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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.
u is the flow velocity; κ is the thermal conductivity; T 0 is the bulk fluid temperature; T w is the wall temperature; Pr is the Prandtl number; Ec is the Eckert number [1] It is the ratio between heat produced by viscous dissipation and heat transported by molecular conduction. i.e., the ratio of viscous heat generation to external heating.
The turbulent Schmidt number is commonly used in turbulence research and is defined as: [3] = where: is the eddy viscosity in units of (m 2 /s); is the eddy diffusivity (m 2 /s).; The turbulent Schmidt number describes the ratio between the rates of turbulent transport of momentum and the turbulent transport of mass (or any passive scalar).
For spheres in uniform flow in the Reynolds number range of 8×10 2 < Re < 2×10 5 there co-exist two values of the Strouhal number. The lower frequency is attributed to the large-scale instability of the wake, is independent of the Reynolds number Re and is approximately equal to 0.2.
The Richardson number (Ri) is named after Lewis Fry Richardson (1881–1953). [1] It is the dimensionless number that expresses the ratio of the buoyancy term to the flow shear term: [2]
As an example, assuming cannula lengths are equal, the flow of a 14G cannula is 1.73 times that of a 16G cannula, and 4.16 times that of a 20G cannula. It also states that flow is inversely proportional to length, meaning that longer lines have lower flow rates.
With C v = 1.0 and 200 psia inlet pressure, the flow is 100 standard cubic feet per minute (scfm). The flow is proportional to the absolute inlet pressure, so the flow in scfm would equal the C v flow coefficient if the inlet pressure were reduced to 2 psia and the outlet were connected to a vacuum with less than 1 psi absolute pressure (1.0 ...
In experimental fluid dynamics, the Stokes number is a measure of flow tracer fidelity in particle image velocimetry (PIV) experiments where very small particles are entrained in turbulent flows and optically observed to determine the speed and direction of fluid movement (also known as the velocity field of the fluid). For acceptable tracing ...
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