# Reynolds number

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Reynolds number
n.
after O. Reynolds (1842-1912), Eng physicist
a dimensionless parameter used to determine the nature of fluid flow along surfaces and around objects, as in a wind tunnel

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In fluid mechanics, a number that indicates whether the flow of a fluid (liquid or gas) is absolutely steady (in streamlined, or laminar flow) or on the average steady with small, unsteady changes (in turbulent flow; see turbulence).

The Reynolds number, abbreviated NRe or Re, has no dimensions (see dimensional analysis) and is defined as the size of the flow
as, for example, the diameter of a tube (D) times the average speed of flow (v) times the mass density of the fluid (ρ)
divided by its absolute viscosity (μ). Osborne Reynolds demonstrated in 1883 that the change from laminar to turbulent flow in a pipe occurs when the value of the Reynolds number exceeds 2,100.

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in fluid mechanics, a criterion of whether fluid (liquid or gas) flow is absolutely steady (streamlined, or laminar (laminar flow)) or on the average steady with small unsteady fluctuations (turbulent). Whenever the Reynolds number is less than about 2,000, flow in a pipe is generally laminar, whereas, at values greater than 2,000, flow is usually turbulent. Actually, the transition between laminar and turbulent flow occurs not at a specific value of the Reynolds number but in a range usually beginning between 1,000 to 2,000 and extending upward to between 3,000 and 5,000.

In 1883 Osborne Reynolds (Reynolds, Osborne), a British engineer and physicist, demonstrated that the transition from laminar to turbulent flow in a pipe depends upon the value of a mathematical quantity equal to the average velocity of flow times the diameter of the tube times the mass density of the fluid divided by its absolute viscosity. This mathematical quantity, a pure number without dimensions, became known as the Reynolds number and was subsequently applied to other types of flow that are completely enclosed or that involve a moving object completely immersed in a fluid.

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Universalium. 2010.

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