“Reynolds number”的概念、定义、翻译、参考文献-科学参考

Reynolds number

Physics

Symbol Re. A dimensionless number used in fluid dynamics to determine the type of flow of a fluid through a pipe, to design prototypes from small-scale models, etc. It is the ratio νρ‎l/η‎, where ν‎ is the flow velocity, ρ‎ is the fluid density, l is a characteristic linear dimension, such as the diameter of a pipe, and η‎ is the fluid viscosity. In a smooth straight uniform pipe, laminar flow usually occurs if Re < 2000 and turbulent flow is established if Re > 3000. It is named after Osborne Reynolds (1842–1912), who popularized its use in 1883.

Mathematics

For a viscous flow with speed u, viscosity ν‎ passing an object of length a, the ratio R = ua/ν‎ is a dimensionless (see dimensions) quantity called the Reynolds number. For low Reynolds numbers, uniform or laminar flows tend to occur, whereas for high Reynolds numbers turbulent flow is common.

Chemical Engineering

A dimensionless number, Re, expressing the ratio of inertial to viscous forces in a flowing fluid, and can be used to determine the flow regime. For a fluid in a pipe of circular cross section:
$Re = \frac{ρ v d}{μ}$

where ρ is the density, v is the mean velocity, d is the diameter of a pipe, and μ is the viscosity. Where the value for circular pipes falls below 2,000, the flow is laminar flow or streamline. For Reynolds numbers above 4,000, the flow is turbulent.

Various forms of Reynolds number are used, such as the flow through an annulus in which case a mean hydraulic diameter is used, or the flow of fluid in the vicinity of an impeller of diameter, D, and rotational speed, N, given as:
$Re = \frac{ρ N D^{2}}{μ}$

It is named after British engineer Osborne Reynolds (1842–1912).

Geology and Earth Sciences

A dimensionless number expressing the balance of viscous and interstitial forces on a small element of moving fluid. The transition from laminar to turbulent flow depends on the Reynolds number (R) which is equal to ρ‎vd/η‎, where ρ‎ is the fluid density, v the fluid velocity, d the diameter of the pore space through which flow occurs, and η‎ the viscosity. For laminar flow, the Reynolds number is less than 500, while turbulent flow occurs when R is greater than 1000. Darcy’s Law for groundwater flow is valid for values of R less than about 1–10.

Geography

Four factors combine to determine whether the flow of water within a channel is turbulent or laminar: the density, velocity, and viscosity of the water, and the hydraulic radius of the channel. Since the density of water is 1, the Reynolds number expresses this combination as:
$R_{e} = \frac{V R}{μ}$
where V = velocity of the liquid, R = hydraulic radius, and μ‎ = viscosity of the liquid. The Reynolds number is a dimensionless quality; in streams, the maximum number for laminar flow is between 500 and 600, depending on temperature, and at high Reynolds numbers, above 2 000 to 25 000, flow is turbulent. Smith et al. (2007) PPG 31, 4 note that the flow is laminar for Reynolds numbers below 2 300 (in circular pipes), and above 4 000 in turbulent. ‘An ill-defined region between these two limits is known as the transitional zone. The critical Reynolds number transition to turbulent flow depends on the exact flow configuration and should be determined experimentally.’

单词	Reynolds number
释义	Reynolds number Physics Symbol Re. A dimensionless number used in fluid dynamics to determine the type of flow of a fluid through a pipe, to design prototypes from small-scale models, etc. It is the ratio νρ‎l/η‎, where ν‎ is the flow velocity, ρ‎ is the fluid density, l is a characteristic linear dimension, such as the diameter of a pipe, and η‎ is the fluid viscosity. In a smooth straight uniform pipe, laminar flow usually occurs if Re < 2000 and turbulent flow is established if Re > 3000. It is named after Osborne Reynolds (1842–1912), who popularized its use in 1883. Mathematics For a viscous flow with speed u, viscosity ν‎ passing an object of length a, the ratio R = ua/ν‎ is a dimensionless (see dimensions) quantity called the Reynolds number. For low Reynolds numbers, uniform or laminar flows tend to occur, whereas for high Reynolds numbers turbulent flow is common. Chemical Engineering A dimensionless number, Re, expressing the ratio of inertial to viscous forces in a flowing fluid, and can be used to determine the flow regime. For a fluid in a pipe of circular cross section: $Re = \frac{ρ v d}{μ}$ where ρ is the density, v is the mean velocity, d is the diameter of a pipe, and μ is the viscosity. Where the value for circular pipes falls below 2,000, the flow is laminar flow or streamline. For Reynolds numbers above 4,000, the flow is turbulent. Various forms of Reynolds number are used, such as the flow through an annulus in which case a mean hydraulic diameter is used, or the flow of fluid in the vicinity of an impeller of diameter, D, and rotational speed, N, given as: $Re = \frac{ρ N D^{2}}{μ}$ It is named after British engineer Osborne Reynolds (1842–1912). Geology and Earth Sciences A dimensionless number expressing the balance of viscous and interstitial forces on a small element of moving fluid. The transition from laminar to turbulent flow depends on the Reynolds number (R) which is equal to ρ‎vd/η‎, where ρ‎ is the fluid density, v the fluid velocity, d the diameter of the pore space through which flow occurs, and η‎ the viscosity. For laminar flow, the Reynolds number is less than 500, while turbulent flow occurs when R is greater than 1000. Darcy’s Law for groundwater flow is valid for values of R less than about 1–10. Geography Four factors combine to determine whether the flow of water within a channel is turbulent or laminar: the density, velocity, and viscosity of the water, and the hydraulic radius of the channel. Since the density of water is 1, the Reynolds number expresses this combination as: $R_{e} = \frac{V R}{μ}$ where V = velocity of the liquid, R = hydraulic radius, and μ‎ = viscosity of the liquid. The Reynolds number is a dimensionless quality; in streams, the maximum number for laminar flow is between 500 and 600, depending on temperature, and at high Reynolds numbers, above 2 000 to 25 000, flow is turbulent. Smith et al. (2007) PPG 31, 4 note that the flow is laminar for Reynolds numbers below 2 300 (in circular pipes), and above 4 000 in turbulent. ‘An ill-defined region between these two limits is known as the transitional zone. The critical Reynolds number transition to turbulent flow depends on the exact flow configuration and should be determined experimentally.’
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