26/04/2013
Reynolds number : Reynolds number can be defined for a number of different situations where a fluid is in relative motion to a surface.[n 1] These definitions generally include the fluid properties of density and viscosity, plus a velocity and a characteristic length or characteristic dimension. This dimension is a matter of convention – for example a radius or diameter are equally valid for spheres or circles, but one is chosen by convention. For aircraft or ships, the length or width can be used. For flow in a pipe or a sphere moving in a fluid the internal diameter is generally used today. Other shapes such as rectangular pipes or non-spherical objects have an equivalent diameter defined. For fluids of variable density such as compressible gases or fluids of variable viscosity such non-Newtonian fluids, special rules apply. The velocity may also be a matter of convention in some circumstances, notably stirred vessels. _______________ _______________ ___ The Reynolds Number, the non-dimensional velocity, is defined by the ratio of - i. dynamic pressure (ρ u2) and ii. shearing stress (μ u / L) and can be expressed as Re = (ρ u2) / (μ u / L) = ρ u L / μ = u L / ν (1) where, Re = Reynolds Number (non-dimensiona l) ρ = density (kg/m3, lbm/ft3 ) u = velocity based on the actual cross section area of the duct or pipe (m/s, ft/s) μ = dynamic viscosity (Ns/m2, lbm/s ft) L = characteristic length (m, ft) ν = kinematic viscosity (m2/s, ft2/s) _______________ _______________ ___ Reynolds Number for a Pipe or Duct For a pipe or duct the characteristic length is the hydraulic diameter. The Reynolds Number for a duct or pipe can be expressed as Re = ρ u dh / μ = u dh / ν (2) where, dh = hydraulic diameter (m, ft) _______________ _______________ ___ Reynolds Number for a Pipe or Duct in common Imperial Units The Reynolds number for a pipe or duct can also be expressed in common Imperial units like Re = 7745.8 u dh / ν (2a) where, Re = Reynolds Number (non dimensional) u = velocity (ft/s) dh = hydraulic diameter (in) ν = kinematic viscosity (cSt) (1 cSt = 10-6 m2/s ) The Reynolds Number can be used to determine if flow is laminar, transient or turbulent. The flow is - i. laminar when Re
