Reynolds Number refers to the dimensionless number that gives a measure to the ratio between the inertia and the viscous forces. The Reynolds Number is denoted by the symbol 'Re'. The Reynolds Number consequently quantifies the relative importance of the inertial and viscous forces fort the given flow conditions. The Reynolds number is termed as an important element in analyzing any type of flow when there is substantial velocity gradient. It indicates the relative significance of the viscous effect compared to the inertia effect. The Reynolds number is proportional to inertial force divided by viscous force. The Reynolds Number is also called as Damkohler number V (DaV)
Reynolds Number :
Re = ρVI/ μ
Density :
ρ = Reμ/ VI
Velocity :
V = Reμ/ ρI
Characteristic Length :
I = Reμ/ ρV
Viscosity :
μ = ρVI/ Re
Where,
Re = Reynolds Number,
ρ = Density,
V = Velocity,
l = Characteristic Length,
μ = Viscosity.
A Reynolds Number is a dimensionless number which is significant in the design of a model of any system in which the effect of viscosity is important in controlling the velocities or the flow pattern of a fluid. The Reynolds Number is equal to the density of a fluid, times its velocity, times a characteristic length, divided by the fluid viscosity.
Example:
Calculate the Reynolds Number for the given details.
Density (ρ) = 5 kg/m^{3}
Velocity (V) = 10 m/s
Characteristic Length (l) = 15 m
Viscosity (μ) = 20 N-s/m^{2}
Solution:
Apply Formula:
Re = ρVI/ μ
Re = 5*10*15/20
Reynolds Number (Re) = 37.5