The ratio of inertia force to the viscous force is called as Reynolds’s number. It is denoted by R.

R_e = Inertia force / Viscous force

     = Mass x Acceleration / Shear stress x c/s area
 
    = (Mass density x Volume) x (Velocity / time) / Shear mass x c/s area

     = (volume/time) mass density x Velocity / Shear stress x c/s area

     = (Velocity x c/s area) Mass density x Velocity / Shear stress x c/s area

     = V . ρ . V / ζ  =  V . ρ . V / μ. du / dy

V . ρ . V / μ . V / L

R_e =  V. L / v

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