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What is Dimensional Formula of Reynolds number?

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Reynolds number is defined as the ratio of dynamic pressure to shearing stress.It is a non dimensional parameter.Reynolds number predicts the extent of turbulence in a fluid, based on how fast the fluid is flowing, the geometry of flow(depth and wide etc…)  density  and viscosity of fluid.

Mathematically,

Reynolds number (Re) = Dynamic Pressure (ρ v2) / Shearing Stress (μ v / L)

Re   = ρ v2 / (μ v / L)

Re = ρ v L / μ

where

Re = Reynolds Number (non-dimensional)

ρ = density

v = velocity

μ = dynamic viscosity

L= characteristic length

Dimensional Formula of Density (ρ) =M1L-3T0
Dimensional Formula of Velocity(v) = M0L1T-1
Dimensional Formula of Dynamic viscosity(μ) = M1L-1T-1
Dimensional Formula of Length(L) = M0L1T0

Putting these values in above equation we get,

Dimensional Formula of Reynolds Number = (M1L-3T0)(M0L1T-1)(M0L1T0)/(M1L-1T-1)

Dimensional Formula of Reynolds Number = M0L0T0
Reynolds Number has no units (non dimensional).

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Comments
  • Damilola.A. July 20, 2014 at 11:40 am

    Nice

  • DHAWAL.S June 25, 2016 at 10:16 am

    Very nice and helpful

  • Post a comment

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