# What is Dimensional Formula of Reynolds number?

Posted in Dimensional Formulae | Email This Post |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 v^{2}) / Shearing Stress (μ v / L)

Re = ρ v^{2} / (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) =M^{1}L^{-3}T^{0}

Dimensional Formula of Velocity(v) = M^{0}L^{1}T^{-1}

Dimensional Formula of Dynamic viscosity(μ) = M^{1}L^{-1}T^{-1}

Dimensional Formula of Length(L) = M^{0}L^{1}T^{0}

Putting these values in above equation we get,

Dimensional Formula of Reynolds Number = (M^{1}L^{-3}T^{0})(M^{0}L^{1}T^{-1})(M^{0}L^{1}T^{0})/(M^{1}L^{-1}T^{-1})

**Dimensional Formula of Reynolds Number = M ^{0}L^{0}T^{0}**

**Reynolds Number has no units (**

**non dimensional).**

Nice

Very nice and helpful