What is Dimensional Formula of Reynolds number?

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).