 # Dimensions of Reynolds Number

## Dimensional Formula of Reynolds Number (Re)

The dimensional formula of Reynolds Number is given by,

M0 L0 T0

Where,

• M = Mass
• L = Length
• T = Time

### Derivation

Reynolds Number (Re) = Density × Velocity × Length × [dynamic viscosity]-1 . . . . . (1)

Since, Density (ρ) = Mass × [Volume]-1

∴ The dimensional formula of density = [M1 L-3 T0] . . . . (2)

Since, Velocity = Displacement × [Time]-1

∴ The dimensions of velocity = [M0 L1 T-1] . . . . (3)

⇒ Viscosity = Distance between layers × Force × [Area × Velocity]-1

Since, the dimensional formula of Force = [M1 L1 T-2]

⇒ η = L × M1 L1 T-2 × [L2 × L1 T-1]-1

∴ the dimensional formula of viscosity = [M1 L-1 T-1] . . . . (4)

On substituting equation (2), (3) and (4) in equation (1) we get,

Reynolds Number = Density × Velocity × Length × [dynamic viscosity]-1

Or, Re = [M1 L-3 T0] × [M0 L1 T-1] × [L] × [M1 L-1 T-1]-1 = [M0 L0 T0]

Therefore, the Reynolds Number is dimensionally represented as M0 L0 T0.

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