Dimensional Formula of Reynolds Number (R_e)

The dimensional formula of Reynolds Number is given by,

M⁰ L⁰ T⁰

Where,

• M = Mass
• L = Length
• T = Time

Derivation

Reynolds Number (R_e) = 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, R_e = [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.

⇒ Check Other Dimensional Formulas:

• Dimensions of Boltzmann Constant
• Dimensions of Weight
• Dimensions of Power of Lens
• Dimensions of Gravitational Potential Energy
• Dimensions of Rotational Kinetic Energy