Dimensional formula of Reynolds number

How to get the dimensional formula of Reynolds number

1. Start from the definition: Reynolds number = density × velocity × length / viscosity.
2. volume = length³, so volume is [L]³ = [L³].
3. density = mass / volume, so density is [M] / [L³] = [M L^-3].
4. velocity = length / time, so velocity is [L] / [T] = [L T^-1].
5. acceleration = velocity / time, so acceleration is [L T^-1] / [T] = [L T^-2].
6. force = mass × acceleration, so force is [M] × [L T^-2] = [M L T^-2].
7. area = length × length, so area is [L] × [L] = [L²].
8. Put in the dimension of each part: [M L^-3] × [L T^-1] × [L] / [M L^-1 T^-1].
9. Add the powers of each base quantity: [M⁰ L⁰ T⁰].

Quantities with the dimensions [M⁰ L⁰ T⁰]

• Angle
• Solid angle
• Coefficient of friction
• Coefficient of restitution
• Relative density
• Strain
• Poisson's ratio
• Emissivity
• Ratio of specific heats
• Sound level
• Relative permittivity
• Magnetic susceptibility
• Relative permeability
• Power factor
• Quality factor
• Refractive index
• Magnification

Equal dimensions do not make them the same quantity. Compare Reynolds number with the others in the full grid.

Three questions on Reynolds number

Related quantities

• P Pressure [M L⁻¹ T⁻²]
• dP/dx Pressure gradient [M L⁻² T⁻²]
• σ Stress [M L⁻¹ T⁻²]
• U Strain energy [M L² T⁻²]
• u Strain energy density [M L⁻¹ T⁻²]
• Y Young's modulus [M L⁻¹ T⁻²]