Dimensional formula of Kinematic viscosity

How to get the dimensional formula of kinematic viscosity

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

Three questions on kinematic viscosity

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]
• ε Strain [M⁰ L⁰ T⁰]