Dimensional formula of Compressibility

How to get the dimensional formula of compressibility

1. Start from the definition: compressibility = 1 / bulk modulus.
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. pressure = force / area, so pressure is [M L T^-2] / [L²] = [M L^-1 T^-2].
7. strain = length / length, so strain is [L] / [L] = [M⁰ L⁰ T⁰].
8. Put in the dimension of each part: 1 / [M L^-1 T^-2].
9. Add the powers of each base quantity: [M^-1 L T²].

Three questions on compressibility

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]