Volume elasticity, often referred to as the Bulk Modulus ($B$ or $K$), is defined as the ratio of hydraulic stress to the corresponding volumetric strain.

1. Formula: $K = \frac{\text{Stress}}{\text{Volumetric Strain}} = \frac{-P}{\Delta V / V}$.
2. Dimensional Analysis:

• Stress (Pressure): Force per unit area. Dimensions = $\frac{[MLT^{-2}]}{[L^2]} = [ML^{-1}T^{-2}]$ .
• Volumetric Strain: Ratio of change in volume to original volume ($\Delta V/V$). Since it is a ratio of identical quantities, it is dimensionless $[M^0L^0T^0]$ .

3. Result: The dimensions of volume elasticity are the same as stress or pressure. $[K] = \frac{[ML^{-1}T^{-2}]}{} = [M^1L^{-1}T^{-2}]$