Bulk Modulus (K = ΔP·V₀/ΔV)

Young's modulus describes stretching in one direction; the bulk modulus describes squeezing from every direction at once. The volumetric strain ΔV/V₀ is the three-dimensional cousin of ε, and K is the pressure needed per unit of it. Water's K ≈ 2.2 GPa means a 2.2 MPa (about 320 psi) pressure rise on one litre squeezes out just one millilitre — the origin of the schoolroom line that "liquids are incompressible". They are not, quite: seawater's compressibility is why sea level sits roughly 40 m lower than it would if the ocean were truly rigid.

Hydraulics is where this bites in the trades. Oil at K ≈ 1.5 GPa in a long, large-bore cylinder line stores real energy and makes a nominally stiff actuator feel spongy; entrained air, which is thousands of times more compressible, destroys the stiffness completely and is the first thing to suspect when a hydraulic system goes soft. The trap in the arithmetic is unit mismatch between V₀ and ΔV — enter 200 L and 0.63 L, or 0.2 m³ and 0.00063 m³, but never one of each with the same number.