Compressibility – Volume change of a fluid with increasing pressure As the pressure applied to a (single-phase) fluid increases, its volume generally:

Introduction:
Compressibility describes how the volume of a substance responds to pressure. In engineering fluids (especially liquids), compressibility is small but non-zero, and understanding the sign of volume change with pressure is important for storage tanks, hydraulic systems, and water-hammer analyses.

Given Data / Assumptions:

• Single-phase homogeneous fluid (no boiling or cavitation).
• Temperature held constant for the conceptual comparison.
• Pressure is increased quasistatically.

Concept / Approach:

By definition, compressibility beta = − (1/V) * (dV/dP). For ordinary fluids, beta > 0, implying dV/dP < 0: as pressure P increases, volume V decreases. The reciprocal K = 1/beta is the bulk modulus, a positive quantity for stable materials, further confirming the inverse relation between pressure and volume.

Step-by-Step Solution:

Verification / Alternative check:

For water at room temperature, K ≈ 2 * 10^9 Pa; a pressure rise of 10 MPa reduces volume by roughly 0.5%, illustrating the small but definite decrease.

Why Other Options Are Wrong:

Remains same: Only an approximation for very small pressure changes in practical calculations.Increases / oscillates / non-monotonic: Contradict the sign derived from positive bulk modulus in single-phase conditions.

Common Pitfalls:

Assuming “incompressible” means zero change; it actually means volume change is negligible for the calculation’s required accuracy.

Final Answer:

decreases