1. What is Compressibility?

Compressibility (κ) is a measure of the relative volume change of a fluid or solid as a response to a pressure change. It quantifies how much a material will compress under pressure.

2. Understanding the Dimensional Formula

The dimensional formula for compressibility is:

Where:

• \( M \) — Mass (kilograms)
• \( L \) — Length (meters)
• \( T \) — Time (seconds)

Explanation: This dimensional formula represents the fundamental physical dimensions that define compressibility in the International System of Units (SI).

3. Physical Significance

Details: Compressibility is the reciprocal of the bulk modulus. Materials with high compressibility undergo large volume changes under pressure, while materials with low compressibility are relatively incompressible.

4. Using the Calculator

Tips: Enter values for mass, length, and time in their respective SI units. The calculator will compute the compressibility value based on the dimensional formula.

5. Frequently Asked Questions (FAQ)

Q1: What are the SI units of compressibility?
A: The SI unit of compressibility is square meters per newton (m²/N) or pascal inverse (Pa⁻¹).

Q2: How does compressibility relate to bulk modulus?
A: Compressibility is the reciprocal of bulk modulus (κ = 1/K). Bulk modulus measures resistance to compression.

Q3: What materials have high compressibility?
A: Gases typically have high compressibility, while liquids and solids have much lower compressibility.

Q4: Why is compressibility important in engineering?
A: Compressibility is crucial in fluid mechanics, aerodynamics, material science, and designing pressure vessels and hydraulic systems.

Q5: Can compressibility be negative?
A: No, compressibility is always positive for stable materials. Negative compressibility would imply expansion under pressure.