1. What is Bulk Modulus?

The bulk modulus (K) is a measure of a substance's resistance to uniform compression. It is defined as the ratio of the infinitesimal pressure increase to the resulting relative decrease of the volume.

2. Understanding the Dimensional Formula

The dimensional formula for bulk modulus is:

Where:

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

Derivation: Bulk modulus has the same dimensions as pressure, which is force per unit area. Force has dimensions [M L T^{-2}] and area has dimensions [L^2], giving pressure dimensions [M L^{-1} T^{-2}].

3. Physical Significance

Details: The bulk modulus quantifies how incompressible a material is. Higher values indicate greater resistance to compression. For example, steel has a high bulk modulus while gases have low bulk modulus values.

4. Using the Calculator

Tips: Enter values for mass (kg), length (m), and time (s) to calculate the dimensional formula representation. All values must be positive numbers.

5. Frequently Asked Questions (FAQ)

Q1: What are the SI units of bulk modulus?
A: The SI unit of bulk modulus is Pascal (Pa), which is equivalent to N/m² or kg/(m·s²).

Q2: How does bulk modulus relate to compressibility?
A: Compressibility is the reciprocal of bulk modulus. Higher bulk modulus means lower compressibility.

Q3: What are typical bulk modulus values for common materials?
A: Water: ~2.2 GPa, Steel: ~160 GPa, Air: ~0.1 MPa (highly compressible).

Q4: Why is bulk modulus important in engineering?
A: It's crucial for designing pressure vessels, hydraulic systems, and understanding material behavior under pressure.

Q5: How does temperature affect bulk modulus?
A: Generally, bulk modulus decreases with increasing temperature as materials become more compressible.