Bulk Modulus and Fluid Compressibility
Bulk modulus is the negative pressure increment divided by the resulting fractional volume change in the small-deformation limit, with the sign chosen so stable materials have positive modulus.
Why this shows up in the exam
Deep-water compression estimates · Hydraulic-system compliance · Pressure-induced size or density changes
Learn the idea
Bulk modulus measures how strongly volume resists a pressure change, so even liquids compress slightly under large pressure. A fluid often behaves incompressibly in ordinary flow, yet deep-ocean or piston pressures can produce a measurable volume change. A larger bulk modulus means a smaller fractional compression.
🧠 Memory hook: Large bulk modulus means small fractional volume change.
Get this one clearly and it pays off every single time it shows up in the paper. 🎯
Formulas & facts to keep ready
- K = -V dP/dV — differential bulk modulus for a quasistatic uniform pressure change
- Delta V/V approximately -Delta P/K — small fractional compression when K is approximately constant
- Delta rho/rho approximately Delta P/K — first-order density increase for fixed mass under small compression
How to approach it
- 1Find the actual pressure increment, not total pressure unless required
- 2Use external volume or density consistently to first order
- 3Check that compression gives negative Delta V and positive Delta rho
Common slip-ups that cost marks
- •Dropping the minus sign without interpreting compression
- •Using Young's modulus for hydrostatic loading
- •Applying a linear approximation to a very large fractional change
🌟 That's the whole idea — you've got this. Try the practice set below; every question you attempt makes it stick a little harder.
Original chapter practice
Original questions for this chapter, not past-paper questions or an exact mapping to this individual concept.
A wire 1 m long and cross-sectional area 2 mm^2 extends by 1 mm under a 200 N load. Find Young modulus.
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