Hydrostatic Pressure and Compression with Depth
For approximately constant fluid density, gauge pressure at depth h is rho g h, and small fractional volume compression is rho g h divided by the relevant bulk modulus.
Why this shows up in the exam
Deep-sea compression · Ocean-bottom water density estimates · Submerged elastic objects
Learn the idea
Depth creates hydrostatic pressure, which bulk modulus converts into fractional compression. Going deeper adds the weight of the fluid column above; the resulting pressure increase squeezes an object or the water itself.
🧠 Memory hook: Depth gives pressure; pressure over bulk modulus gives fractional squeeze.
Get this one clearly and it pays off every single time it shows up in the paper. 🎯
Formulas & facts to keep ready
- Delta P = rho g h — gauge pressure increase at depth in a uniform fluid
- |Delta V|/V = rho g h/K — small compression caused by depth
- h = K(|Delta V|/V)/(rho g) — depth required for a target compression
How to approach it
- 1Translate depth into gauge pressure
- 2Select the bulk modulus of the compressed material
- 3Convert fractions and percentages consistently
Common slip-ups that cost marks
- •Adding atmospheric pressure when only the increase matters
- •Using object density instead of fluid density
- •Entering percent compression without dividing by 100
🌟 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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