Fluids in Accelerating and Rotating Frames
For a fluid stationary relative to a uniformly accelerating frame, hydrostatic balance uses the effective body acceleration g_eff = g - a_frame; rigid rotation adds a centrifugal potential.
Why this shows up in the exam
Liquid surfaces in accelerating vehicles · Rotating separators and centrifuges · Pressure fields in spinning containers
Learn the idea
A fluid at relative rest aligns its pressure gradient and free surface with the frame's effective gravity. Inside an accelerating tank, the fluid behaves as if gravity has tilted. In rotation, outward effective acceleration grows with radius, so the free surface becomes curved.
🧠 Memory hook: Replace gravity by effective gravity before using hydrostatics.
Get this one clearly and it pays off every single time it shows up in the paper. 🎯
Formulas & facts to keep ready
- grad(P) = rho g_eff — hydrostatic balance in a frame where the fluid is at rest and rho is treated as constant
- tan(theta) = a_horizontal/g — free-surface tilt magnitude for uniform horizontal frame acceleration
- z(r)-z(0) = omega² r²/(2g) — parabolic free surface in steady rigid rotation about a vertical axis
How to approach it
- 1Draw the frame acceleration and construct g_eff
- 2Make the free surface perpendicular to g_eff
- 3Integrate pressure only along the correct effective field
Common slip-ups that cost marks
- •Keeping the free surface horizontal in an accelerating frame
- •Using tangential instead of centrifugal acceleration in rigid rotation
- •Applying ordinary buoyancy unchanged in free fall
🌟 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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