Stokes Drag on a Sphere
Stokes' law gives the viscous drag on an isolated rigid sphere moving slowly relative to an unbounded Newtonian fluid when the particle Reynolds number is much less than one.
Why this shows up in the exam
Falling-sphere viscometers · Motion of fine droplets and particles · Estimating low-speed viscous resistance
Learn the idea
At very low Reynolds number, viscous drag on a sphere is proportional to its radius and relative speed. A slowly moving small sphere drags nearby fluid layers with it. In creeping flow the disturbance is smooth, so doubling speed doubles the resisting force.
🧠 Memory hook: Stokes drag is linear in eta, radius, and relative speed.
Get this one clearly and it pays off every single time it shows up in the paper. 🎯
Formulas & facts to keep ready
- F_d = 6 pi eta r v_rel — Stokes drag magnitude for creeping flow around an isolated sphere
- Re_p = 2 rho_f r v_rel/eta << 1 — particle Reynolds-number condition supporting the Stokes approximation
How to approach it
- 1Check that the moving object is effectively spherical
- 2Use relative velocity and consistent viscosity units
- 3Combine drag with weight and buoyancy using force balance
Common slip-ups that cost marks
- •Using diameter where the formula uses radius
- •Applying the law at high Reynolds number
- •Using ground speed instead of speed relative to the fluid
🌟 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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