Capillary Rise, Depression, and Tube Geometry
In static capillarity, the vertical component of surface tension around the contact perimeter balances the hydrostatic weight associated with rise or depression relative to the external free surface.
Why this shows up in the exam
Wicks, porous media, and soil moisture · Capillary-tube surface-tension measurement · Rise differences in unequal arms
Learn the idea
Capillary height follows from balancing the vertical surface-tension force with the weight of the supported liquid column. Wetting makes the meniscus pull liquid upward along the contact line; non-wetting reverses the vertical component. Narrower tubes need less liquid weight to balance that pull.
🧠 Memory hook: Narrower rises more; contact angle decides rise or depression.
Get this one clearly and it pays off every single time it shows up in the paper. 🎯
Formulas & facts to keep ready
- h = 2T cos(theta)/(rho g r) — capillary rise in a clean circular tube of radius r, neglecting meniscus-volume correction
- rho g h = 2T cos(theta)/r — equivalent balance between hydrostatic and Laplace pressure
- l = h/cos(alpha) — liquid-column length in a straight tube inclined by alpha from the vertical
How to approach it
- 1Identify radius, contact angle, and vertical height
- 2Write force or pressure balance before handling inclination
- 3For unequal arms, compare each meniscus with the shared liquid level
Common slip-ups that cost marks
- •Using tube diameter where radius is required
- •Measuring an inclined column length as vertical rise
- •Taking cos theta positive for a non-wetting liquid without checking convention
🌟 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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