Capillary rise | Mechanical properties of Solids | Grade 11 | Physics | Khan Academy

In this video, we dive deep into the fascinating phenomenon of capillary rise—why and how liquids rise in narrow tubes against gravity! 💧

0:00 – Introduction to capillary rise
0:10 – Water rises in a narrow tube: Observation
0:19 – Definition of capillary rise
0:29 – Cause: Adhesive vs cohesive forces
0:43 – Angle of contact explanation
1:02 – Understanding the curvature and rise
1:24 – Initial condition: t = 0
1:37 – Pressure difference causes rise
1:47 – Goal: Find height of capillary rise
2:01 – Introducing excess pressure formula (2σ/r)
2:24 – Relating bubble surface to capillary curvature
2:46 – Pressure difference: P_inside - P_outside = excess pressure
3:31 – Pressure at points inside/outside the meniscus
4:06 – Equating pressure at same horizontal level
4:19 – Pressure due to liquid column (ρgh)
4:44 – Substituting pressures into equation
5:33 – Final derivation: 2σ/r = ρgh
5:52 – Solving for h (height of capillary rise)
6:25 – Relating bubble radius r to capillary tube radius R
7:08 – Geometry: using cos(θ) to relate r and R
7:49 – Final formula: h = (2σ cosθ) / (ρgR)
8:16 – Summary and goodbye

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Created by Chandan Ganotra