9.2 Rise of a liquid in a tube of insufficient lengthz

1.1 Ideal liquid
1.2 Density of a liquid $\left( \rho \right)$
1.3 Relative density of a liquid $(RD)$
1.4 Density of a mixture of two or more liquid
1.5 Density variation with temperature
1.6 Density variation with pressure

2.1 Atmospheric pressure
2.2 Pressure variation with depth
2.3 Measurement of pressure
2.4 Pressure difference in accelerating fluids

5.1 Equation of continuity
5.2 Bernoulli's theorem
5.3 Application of Bernoulli's theorem

7.1 Terminal velocity $\left( {{v_T}} \right)$

8.1 Surface tension
8.2 Variation in surface tension
8.3 Surface energy $(E)$
8.4 Excess pressure

9.1 Capillarity
9.2 Rise of a liquid in a tube of insufficient lengthz

We know, $$h = \frac{{2T}}{{r\rho g}}$$ or $$rh = \frac{{2T}}{{\rho g}}$$ where,

$T$: Surface tension

$\theta $: Angle of contact

$\rho $: Density of the liquid

$r$: Radius of the meniscus

$g$: Acceleration due to gravity

If a capillary tube is of insufficient length as compared to height to which liquid can rise in the capillary tube, then the liquid rises upto the full length of capillary tube but there is no overflowing of the liquid in the form of fountain.

It is so because the liquid meniscus adjusts its radius of curvature so that, $$hr = {\text{constant}}$$ or $$hr = h'r'$$