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  4. In the bottom of a vessel with mercury of density ρ there is a round hole of radius r . At what maximum height of the mercury layer will the liquid still not flow out through this hole? (Surface tension = T )

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Q. In the bottom of a vessel with mercury of density $\rho $ there is a round hole of radius $r$ . At what maximum height of the mercury layer will the liquid still not flow out through this hole? (Surface tension = $T$ )

NTA AbhyasNTA Abhyas 2020

Solution:

Because mercury meniscus is convex, the pressure just inside the hole will be less than the outside pressure by $\frac{2 T}{r}$
$\therefore \, \, h\rho g=\frac{2 T}{r}$
or $h=\frac{2 T}{r \rho g}$