There is a circular hole of diameter d = 140 μ m at the bottom of a vessel containing mercury. The minimum height of mercury layer so that the mercury will not flow out of this hole is Surface tension

Question

There is a circular hole of diameter d = 140 μ m at the bottom of a vessel containing mercury. The minimum height of mercury layer so that the mercury will not flow out of this hole is Surface tension , σ = 490 × 10 - 3 Nm - 1

TestHub · Accepted Answer

The pressure just inside the hole will be less than the outside pressure by $\frac{4 σ}{d} (i.e., \frac{2 σ}{r})$ since mercury meniscus is convex.

Let a column of length $h$ is required to balance the forces at Critical equilibrium such that

$h ρ g = \frac{4 σ}{d}$

i.e., $h = \frac{4 σ}{d ρ g}$

$= \frac{4 \times 490 \times 10^{- 3}}{140 \times 10^{- 6} \times 13600 \times 10}$

$= \frac{1960}{140 \times 136} = 0.103 m$

$= 1.03 cm$

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