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 )

Question

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 ) (A) (T/r ρ g) (B) (T/2 r ρ g) (C) (2 T/r ρ g) (D) (4 T/r ρ g)

Tardigrade Admin · Accepted Answer

Because mercury meniscus is convex, the pressure just inside the hole will be less than the outside pressure by (2 T/r) ∴ hρ g=(2 T/r) or h=(2 T/r ρ g)

Q. 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 = $T$ )

$\frac{T}{r ρ g}$

$\frac{T}{2 r ρ g}$

$\frac{2 T}{r ρ g}$

$\frac{4 T}{r ρ g}$

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

Q. 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 )

rρgT​

2rρgT​

rρg2T​

rρg4T​