Question

A cylindrical vessel of height $500mm$ has an orifice (small hole) at its bottom. The orifice is initially closed and water is filled in it up to height $H$ . Now the top is completely sealed with a cap and the orifice at the bottom is opened and some water is allowed to comes out slowly from the orifice. Eventually, the water level in the vessel becomes steady with the height of the water column being $200mm$ . Find the fall in height $\text{(}$ in $mm$ $\text{)}$ of water level due to opening of the orifice.
$\left[\right.$ Take atmospheric pressure $=1.0\times 10^{5} \, Nm^{- 2}$ , density of water $=1000 \, kg \, m^{- 3}$ and $g=10ms^{- 2}$ . Assume temperature to be constant and neglect any effect of surface tension.]

Answer 1

In this question, we will have to assume that temperature is constant for enclosed air above water (or pV = constant) (∵ Boyle's Law)

$10^{5}(500-H)=\left(10^{5}-10^{3} \times 10 \times 0.2\right) \times 300$
Solving these two equations,
$10^{5}(500-H)=\left(10^{5}-10^{3} \times 10 \times 0.2\right) \times 300$
we get H = 206 mm .
Therefore, Level fall = (206 - 200) mm = 6 mm