Question

A cylindrical vessel of height $\text{500 mm}$ has an orifice (small hole) at its bottom. The orifice is initially closed and water is filled in it upto height $\text{H}$ . 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 a height of water column being $\text{200 mm}$ . Find the fall in height $\text{(}$ in $\text{mm}$ $\text{)}$ of water level due to opening of the orifice.

$[$ Take atmospheric pressure $=1.0\times 10^5{\text{N m}}^{\text{-2}}$ , density of water $=1000\text{kg}{\text{m}}^{\text{-3}}$ and $g=10{\text{ms}}^{\text{-2}}$ . Assume temperature to be constant and neglect any effect of surface tension.]

Answer 1

Answer: 6

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

p = p₀ - ρgh ...(i)
p₀ [A(500 - H)] = p[A(300)] ...(ii)
Solving these two equations, we get H = 206 mm .
Therefore, Level fall = (206 - 200) mm = 6 mm