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 orifice at the bottom is opened. Some water comes out from the orifice and the water level in the vessel becomes steady with height of water column being $200mm$. Find the fall in height (in $mm$) of water level due to opening of the orifice. (Take atmospheric pressure $=1.0\times {10}^{5}N/m^2$, density of water $=1000kg/m^3$ and $g=10m/s^2.$ (Neglect any effect of surface tension.)

Answer 1

$P=P_0-\rho gh=98\times {10}^{3}N/m^2$

$P_0{V}_0=PV$

${10}^5\left[A\right(500-H\left)\right]=98\times {10}^3$ $\left[A\right(500-200\left)\right]$

$H=206mm$

Level fall = $206+200=6mm$