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. 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 `=1.0xx10^5N//m^2`, density of water=1000kg//m^3` and `g=10m//s^2`. Neglect any effect of surface tension.]

Answer

6

Explanation

Water will stop coming out when pressure at orifice will become equal to atmospheric pressure `P_(0)` (P is the pressure above water level) `P_(0)=P+hrhog`
`P=P_(0)-hrhog" "implies " "P=1.0xx10^(5)-200xx10^(-3)xx1000xx10`
`P=0.98xx10^(5)Nm^(-2)` If A is the cross sectional area of the vessel,
`V_(0)=(500-H)A,V=300A`,
Using Boyle's law `P_(0)V_(0)=PV`
`implies 1.0xx10^(5)xx(500-H)A=(0.98xx10)^(5)xx300A`
`implies500-H=294impliesH=206mm`
`therefore` Fall in height `=206-200 =6mm`