Question

A cylindrical vessel of height $500$mm 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 $200$mm. Find the fall in height (in mm) of water level due to opening of the office. [Take atmospheric pressure $=1.0\times {10}^{5}N/m^2$, density of water $=1000$ kg$/m^3$ and $g=10m/s^2$. Neglect any effect of surface tension].

Answer 1

A cylinder vessel of high $h=500mm$

$P=P_0-\rho gh=98\times {10}^{3}N/m^2{P}_0{V}_0=PV$

(according to Charles and Boyle's law)

${10}^{5}A(500-H)=98\times {10}^{3}A(500-200)500A\times {10}^5-AH\times {10}^5=9.8\times {10}^{3}A\times 500-98\times {10}^3\times A\times 200500A\times {10}^5+98\times {10}^{3}A\times 200=98\times {10}^{3}A\times 500+AH\times {10}^{5}A(500\times {10}^5+98\times 200\times {10}^3)=A(98\times {10}^3\times 500+H\times {10}^5)H=206mmLevelfall=206-200mm=6mm$