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Figure shows a large closed cylindrical tank containing water. Initially, the air trapped above the water surface has a height h0 and pressure 2P0 where P0 is the atmospheric pressure. There is a hole in the wall of the tank at a depth h1 below the top from which water comes out. A long vertical tube is connected as shown.


Find the height h2 of the water in the long tube above the top initially.
  1. 3P0ρgh03
  2. 2P0ρgh02
  3. P0ρgh0
  4. P02ρg2h0


Solution

The correct option is C P0ρgh0

Form the above diagram we can see that, PA=PB
and PB=2P0 (Given)
If, P0 is the atmoshperic pressure then PA will be
PA=P0+ρ×g×(h2+h0)=2P0
ρ×g×(h2+h0)=P0
(h2+h0)=P0ρ×g
h2=P0ρ×gh0
 

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