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Physics Question on Bernauli Theorem

A hole is in the bottom of the tank having water. If total pressure at the bottom is 33 atm (1 atm=105 Nm−2)(1 \,atm = 10^{5}\, Nm^{-2}), then velocity of water flowing from hole is

A

400 ms−1\sqrt{400}\,ms^{-1}

B

600 ms−1\sqrt{600}\,ms^{-1}

C

60 ms−1\sqrt{60}\,ms^{-1}

D

none of these

Answer

400 ms−1\sqrt{400}\,ms^{-1}

Explanation

Solution

Total pressure (P)( P ) = atmospheric pressure (P0)(P_{0}) + pressure due to water columnn pp' P=P0+P′P=P_{0}+P' ∴P′=P−P0=3−1=2\therefore P'=P-P_{0}=3-1=2 atm or, ρgh=2\rho gh =2 atm or, h×10×103=2×105h\times 10 \times 10^{3}=2\times 10^{5} or, h=20 mh=20\,m Velocity of water coming from hole is v=2gh=2×10×20v=\sqrt{2gh}=\sqrt{2\times10\times20} =400 ms−1=\sqrt{400}\,ms^{-1}