Question

There is a hole in the bottom of tank having water. If total pressure at bottom 3 atm (1 atm) then the velocity of water flowing from hole is 

(A) √400 (m/s) 

(B) √60 (m/s) 

(C) √600 (m/s) 

(D) None of these

Answer 1

Correct option: (A) √400 (m/s)

Explanation:

P = 3 atm

P = \(3\times 10^5\)

Pressure at the bottom P = \(\rho gh\) 

\(3\times 10^5\) = \(\rho gh\)

Pressure due to liquid column.

\(P_1\) = \(3\times 10^5\) - \(1\times 10^5\)

\(P_1\) = \(2\times 10^5\,N/m^2\)

Velocity at water v = \(\sqrt{2gh} \) 

\(\because \) P = \(\rho gh\)

h = \(\frac{P_1}{\rho g}\) 

v = \(\sqrt{\frac{2g.P _1}{\rho g}}\) 

v = \(\sqrt{\frac{2P _1}{\rho}}\) 

v = \(\sqrt{\frac{2\times 2\times 10^5 }{10^3}}\)

v = \(\sqrt{4\times 10^2}\)

v = \(\sqrt{400}\,m/s\)