Question:
A hole is in the bottom of the tank having water. If total pressure at the bottom is $3$ atm $(1 \,atm = 10^{5}\, Nm^{-2})$, then velocity of water flowing from hole is
A hole is in the bottom of the tank having water. If total pressure at the bottom is $3$ atm $(1 \,atm = 10^{5}\, Nm^{-2})$, then velocity of water flowing from hole is
Updated On: Jul 5, 2022
- $\sqrt{400}\,ms^{-1}$
- $\sqrt{600}\,ms^{-1}$
- $\sqrt{60}\,ms^{-1}$
- none of these
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The Correct Option is A
Solution and Explanation
Total pressure $( P )$ = atmospheric pressure $(P_{0})$ + pressure due to water columnn $p$'
$P=P_{0}+P'$
$\therefore P'=P-P_{0}=3-1=2$ atm
or, $\rho gh =2$ atm or, $h\times 10 \times 10^{3}=2\times 10^{5}$
or, $h=20\,m$
Velocity of water coming from hole is
$v=\sqrt{2gh}=\sqrt{2\times10\times20}$
$=\sqrt{400}\,ms^{-1}$
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Concepts Used:
Bernauli Theorem
In fluid dynamics, Bernoulli's principle states that an increase in the speed of a fluid occurs simultaneously with a decrease in static pressure or a decrease in the fluid's potential energy. The principle is named after Daniel Bernoulli who published it in his book Hydrodynamica in 1738.
