Question 62 of 192

Consider a water tank as shown in the figure. It's cross-sectional area is $0.4{m}^{2}$. The tank has an opening $B$ near the bottom whose cross-section area is $1{cm}^{2}$. A load of $24kg$ is applied on the water at the top when the height of the water level is $40cm$ above the bottom, the velocity of water coming out the opening $B$ is $vm{s}^{-1}$. The value of $v$, to the nearest integer, is ___ .[Take the value of $g$ to be $10{ms}^{-2}$]

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Answer: 3

$m=24kg$
$A=0.4{m}^{2}$
$a=1{cm}^{2}$
$H=40cm$
Using Bernoulli's equation,
$\Rightarrow \left({P}_{0}+\dfrac{mg}{A}\right)+\rho gH+\dfrac{1}{2}P{v}_{1}^{2}$
$={P}_{0}+0+\dfrac{1}{2}\rho {v}^{2}...\left(1\right)$
$\Rightarrow$ Neglecting ${v}_{1}$
$\Rightarrow v=\sqrt{2gH+\dfrac{2mg}{A\rho }}$
$\Rightarrow v=\sqrt{8+1.2}$
$\Rightarrow v=3.033m{s}^{-1}$
$\Rightarrow v≃3m{s}^{-1}$