Question

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 $24\,kg$ is applied on the water at the top when the height of the water level is $40\,cm$ above the bottom, the velocity of water coming out the opening $B$ is $v\,ms ^{-1} .$ The value of $v$, to the nearest integer, is ________. [Take value of $g$ to be $10\,ms ^{-2}$]

Answer 1

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