Question

Consider a water tank as shown in the figure. It's cross-sectional area is $0.4m^2$. The tank has an opening $B$ near the bottom whose cross- section area is $1c{m}^2$. 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 value of $g$ to be $10m{s}^{-2}$]

Answer 1

Answer: 3

$m=24kg$
$A=0.4m^2$
$a=1c{m}^2$
$H=40cm$
Using Bernoulli's equation
$\Rightarrow \left(P_0+\frac{mg}{A}\right)+\rho gH+\frac{1}{2}\varphi v_1^{\prime 2}$
$=P_0+0+\frac{1}{2}\rho V^2\dots (1)$
$\Rightarrow$ Neglecting $v_1$
$\Rightarrow v=\sqrt{2gH+\frac{2mg}{A\rho }}$
$\Rightarrow v=\sqrt{8+1.2}$
$\Rightarrow v=3.033m/s$
$\Rightarrow v=3m/s$