Tank Drainage problem. Apply the unsteady Bernoulli equation to determine the exit $($drainage$)$

velocity $($v$2)$ from a tank $($cross$-$sectional area, A$)$ with hole cross$-$section, a$.$ Do NOT assume v$1$

$($velocity in the tank$)$ is zero. Let the height at the starting time be $H.$

$v2(h=H)=0,$ where $h$ is the height at any time.

$1.$ Find $v2$ as a function of $h$

$2.$ Plug $\frac{a}{A}=1$ into the expression and find out you are getting free fall

$3.$ Render your equation dimensionless as $y(x)$ where $y=\frac{v_2}{\sqrt[\phantom{2}]{2gH}}$ and $x=\frac{h}{H}$

$4.$ Plot $y$ as a function of $x$ for various values of $r$