Make plots of water height (h) and time (t)
The mass conservation equation leads to the following ordinary differential equation for the water (h) and
time (t)
$\frac{dh}{dt} = \frac{-V_{jet}\pi d^2}{4A}$
Where A is the cross-sectional area, d is diameter of nozzle, $V_{jet}$ is velocity of jet exiting the nozzle.
According to Bernoulli's equation, $V_{jet} = \sqrt{(2gh)}$
g is the gravitational acceleration. Substituting Eqn. 2 into eqn. 1 is,
$\frac{dh}{dt} = \frac{-\pi d^2}{4A}(2gh)^{\frac{1}{2}}$
Together with the initial condition, h(0)=h0, the following solution for water height as function of time,
$h = (h_0 - \frac{(2g)^{\frac{1}{2}}\pi d^2}{8A}t)^2$
Make a plot of h with respect of t.
Where, d=25 mm, A=2000 mm$^2$, $h_0$= 6000 mm.
