$\mathrm{restart}\;$

$A_1≔1\:$$A_2≔5\:A_3≔2\:$

$\mathrm{Dia}≔0.3\:$$L≔100\:$$e≔0.001\:$

$\mathrm{\ρ}≔1000\:$$\mathrm{\μ}≔0.001\:$

$g≔9.81\:$

$$\begin{gathered} \mathrm{res}≔\mathrm{dsolve}\left(\left\{{\mathrm{height}}_1\,{\mathrm{height}}_2\,{\mathrm{height}}_3\,{\mathrm{momentumBalance}}_1\,{\mathrm{momentumBalance}}_2\,\mathrm{initialConditions}\right\}\, \\ \left\{H_1\left(t\right)\,H_2\left(t\right)\,H_3\left(t\right)\,Q_1\left(t\right)\,Q_2\left(t\right)\right\}\, \\ \mathrm{numeric}\,\mathrm{output}\=\mathrm{listprocedure}\,\mathrm{known}\=\mathrm{friction}\right)\: \end{gathered}$$

$H_1≔\mathrm{subs}\left(\mathrm{res}\,H_1\left(t\right)\right)\:$$H_2≔\mathrm{subs}\left(\mathrm{res}\,H_2\left(t\right)\right)\:H_3≔\mathrm{subs}\left(\mathrm{res}\,H_3\left(t\right)\right)\:$$Q_1:=\mathrm{subs}\left(\mathrm{res}\,Q_1\left(t\right)\right)\:Q_2≔\mathrm{subs}\left(\mathrm{res}\,Q_2\left(t\right)\right)\:$

$$\begin{gathered} \mathrm{plot}\left(\left[H_1\left(t\right)\,H_2\left(t\right)\,H_3\left(t\right)\right]\,t\=0..200\, \\ \mathrm{legend}\=\left(\left[''Level\; in\; Reservoir\; 1''\, ''Level\; in\; Reservoir\; 2''\,''Level\; in\; Reservoir\; 3''\right]\right)\, \\ \mathrm{labels}\=\left(\left[''Time''\, ''Liquid\; Height''\right]\right)\, \\ \mathrm{labeldirections}\=\left(\left[\mathrm{horizontal}\,\mathrm{vertical}\right]\right)\, \\ \mathrm{labelfont}\=\left[\mathrm{Calibri}\right]\, \\ \mathrm{titlefont}\=\left[\mathrm{Calibri}\,16\,\mathrm{bold}\right]\, \\ \mathrm{background}\=\mathrm{ColorTools}:-\mathrm{Color}\left(''RGB''\,\left[218\/255\,223\/255\,225\/255\right]\right)\, \\ \mathrm{legendstyle}\=\left[\mathrm{font}\=\left[\mathrm{Calibri}\right]\right]\, \\ \mathrm{axis}\=\left[\mathrm{gridlines}\=\left[\mathrm{color}\=\mathrm{ColorTools}:-\mathrm{Color}\left(''RGB''\,\left[1\,1\,1\right]\right)\right]\right]\, \\ \mathrm{size}\=\left[1000\,400\right]\right)\; \end{gathered}$$