$\mathrm{restart}\:$$\mathrm{with}\left(\mathrm{ThermophysicalData}\right)\:$

$\mathrm{\μ}≔\mathrm{Property}\left(''viscosity''\,''water''\,''pressure''\=1⟦\mathrm{atm}⟧\,''temperature''\=298⟦\mathrm{K}⟧\right)$$\mathrm{\ρ}≔\mathrm{Property}\left(''density''\,''water''\,''pressure''\=1⟦\mathrm{atm}⟧\,''temperature''\=298⟦\mathrm{K}⟧\right)$

$893.07\times {10}^{-6}⟦\mathrm{Pa}\mathrm{s}⟧$

$997.09⟦\frac{\mathrm{kg}}{{\mathrm{m}}^3}⟧$

$\mathrm{z\_\_1}≔90 ⟦\mathrm{m}⟧\:$$\mathrm{z\_\_2}≔85 ⟦\mathrm{m}⟧\:$$\mathrm{z\_\_3}≔60 ⟦\mathrm{m}⟧\:$

$\mathrm{e}≔0.0005⟦\mathrm{m}⟧\:$

${\mathrm{Q}}_{\mathrm{outflow}}≔0.03⟦{\mathrm{m}}^3 {\mathrm{s}}^{-1}⟧\:$

$\mathrm{g}≔9.81⟦\mathrm{m} {\mathrm{s}}^{-2}⟧\:$

$$\begin{gathered} \mathrm{sys}≔ \\ \mathrm{z\_\_1}\&equals;\mathrm{fric\_\_1}\mathrm{L\_\_1} \mathrm{Q\_\_1} \left|\mathrm{Q\_\_1}\right|\&sol;\left(2 \mathrm{g}\mathrm{D\_\_1} {\mathrm{A\_\_1}}^2\right)\&plus;\mathrm{H}\&comma; \\ \mathrm{z\_\_2}\&equals;\mathrm{fric\_\_2}\mathrm{L\_\_2} \mathrm{Q\_\_2} \left|\mathrm{Q\_\_2}\right|\&sol;\left(2 \mathrm{g}\mathrm{D\_\_2} {\mathrm{A\_\_2}}^2\right)\&plus;\mathrm{H}\&comma; \\ \mathrm{z\_\_3}\&equals;\mathrm{fric\_\_3} \mathrm{L\_\_3} \mathrm{Q\_\_3} \left|\mathrm{Q\_\_3}\right|\&sol;\left(2 \mathrm{g}\mathrm{D\_\_3} {\mathrm{A\_\_3}}^2\right)\&plus;\mathrm{H}\&comma; \\ \mathrm{Q\_\_1}\&plus;\mathrm{Q\_\_2}\&plus;\mathrm{Q\_\_3}\&equals;{\mathrm{Q}}_{\mathrm{outflow}}\&comma; \\ \mathrm{Rey\_\_1} \&equals; 4 \mathrm{abs}\left(\mathrm{Q\_\_1}\right) \mathrm{\&rho;}\&sol;\left(\mathrm{\pi } \mathrm{D\_\_1} \mathrm{\&mu;}\right)\&comma; \\ \mathrm{Rey\_\_2} \&equals; 4 \mathrm{abs}\left(\mathrm{Q\_\_2}\right) \mathrm{\&rho;}\&sol;\left(\mathrm{\pi } \mathrm{D\_\_2} \mathrm{\&mu;}\right)\&comma; \\ \mathrm{Rey\_\_3} \&equals; 4 \mathrm{abs}\left(\mathrm{Q\_\_3}\right) \mathrm{\&rho;}\&sol;\left(\mathrm{\pi } \mathrm{D\_\_3} \mathrm{\&mu;}\right)\&comma; \\ \mathrm{fric\_\_1} \&equals; \mathrm{piecewise}\left(\mathrm{Rey\_\_1}<2500\&comma; 64\&sol;\mathrm{Rey\_\_1}\&comma; 1\&sol;{\left(1.8 \mathrm{log10}\left({\left(\mathrm{e}\&sol;\left(3.7 \mathrm{D\_\_1}\right)\right)}^{1.11}\&plus;6.9\&sol;\mathrm{Rey\_\_1}\right)\right)}^2\right)\&comma; \\ \mathrm{fric\_\_2} \&equals; \mathrm{piecewise}\left(\mathrm{Rey\_\_2}<2500\&comma; 64\&sol;\mathrm{Rey\_\_2}\&comma; 1\&sol;{\left(1.8 \mathrm{log10}\left({\left(\mathrm{e}\&sol;\left(3.7 \mathrm{D\_\_2}\right)\right)}^{1.11}\&plus;6.9\&sol;\mathrm{Rey\_\_2}\right)\right)}^2\right)\&comma; \\ \mathrm{fric\_\_3} \&equals; \mathrm{piecewise}\left(\mathrm{Rey\_\_3}<2500\&comma; 64\&sol;\mathrm{Rey\_\_3}\&comma; 1\&sol;{\left(1.8 \mathrm{log10}\left({\left(\mathrm{e}\&sol;\left(3.7 \mathrm{D\_\_3}\right)\right)}^{1.11}\&plus;6.9\&sol;\mathrm{Rey\_\_3}\right)\right)}^2\right)\&colon; \end{gathered}$$

$\mathrm{estimates}≔\mathrm{H}\&equals;1 ⟦\mathrm{m}⟧\&comma;\mathrm{Q\_\_1}=0.1 ⟦{\mathrm{m}}^3 {\mathrm{s}}^{-1}⟧\&comma;\mathrm{Q\_\_2}=0.1 ⟦{\mathrm{m}}^3 {\mathrm{s}}^{-1}⟧\&comma;\mathrm{Q\_\_3}=0.1 ⟦{\mathrm{m}}^3 {\mathrm{s}}^{-1}⟧\&comma;\mathrm{Rey\_\_1}=1\&comma;\mathrm{Rey\_\_2}\&equals;1\&comma;\mathrm{Rey\_\_3}\&equals;1\&comma;\mathrm{fric\_\_1}=1\&comma;\mathrm{fric\_\_2}\&equals;1\&comma;\mathrm{fric\_\_3}\&equals;1\&colon;$

$\mathrm{Digits}≔20\&colon;$

$\mathrm{results}≔\mathrm{fsolve}\left(\left\{\mathrm{sys}\right\}\&comma;\left\{\mathrm{estimates}\right\}\right)$

$\left\{\mathrm{H}=8.31\times {10}^1⟦\mathrm{m}⟧\&comma;\mathrm{Q\_\_1}=6.67\times {10}^{-2}⟦\frac{{\mathrm{m}}^3}{\mathrm{s}}⟧\&comma;\mathrm{Q\_\_2}=2.49\times {10}^{-2}⟦\frac{{\mathrm{m}}^3}{\mathrm{s}}⟧\&comma;\mathrm{Q\_\_3}=-6.16\times {10}^{-2}⟦\frac{{\mathrm{m}}^3}{\mathrm{s}}⟧\&comma;\mathrm{Rey\_\_1}=3.16\times {10}^5\&comma;\mathrm{Rey\_\_2}=1.42\times {10}^5\&comma;\mathrm{Rey\_\_3}=3.50\times {10}^5\&comma;\mathrm{fric\_\_1}=2.29\times {10}^{-2}\&comma;\mathrm{fric\_\_2}=2.46\times {10}^{-2}\&comma;\mathrm{fric\_\_3}=2.39\times {10}^{-2}\right\}$