(a) Set up a linear system whose solution provides the unknown flow rates.

(b) Solve the system for the unknown flow rates

Question

(a) Set up a linear system whose solution provides the unknown flow rates.

(b) Solve the system for the unknown flow rates

moonlitfate · Answer

Figure is here.

michele_laino · Answer

if I apply this rule:
"algebraic sum of the flow rates at each node has to be equal to zero"
namely the conservation of matter at each node, I can write this algebraic system:
$$\Large   \left\{ \begin{gathered}
  500 + 300 = {x_1} + {x_3} \hfill \
   \hfill \
  {x_1} + {x_4} = 200 + {x_2} \hfill \
   \hfill \
  {x_2} + 100 = 600 + {x_5} \hfill \
   \hfill \
  {x_3} + {x_6} = 400 + 350 \hfill \
   \hfill \
  {x_7} + 600 = {x_4} + {x_6} \hfill \
   \hfill \
  {x_5} + 450 = {x_7} + 400 \hfill \ 
\end{gathered}  \right.$$