I've been stuck on this problem for hours. I keep starting and stopping because I'm not exactly sure what I'm doing. The examples the teacher worked in class were much more straight forward.
If possible, could you please help me to get started on this problem? I primarily get confused with how to handle the middle nodes. For example I know the following:
$x_1+x_3=600$
$x_2+x_5=500$
$x_3+x_6=600$
$x_4+x_7=x_6$
$x_5+x_7=500$
Am I headed down the correct path?
Best Answer
Your five equations are correct. The sixth equation is $x_1=x_2+x_4$. You'll then have six linear equations in seven real unknowns, which is not enough to find a unique solution.
Question (a) is very vague, since no unique solution exists. Perhaps what is being asked is a list of the six equations. Or perhaps you can choose a variable, say $x_1$, and express the other variables in terms of $x_1$.
Question (b) is very easy. Look at the drawing and imagine $x_6$ and $x_7$ as closed pipes. It should be obvious that $x_3=600$, $x_4=0$, and $x_5=500$. (I'll leave $x_1$ and $x_2$ to you.)
Question (c) is also easy. Look at the drawing and imagine $x_6$ as a closed pipe. Then it should be obvious that $x_3=600$ and $x_1=0$. I'll leave the rest to you. (Hint: $x_2$ and $x_7$ are negative.)