For a pipe network shown bellow, answer questions $1$ and $2.$

Assuming water demand is known, analyze the network by determining the number of unknown variables, number of available equations, and whether the problem has a unique solution or not. Also write a list of unknown variables.

Write the equations that are needed to solve for the unknown values.

Note: If you find it hard to express the equations mathematically, you can describe them verbally instead $($e$.$g$.$ The sum of heads at node $1$ should be equal to$...).$