Consider the pipe network shown below containing water at $20\backslash$deg C flowing at steady state. The pressure drop from point $($A$)$ to point $($B$)$ is found to be $5$ m$.$ The pipes are wrought iron, and at the same elevation at all points. Though not drawn to scale, note that the pipe branch with the shorter length has a smaller diameter. You can neglect the minor losses of the T fittings. What is the flow rate through each pipe, and the total flow rate through the system?