HSC · Topic explainer
Finding a missing network flow at a node
At an intermediate node in a steady flow network, total flow in equals total flow out. Follow each arrow and write an equation for the node. Flow is the amount actually travelling along an edge, while capacity is the largest amount the edge can carry.
Worked example
A junction receives 12 and 7 L/min through two pipes. One outgoing pipe carries 8 L/min. Let the other outgoing flow be x. Then 12 + 7 = 8 + x, so x = 11 L/min.
If the second pipe has capacity 14 L/min, it can carry that flow and has 3 L/min spare. If its capacity is 10 L/min, this set of flows is infeasible even though the amounts balance at the junction.
Official exam practice
Find other years and marking guidance in the Mathematics Standard 2 official exam archive.