Interactive oil pipe network showing flow from a tank to a terminal, with four selectable cuts to compare against the maximum flow

The obvious bottleneck is rarely the real bottleneck

An oil tank feeds a terminal through five pipes. The tank can release 24 units an hour, so 24 should arrive. Raise the attempted flow and watch where it stalls, then pick a cut and compare its capacity with what actually gets through.

Flow network
Through 18 of 23
Raise the flow. Pick a cut.
Choose a cut

Attempted flow18
0 10 20 23 max 30
A→B pipe capacity

Flow through
18
This cut
24

Know This

The maximum flow equals the capacity of the minimum cut, so value every source–sink partition before you trust the obvious bottleneck.