It takes a long time to fill a dam. During that time the amount allowed to flow through will be reduced.
In addition the owner has the ability to increase or decrease the flow (to a degree) from then on.
Interestingly the current conflict over the Ethiopian dam is primarily a concern to Egypt, a nation that already has multiple dams on the Nile. It could, potentially, make up for a reduced flow by releasing water from those dams, although that would reduce its own ability to generate power or control flow later on.
Its a very complex situation. Simpler problems have occurred in the American West, where water is a precious resource.
Latest Answers