Authors’ abstract: We consider a tree-like network of open channels with outflow at the root. Controls are exerted at the boundary nodes of the network except for the root. In each channel, the flow is modelled by the de St.Venant equations. The node conditions require the conservation of mass and the conservation of energy. We show that the states of the system can be controlled within the entire network in finite time from a stationary supercritical initial state to a given supercritical terminal state with the same orientation. During this transition, the states stay in class of \(C^1\)-functions, so no shocks occur.