  We consider an application of pooled stepped chutes where the transport in
each pooled step is described by the shallow--water equations. Such systems can
be found for example at large dams in order to release overflowing water. We
analyze the mathematical conditions coupling the flows between different chutes
taken from the engineering literature. We present the solution to a Riemann
problem in the large and also a well--posedness result for the coupled problem.
We finally report on some numerical experiments.
