If the flow of a liquid in the channel is open to the atmosphere or partially filled in conduits and characterized by the presence of a liquid-gas interface called the free surface, it is called as an open channel.
If a flow of fluid completely fills a conduit and remains unexposed to atmosphere, it is called as internal flow.
The main difference between an open channel and an internal flow is that in an internal flow the controlling rule is the pressure at the free surface of the liquid must be equal to the pressure of the gas above it whereas in an internal flow there is no such restriction because there is no free surface.