The maximal steady frictional exchange flow through a rectangular channel of constant width is analysed within the context of internal hydraulics. A one-dimensional analytical solution to the fully nonlinear problem of two-layer frictional exchange is developed and shown to compare well with experimental and field data. The analytical solution gives the maximal exchange flow rate and the variation in the height of the density interface along the channel for the case of zero barotropic forcing. In contrast to the assumed constant interface slope of previous theoretical formulations of frictional exchange flows, the resulting density interface is found to be nonlinear and asymmetric. Both interfacial and bottom friction play important roles in determining the exchange flow rate. It is shown that the frictional effects are important even in relatively short channels.