For a rectangular and prismatic channel of constant width B, i.e. with A = B h and c = √ gh, the Riemann invariants are: r + = u + 2 g h and r − − = u − − 2 g h , so the equations in characteristic form are: d d t ( u + 2 g h ) = g ( S − − S f ) along d x d t = u + g h and d d t ( u − − 2 g h ) = g ( S − − S f ) along d x d t = u − − g h .