We study the variation of the Froude number at the front of gravity currents developed in uniform channels whose cross-section shape depends on a parameter usually used in many numerical and theoretical models. The thickness and front velocity of the dense currents running on the bottom are greater for all the cases studied, resulting in a Froude number greater than that corresponding to the rectangular cross-section shape. The light currents developing along the upper boundary show the opposite trend. It is found that the results are not related to the depth and width of the channel. The relationships obtained agree with the results of laboratory experiments in which open and closed channels of different cross-section shapes are used.