In some flute-like instruments, the musician places their mouth near an open-end of the pipe, which modifies the radiation of the pipe and its acoustic resonances. To improve the prediction of this modification, this work presents a study on the effect of an inclined plane at the end of a radiating pipe. The radiation impedance is first measured for different positions of the plane. After verifying that the plane mainly adds an inertance to the radiation, a new simpler and more convenient measurement method is proposed. The behavior observed in these measurements is generalized with the use of finite element simulations. Finally, a global low-frequency model of the effect of an inclined plane on both the imaginary and the real part of the radiation impedance is proposed. This model is consistent with the well-established radiation impedances for unflanged and flanged pipes.