To analyze the impact of the magnetohydrodynamics (MHD) effect on the fast draining of a LiPb channel (lithium-lead eutectic, 15.7 at. % Li) for a liquid metal fusion blanket such as the water-cooled lithium-lead test blanket system of ITER or DEMO, an experimental campaign was carried out with the support of the Integrated European Lead Lithium LOop experimental facility (IELLLO), installed at the ENEA Brasimone research center, Italy. The experiments were carried out by measuring the drainage time of the internal permanent magnet pump channel, normally used to circulate the LiPb in the loop, with and without the magnetic field. Moreover, this paper proposes a new numerical methodology to study the time delay induced by the MHD by using the commercial software COMSOL Multiphysics. In this way, it was possible to evaluate the LiPb fraction present at each time step in the computational domain and to estimate the time necessary for the complete drainage of the channel. The level set method was used to describe the transient behavior of the MHD flow under low-Rm approximation. The developed code was compared with the experimental results and showed good agreement, and it constitutes the first step in model validation as a possible application to ITER and DEMO. The experimental and numerical analyses performed in this work can be used as a benchmark case for MHD code development.