A quantitative predictive model of the electrophoretic mobility of a bent molecule of cylindrical symmetry relative to a straight one in gel is described. The force acting on the surface of the molecule is shown to be the minimum value of a variational functional of the fluid velocities whose minimizer satisfies the large viscosity solution of the incompressible Brinkman-Navier-Stokes equations. By exploiting the variational approach, our model readily predicts, in agreement with experimental data, that the electrophoretic mobility of the molecule bent at the middle is smaller than that of the same molecule with a bend at the end. We apply the methodology to describe the electrophoretic mobility of intrinsically bent DNA molecules in polyacrylamide gels. The predictions are compared with available experimental data as well as a semiempirical relation between the relative electrophoretic mobility and the bend angle by Thompson and Landy.