Net vertically averaged velocity v_p,1D as a function of S = St(R,0)/ ⟨ α ⟩ _P for the viscous prescription (dashed line) and the MHD prescription (solid line), for three values of Sc_z (0.1 in blue, 1 in green and 10 in red). The velocities are always inward and we plot here their absolute value. We have taken Σ,T ∝ R^-0.75, ∂α(R,0)/∂R = 0, δ_R = δ_z and ⟨ α ⟩ _P = 10^-2. The dotted line corresponds to the simple one-dimensional approximation (see Eq. (42)) which is common to both prescriptions and independent of Sc_z. The approximation is arbitrarily good in the limits S ≪ 1 and S ≫ 1 and the imparted error does not exceed a factor of two when S ~ 1 except for the viscous prescription at Sc_z = 10 where it can reach one order of magnitude.