It is often desirable to operate industrial pipelines transporting non-Newtonian materials near the transition from laminar to turbulent flow. For the commonly used Bingham plastic model, the Hedstrom technique overestimates turbulent flow friction losses because it does 'not take account of viscous-layer thickening. In the present paper, the Wilson-Thomas model is applied to predict the transition, point for Bingham plastics. Laminar and turbulent friction losses are calculated to show that conditions at transition depend only on the Hedstrom number. The results are approximated by simplified fit functions. Comparison with existing empirical correlations and experimental data from various sources shows satisfactory agreement.