This work presents a numerical study on the development length (L = L/H) required to reach fully-developed flow conditions at the entrance of a planar channel for inelastic non-Newtonian fluids modeled by the Sisko model. The simulations were carried out for low Reynolds number flows in the range 0 < Re <= 100, for a power law index, n, in the range 1/3 <= n <= 1 and for a dimensionless infinite viscosity, <(mu)over bar>(infinity), varying in the range 0 <= (mu) over bar (infinity) <= 0.1. A new non-linear relationship between L and Re was derived, taking into account the different values of n and (mu) over bar (infinity) Moreover, new exact solutions are presented for the velocity profile under fully developed flow conditions (for specific values of n).