We consider and develop mathematically a new equation for Newtonian fluid flow in the presence of slip at a solid surface. Slip is envisaged to occur only when a critical surface shear stress is reached, and once slip begins, it takes place at a constant slip length. Three instances are explored theoretically: slip possible at one surface only, slip possible at both surfaces with equal facility, and slip possible at both surfaces with differing facility. Quantitative comparison is made to experiments using the surface forces apparatus, and it is shown that this new slip model is able to reconcile results from different experimental studies.