Synovial fluid is a polymeric liquid which generally behaves as a viscoelastic fluid due to the presence of hyaluronan molecules. We restrict ourselves to the regime in which the fluid responds as a viscous fluid. A novel generalized power-law fluid model is developed wherein the power-law exponent depends on the concentration of the hyaluronan. Such a model will be adequate to describe the flows of such fluids as long as they are not subjected to instantaneous stimuli. Assuming two different structures for the form of the power law exponent, both in keeping with physical expectations, we numerically solve for the flow of the synovial fluid (described by the constraint of incompressibility, the balance of linear momentum, and a convection-diffusion equation for the concentration of hyaluronan) in a rectangular cavity. The solutions obtained with our models are compared with the predictions of those based on a model that has been used in the past to describe synovial fluids. While all the three models seem to agree well with available experimental results, one of the models proposed by us seems to fit the data the best; it would, however, be hasty to pass judgment based on this one particular experimental correlation.