Flow of Bingham fluids in plane Couette-Poiseuille flow is studied. We present a set of analytically flow equations for flow between parallel plates/slots in a most compact form, and use this set as a basis for developing simpler flow equations. The new equations approximate the full analytical solution over a wide range of flow rates, and they are explicit in the frictional pressure gradient. Thus, they are well suited for application in fast dynamic flow models, where the implicit analytical solution is not applicable. We illustrate the application of the new equations in a dynamic model of the tripping operation in oil well drilling. The accuracy is shown to be absolutely satisfactory. Such a model may be coupled with control system theory and parameter estimation techniques, which enables automatic pressure control and adaptation of unknown model parameters.