A simplified model for unsteady pressure driven flows in circular microchannels of variable cross-section

•A fast model for unsteady flows in circular channels is presented.•Channels have a small aspect ratio but can have large diameter variations.•The simplified model is up to 2 orders of magnitude faster than CFD.•It accounts for some inertia with no restrictions on forcing frequency or shape.•The model can be applied to a wide spectrum of problems in MEMS and bio-mechanics.