The relative motion of the friction and separator plates in wet clutches during the disengaged mode causes viscous shear stresses in the fluid passing through the $100microns$ gap. This results in a drag torque on both the disks that wastes energy and decreases fuel economy. The objective of the study is to develop an accurate mathematical model for the above problem with verification using FLUENT and experiments. Initially we two consider flat disks. The mathematical model calculates the drag torque on the disks and the 2D axisymmetric solver verifies the solution. The surface pressure distribution on the plates is also verified. Then, 3D models of one grooved and one flat disk are tested using CFD, experiments and an approximate 3D mathematical model. The number of grooves, depth of groove and clearance between the disks are studied to understand their effect on the torque. The study determines the pressure field that eventually affects aeration incipience (not studied here). The results of the model, computations and experiments corroborate well in the single-phase regime.