Flow through a single mechanically sheared Marcellus shale fracture was investigated computationally and experimentally. To provide a better understanding of the variation of hydraulic and geometrical characteristics of a fracture subjected to shearing, coupled shear flow tests on the fracture for four shearing displacement steps under constant normal stress were performed. At the end of each shearing step, computed tomography (CT) scans with resolution 26.8 mu m were obtained and the corresponding fracture geometries were evaluated. The CT images were used to generate full aperture maps of the fracture configuration. In addition, average aperture maps were also created by averaging the full-resolution data over 10 x 10 pixels, smoothing out fine structural details. Computational modeling of water flow through the fractures at different shearing steps was performed using a modified local cubic law approach and the 3D full Navier-Stokes equations with the use of the ANSYS-Fluent software. Both the average aperture maps and full maps were used in these simulations. The experimental pressure drops of the fracture at shearing step 1, which has very small apertures, poorly matched the numerical results, quite likely because the fracture structure was inadequately captured by the scanning resolution. Shearing typically increased the aperture height of the fracture, whose features were then better captured by the CT scan. Good agreement between the experimental data and the numerical results of the full map for shearing step 2 was observed. The simulations were performed for both full and average aperture maps, and the effects of scan resolution and surface roughness on the accuracy of the results were studied. The modified local cubic law and full Navier-Stokes simulations of the averaged map fracture were found to be in good agreement. It was conjectured that this was because the nonlinear losses were insignificant for the smoothed out averaged map fracture. Similar comparisons with those of the full map showed agreement in trends, but there were some quantitative differences. The averaged fracture map simulations also predicted lower pressure drops compared to the full map, particularly for high flow rates. These differences were due to the fine-scale geometrical complexity (surface roughness) of fracture geometry that affects the fluid flow in the fracture. An improved cubic law model was also proposed, and its accuracy was verified by comparing its predictions with those of the Navier-Stokes simulations.