The crack profile and the stress intensity factors for a two-dimensional crack with fluid flowing through it are determined for flow rates applicable to geothermal heat extraction. The entrance and exit portals for the fluid are placed away from the tips of the crack. For vertical cracks of half heights greater than 50 m that have fluids of the viscosity and density of water flowing through them at physically practival velocities it is found that the crack profile and stress intensity factors are essentially the same as those of a crack in which the fluid is stationary.