Contaminants that are highly soluble in groundwater are rapidly transported via fractures in mechanically resistant sedimentary rock aquifers. Hence, a rigorous methodology is needed to estimate groundwater flow velocities in such fractured aquifers. Here, we propose an approach using borehole hydraulic testing to compute flow velocities in an un-faulted area of a fractured carbonate aquifer by applying the cubic law to a parallel plate model. The Cadeby Formation (Yorkshire, NE England) - a Permian dolostone aquifer present beneath the University of Leeds Farm - is the fractured aquifer selected for this hydraulic experiment. The bedding plane fractures of this dolostone aquifer, which are sub-horizontal, sub-parallel and laterally persistent, largely dominate the flow at shallow (<~40 mBGL) depths. These flowing bedding plane discontinuities are separated by a rock matrix which is relatively impermeable (Kwell-test/Kcore-plug~104) as is common in fractured carbonate aquifers. In the workflow reported here, the number of flowing fractures - mainly bedding plane fractures - intersecting three open monitoring wells are found from temperature/fluid conductivity and acoustic/optical televiewer logging. Following well installation, average fracture hydraulic apertures for screened intervals are found from analysis of slug tests. For the case study aquifer, this workflow predicts hydraulic apertures ranging from 0.10 up to 0.54 mm. However, groundwater flow velocities range within two order of magnitude from 13 up to 242 m/day. Notably, fracture apertures and flow velocities rapidly reduce with increasing depth below the water table; the upper ~10 m shows relatively high values of hydraulic conductivity (0.30-2.85 m/day) and corresponding flow velocity (33-242 m/day). Permeability development around the water table in carbonate aquifer-types is common, and arises where high pCO2 recharge water from the soil zone causes calcite/dolomite dissolution. Hence, agricultural contaminants entering the aquifer with recharge water are laterally transported rapidly within this upper part. Computation of groundwater flow velocities allows determination of the Reynolds number. Values of up ~1, indicating the lower limit of the transition from laminar to turbulent flow, are found at the studied site, which is situated away from major fault traces. Hence, turbulent flow is likely to arise in proximity to tectonic structures, such as normal faults, which localize flow and enhance karstification. The occurrence of turbulent flow in correspondence of such tectonic structures should be represented in regional groundwater flow simulations.