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Electrically driven, unmagnetized plasma flows have been generated in the Madison plasma dynamo experiment with magnetic Reynolds numbers exceeding the predicted Rm_crit = 200 threshold for flow-driven MHD instability excitation. The plasma flow is driven using ten thermally emissive lanthanum hexaboride cathodes which generate a J × B torque in helium and argon plasmas. Detailed Mach probe measurements of plasma velocity for two flow topologies are presented: edge-localized drive using the multi-cusp boundary field and volumetric drive using an axial Helmholtz field. Here radial velocity profiles show that the edge-driven flow is established via ion viscosity but is limited bymore » a volumetric neutral drag force, and measurements of velocity shear compare favorably to the Braginskii transport theory. Volumetric flow drive is shown to produce larger velocity shear and has the correct flow profile for studying the magnetorotational instability.« less