A turbine rotor blade that includes an airfoil defined between a concave pressure face and a laterally opposed convex suction face, and a cooling configuration that includes a cooling channel for receiving and directing a coolant through an interior of the rotor blade. The cooling channel may include fluidly connected segments, in which: a supply segment extends radially through the airfoil; an outlet segment discharges the coolant from the rotor blade at a shallow angle relative to a flow direction of a working fluid through the turbine; and an elbow segment connects the supply segment to the outlet segment and is positioned near the outboard tip of the airfoil. The elbow segment may be configured for accommodating a change of direction between the supply segment and the outlet segment.