A turbine airfoil includes pressure and suction sidewalls extending along a span from a base to a tip. Spanwise spaced apart trailing edge cooling holes in the pressure sidewall end at corresponding spanwise spaced apart trailing edge cooling slots extending chordally substantially to the trailing edge. Each cooling hole includes in downstream serial cooling flow relationship, a curved inlet, a constant area and constant width metering section, and a spanwise diverging section leading into the trailing edge cooling slot, and a spanwise height substantially greater than a hole width through the cooling hole. A pressure sidewall surface of the pressure sidewall may be planar through the metering and diverging sections. The width may be constant through the metering and diverging sections. A raised floor may include a flat up ramp in the diverging section, a flat down ramp in the slot.