A surgical hand piece has a source of ultrasonic energy provided to a connecting body having a first passage with one end to receive fluid from a first source and the other end at the connecting body distal end. A work tip has first and second tubes each having at least one opening at its distal end and the proximal end of one or both of the tubes connected to the connecting body distal end to receive the ultrasonic energy and to selectively receive or discharge fluid from either the first or second source as controlled by a valve. A cannula is provided which is adapted to be placed in an opening in the cornea through which the work tip extends during the removal of cataracts from the eye by phacoemulsification. The cannula may be equipped with channels that permit additional infusion of fluid into the eye during the procedure, which infusion also cools the surrounding corneal tissue to protect against heat generated by the ultrasonic vibration of the work tip.