The board of county commissioners of any organized county in this state, at any meeting of the board, by a majority vote of all the members, upon its own motion or on the petition of any person or persons interested, may appoint five property owners whose property lies within a flood irrigation project as a board of flood irrigation of the county. If the board of county commissioners appoints a board of flood irrigation it must appoint a board for each flood irrigation project in the county. One member of the board must be appointed for a term of one year, one for a term of two years, one for a term of three years, one for a term of four years, and one for a term of five years. Subsequent appointments must be made for terms of five years. All persons so appointed hold office until their successors are appointed and qualified. In case of a vacancy, the board of county commissioners may fill the vacancy for the unexpired term by appointment. The board of county commissioners shall provide an office for the board of flood irrigation at the county seat suitable for its use and the keeping of its records and shall provide suitable record books for its use.