In any case where the boundaries of any flood control district shall embrace all or any part of any county, city, town, diking, or drainage district, subject to flood conditions, the governing authorities thereof may contract with the directors of such flood control district, with the written approval of the state director, for the maintenance, repair, renewal and extension of any existing flood control works of such county, city, town, diking, or drainage district, situated within the flood control district, and for the construction and maintenance of specific flood control projects, for such term of years and for the payment to such flood control district therefor of such annual sums as in said contract specified.