Whenever a petition describing the upper and lower boundaries of any proposed drainage district, and containing the names of at least two-fifths of the owners of the acreage of such district resident in Kansas whose lands in whole or in part are included within the proposed drainage district, shall be presented to the board of county commissioners of the county in which such lands are located, praying that a drainage district be incorporated and organized under the provisions of this act, it shall be the duty forthwith of such board of county commissioners to fix a time for the hearing of such petition, and to cause the county clerk to give notice thereof by one publication in some newspaper published and of general circulation in the county at least five days before the day fixed for the hearing.