(a) Whenever the landowners within any proposed irrigation district, who shall be residents of the county in which such proposed irrigation district is located, shall desire the erection of such district as provided for in Kan. Stat. Ann. § 42-357, and amendments thereto, such landowners shall cause to be presented to the board of county commissioners of such county a petition signed by not less than 3/4 of the landowners within such proposed district who are residents of such county, which petition shall define the boundaries of such irrigation district, and shall ask for the erection of such district. Such petition shall be accompanied by an outlined map or plat showing the tracts of territory to be erected into such district, together with the numbers of sections and parts of the sections of land to compose such irrigation district; and such map or plat shall contain a drawing and profile of the proposed main ditch to the source of supply, and of all other ditches and laterals proposed to be constructed or purchased for the purpose of irrigating said described lands in such proposed district.

(b) Such petition shall be accompanied by an estimate, to be made by the county engineer of such county, of the probable cost of building the main ditch, ditches and laterals and all other works necessary to be built in order to furnish a sufficient supply of water to irrigate the lands in such proposed district; or the costs of reconstruction and repair of such ditches, laterals and other works in case it is proposed to purchase the same; and at any time after the filing of such petition the county commissioners may, on the written application of any 10 of such petitioners, order such county engineer to make the estimates herein provided for, and such county engineer shall receive such reasonable compensation as such board of commissioners shall allow for such work performed.