Upon the presentation of a petition, as provided for in section 61-12-06 and the filing of the same, the board of flood irrigation, as soon as practicable, shall proceed to examine the site of the proposed improvement and the territory or district to be benefited thereby. If, in its opinion, it is necessary for the public good, it shall adopt a resolution to that effect and a further resolution designating a competent engineer who shall make all necessary and proper surveys of the lands that may be benefited or injured by the establishment of such improvement and who shall prepare all proper and necessary plans and specifications for the improvement required to be constructed. Upon the completion of such plans and specifications, such engineer shall file the same with the said board of flood irrigation, together with an estimate of the cost of the construction of the proposed improvement as well as of the annual maintenance thereof.