Whenever any number of natural persons, not less than three, shall file with the governing body of any county of this state an application in writing for authority to incorporate in such county a public corporation under the provisions of this chapter, and shall set forth in said application a brief description of the project to be acquired or improved by such corporation, and if it shall be made to appear to such governing body that each of said persons is a duly qualified elector of and owner of property in said county and if the governing body of said county shall adopt a resolution which shall be duly entered upon the minutes of such governing body wherein it shall be found and determined that there is a public need for the proposed project, that it is wise, expedient, necessary, or advisable that such a corporation be formed and that the persons filing said application shall be authorized to proceed to form such corporation, then said persons shall proceed to organize such corporation by executing, acknowledging, and filing a certificate of incorporation as herein provided. No corporation shall be formed unless the application provided for herein shall be made and unless the resolution provided for herein shall be adopted; provided, that the inadequacy of the description of the proposed project in the application for incorporation shall not affect the validity of the incorporation of such corporation. The granting of authority for the incorporation of one public corporation under this chapter shall not preclude the granting of authority by the governing body of the same county for the incorporation of other public corporations hereunder; provided, that such other public corporations shall be required to adopt a name or designation sufficient to distinguish them from any public corporation theretofore incorporated by such county under this chapter.