The directors shall have authority to employ a competent engineer whose term of office shall be at the will of the directors. He shall make all necessary surveys, examinations, investigations, maps, plans, and drawings with reference to the proposed improvements. He shall make an estimate of the cost of such improvements, shall supervise the work thereon, and perform all such duties as may be required of him by the directors. If any proposed improvement or construction work necessary to the accomplishment of the purposes authorized in this chapter requires the permission or consent of the Federal Government or any department or officer thereof, the directors shall have authority to obtain such consent, and in lieu of or in addition to the employment of the district engineer, they shall have power to adopt any survey of any waters theretofore made by the United States, and to arrange for surveys, examination and investigation of the proposed improvements, and supervision of such work by the United States or the proper department or officer thereof.