Whenever in any county of this state the owners of lands bordering upon or accessible to any navigable water shall desire to improve their said lands, hereinafter designated as the “district,” by the construction of a new public waterway, or the deepening or enlargement of an existing public waterway, for the floatage of vessels and the drainage of swamp and overflowed lands, and the proposed improvement will increase the public revenues and be of other public benefit, they may present the plan of such proposed waterway to the board of county commissioners of such county, hereinafter designated the “board,” and have the same acted upon as provided in this chapter.