Whenever any work to be done by the board of the drainage district under any of the provisions of this part is such that it can be so done in connection with work of public improvement of rivers and harbors authorized by the United States as to bring it within the provisions of Section 4 of the United States River and Harbor Act, approved March 4, 1915, authorizing the receipt by the United States agencies of funds to be contributed for expenditures in connection with funds appropriated by the United States for such work, the funds under the control of the board and available for such work may be contributed by the board to the United States under the provisions of the act in order that the work may be done in the manner contemplated in the act.