Upon acquiring the right of way, and after the completion of the assessment of damages as provided in this chapter, the board of flood irrigation shall assess the percentage of the cost of constructing and maintaining the flood irrigation project and providing the right of way therefor and of paying all damages incurred by the owners of land affected thereby which any lot, piece, or parcel of land shall be liable to pay by reason of the benefits accruing thereto, either directly or indirectly, by reason of the construction of such project.