After the classification of the land and the ratio of assessment of the different classes to be made thereon has been confirmed by the clerk of court the drainage commission shall prepare an assessment roll or drainage tax duplicate, giving a description of all the land in the drainage district, the name of the owner, so far as can be ascertained from the public records, and the amount of assessment against each of the several tracts of land and other property in the district which is benefited by the proposed works. In preparing this assessment roll the board shall ascertain the total cost of the improvement, including the damages awarded and to be paid to the owners of lands, and all incidental expenses and deduct therefrom any special assessment made against any railroad or highway and the remainder shall be the amount to be borne and paid by the lands benefited. This amount shall be assessed against the several tracts of land according to the benefit received as shown by the classification and ratio of assessment made by the viewers and confirmed by the clerk of the court. This drainage tax roll shall be made in duplicate, signed by the chairman and secretary and one copy filed with the drainage record and the other delivered to the sheriff or other tax collector, except when the land of the district lies in more than one county when, in addition to the copy of the tax roll which shall be filed with the drainage records, a copy thereof shall be delivered to the treasurer of each of such counties. There shall be appended an order to collect such assessments and the same shall have the force and effect of a judgment as in the case of State and county taxes.