Within ten days after the hearing under section 61-35-62, affected landowners and any political subdivision subject to assessment, having not less than twenty-five percent of the possible votes as determined under section 61-35-60, who believe that the assessment has not been fairly or equitably made, or that the project is not properly located or designed, may appeal to the department of water resources by petition, to review the assessments and examine the     location and design of the proposed project. Upon receipt of a petition, the department shall examine the lands assessed and the location and design of the proposed project, and if it appears that the assessments have not been made equitably, the department may correct the assessments, and the department’s correction and adjustment of assessments is final. If it appears to the department the project has been located or designed improperly, the department may order a relocation and redesign, which must be followed in the construction of the proposed project. Upon filing a bond for two hundred fifty dollars with the board for the payment of the costs of the department in the matter, any landowner or political subdivision claiming to receive no benefit from the project may appeal to the department the question of whether there is any benefit. The appeal must be filed with the department within ten days after the hearing on assessments in section 61-35-62. The department may not determine the specific amount of benefit upon an appeal by an individual landowner or political subdivision but may determine only if there is any benefit to the landowner or political subdivision. The determination of the department upon the appeal is final.