Special assessments may be levied by the mayor and city council of a city of the first class for the purpose of paying the cost of constructing sewers, drainage, or water systems or mains within the city. Such assessment shall be levied on the real estate lying and being within the sewerage, drainage, or water service district in which such improvements may be situated to the extent of benefits to such property by reason of such improvement. The benefits to such property shall be determined by the city council sitting as a board of equalization, after notice to property owners is provided as in other cases of special assessment. If the city council, sitting as such board of equalization, shall find such benefits to be equal and uniform, such levy may be according to the front foot of the lots or real estate within such sewerage district, according to such other rule as the city council sitting as such board of equalization may adopt for the distribution or adjustment of such cost upon the lots or real estate in such district benefited by such improvement. All assessments made for sewerage, drainage, or water purposes shall be collected as special assessments and shall be subject to the same penalty as other special assessments. If sewers, drainage, or water systems or mains are constructed and any assessments to cover the costs thereof shall be declared void, or doubts exist as to the validity of such assessment, the mayor and city council, for the purpose of paying the cost of such improvement, may make a reassessment of such costs on lots and real estate lying and being within the district in which such improvements may be situated, to the extent of the benefits to such property by reason of such improvements. Such reassessment shall be made substantially in the manner provided for making original special assessments as provided in this section. Any sums which may have been paid toward such improvement upon any lots or real estate included in such assessment shall be applied under the direction of the city council to the credit of the persons and property on account of which the sums were paid. If the credits exceed the sum reassessed against such persons and property, the city council shall cause such excess, with lawful interest, to be refunded to the party who made payment thereof. The sums so reassessed and not paid under a prior special assessment shall be collected and enforced in the same manner and be subject to the same penalty as other special assessments.