Whenever any person shall desire to construct a driveway or obstruction in a gutter of the character mentioned in § 90.050 of this code, he or she shall make application to the Department of Public Works for a permit for that installation. If there appears to be no objection to the installation by the applicant, the Department of Public Works will issue a permit for the installation in the manner provided in § 90.050 hereof and shall make a record of the permit. Should the applicant desire to have the work done by the city, he or she will be required to make application to the Department of Public Works and to pay to the City Treasurer a sum equal to the cost of materials, labor, supervision, and administration, as determined by the Department of Public Works. Upon payment to the City Treasurer of this sum, the city will, as soon thereafter as convenient, install the pipe and cover same with some material suitable for the use intended. The material used in construction of all driveways or culverts built by the city shall remain the property of the city. If at any time the character of any street is changed so that a driveway or culvert is no longer required, then all material used in the driveway or culvert constructed by the city shall be salvaged by it, and all material shall be removed from the site by the city.