§ 4813. Maintenance by city. The board of estimate and apportionment or other similar body or officer shall provide for the maintenance of such school, the repair and improvement of the lands and buildings used or occupied thereby, and the equipment thereof with necessary machinery, tools, apparatus and supplies. The cost thereof, and the expenses incurred for such purposes, shall be charged against the city and shall be audited and paid in the same manner as other charges against the city. The maintenance herein provided for shall include the support, instruction, care, board and clothing of pupils and such other expenses as are necessarily incurred in the operation of the school.