The board of public utilities shall fix reasonable rates for water furnished to consumers which: (1) Will secure an income sufficient to pay all salaries and wages of all officers and employees in such departments; (2) will cover the cost of all materials and supplies used in the operation of the plant; (3) will cover the cost of all repairs; (4) will cover all miscellaneous expenses; (5) will pay the principal of and the interest on all revenue bond indebtedness of the city incurred for the purpose of purchasing, improving or extending the waterworks, and will provide a sinking fund sufficient to pay the principal of and the interest on such indebtedness at maturity; and (6) will cover the cost of all repairs and renewals of the plant and all material used, together with a reasonable allowance for emergency and unforeseen expenses. Upon direction of the city, the board shall install, repair, replace and remove fire hydrants at a reasonable cost determined by the city and shall provide an adequate water supply through such hydrants at a reasonable cost determined by the city. The city may fix special rates for water furnished to the city for public purposes, or to organized institutions of charity.