The city engineer in a city of the second class, when ordered to do so by the city council, shall make all surveys, estimates, and calculations necessary to be made for the establishment of a sewerage system and of the cost of labor and materials for such system. The mayor and city council may employ a special engineer to make or assist in making any such estimate or survey, and any such estimate or survey shall have the same validity and serve in all respects as though made by the city engineer. Before the city council shall make any contract for building any such sewers or any part of such sewers, an estimate of the cost of such sewers shall be made by the city engineer, or by a special engineer as provided by this section, and submitted to the city council, and no contract shall be entered into for the building of any such sewers or any part of such sewers for a price exceeding such estimate. In advertising for bids for any such work or materials, the city council shall cause the amount of such estimate to be published with such advertisement for at least twenty days in a legal newspaper in or of general circulation in the city.